alarsyo/spot
1
0
Fork 0
Code Issues Pull requests Projects Releases Wiki Activity
spot/tests/python/alternation.ipynb
Alexandre Duret-Lutz 2072151499 twa_graph: swap the two passes of merge_edges() 
This improves the determinism in a few cases.

* spot/twa/twagraph.cc (merge_edges): Encapsulate the two
passes into lambdas so that they are very easy to swap.
* spot/twa/twagraph.hh (merge_edges): Adjust documentation.
* tests/python/mergedge.py: Add test case.
* tests/core/alternating.test, tests/python/alternation.ipynb:
Determinism was improved.
* tests/core/parity2.test, tests/core/readsave.test,
tests/core/sbacc.test, tests/python/_product_susp.ipynb,
tests/python/atva16-fig2a.ipynb, tests/python/decompose.ipynb,
tests/python/highlighting.ipynb, tests/python/satmin.ipynb,
tests/python/simstate.py: Adjust expected order of edges.
* NEWS: Mention the change.
2021-01-20 00:16:12 +01:00

4304 lines
315 KiB
Text
Raw Blame History

{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import spot\n",
"from spot.jupyter import display_inline\n",
"spot.setup(show_default='.bav')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Support for alternating automata"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The following automata are what we will use as examples."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"aut1, aut2, aut3, aut4, aut5 = spot.automata('''\n",
"HOA: v1 tool: \"ltl3ba\" \"1.1.3\" name: \"VWAA for FGa && GFb\" States: 6\n",
"Start: 0 acc-name: co-Buchi Acceptance: 1 Fin(0) AP: 2 \"a\" \"b\" properties:\n",
"trans-labels explicit-labels state-acc univ-branch very-weak --BODY--\n",
"State: 0 \"(FG(a) && GF(b))\" [t] 3&1 State: 1 \"GF(b)\" [(1)] 1 [(!1)]\n",
"2&1 State: 2 \"F(b)\" {0} [(1)] 5 [(!1)] 2 State: 3 \"FG(a)\" {0} [(0)] 4\n",
"[t] 3 State: 4 \"G(a)\" [(0)] 4 State: 5 \"t\" [t] 5 --END--\n",
"/* Example from ADL's PSL2TGBA talk. */\n",
"HOA: v1 States: 3 Start: 0 acc-name: co-Buchi Acceptance: 1 Fin(0) AP:\n",
"3 \"a\" \"b\" \"p\" --BODY-- State: 0 \"(a;a*;b)*\" {0} [0] 1 [!0] 2 State: 1\n",
"\"a*;b;(a;a*;b)*\" {0} [0&1&2] 0&1 [!1&2] 1 [!0&!1] 2 [!0&1&2] 0 State:\n",
"2 [t] 2 --END--\n",
"HOA: v1 States: 5 Start: 3 acc-name: co-Buchi Acceptance: 1 Fin(0) AP:\n",
"3 \"a\" \"b\" \"p\" --BODY-- State: 0 \"(a;a*;b)*\" {0} [0] 1 [!0] 2 State: 1\n",
"\"a*;b;(a;a*;b)*\" {0} [0&1&2] 0&1 [!1&2] 1 [!0&!1] 2 [!0&1&2] 0 State:\n",
"2 [t] 2 State: 3 [0] 4&0 State: 4 [t] 3 --END--\n",
"HOA: v1 States: 3 Start: 0 acc-name: co-Buchi Acceptance: 1 Fin(0) AP:\n",
"3 \"a\" \"b\" \"p\" --BODY-- State: 0 \"(a;a*;b)*\" {0} [0] 1 [!0] 2 State: 1\n",
"\"a*;b;(a;a*;b)*\" {0} [0&1&2] 0&1 [!1&2] 1 [!0&!1] 2 [!0&1&2] 0 State:\n",
"2 [t] 2 --END--\n",
"HOA: v1 tool: \"ltl3dra\" \"0.2.2\" name: \"VWAA for GFa\" States: 3 Start: 0\n",
"acc-name: co-Buchi Acceptance: 1 Fin(0) AP: 1 \"a\" properties: trans-labels\n",
"explicit-labels state-acc univ-branch very-weak --BODY-- State: 0 \"GF(a)\"\n",
"[t] 1&0 State: 1 \"F(a)\" {0} [(0)] 2 [t] 1 State: 2 \"t\" [t] 2 --END--\n",
"''')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Various display options"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here is the default output, using the `bav` options as set by default in the first cell. "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Title: VWAA for FGa &amp;&amp; GFb Pages: 1 -->\n",
"<svg width=\"129pt\" height=\"360pt\"\n",
" viewBox=\"0.00 0.00 129.40 360.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(0.7246376811594204 0.7246376811594204) rotate(0) translate(4 492.6)\">\n",
"<title>VWAA for FGa &amp;&amp; GFb</title>\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-492.6 174.5,-492.6 174.5,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"63.75\" y=\"-474.4\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"86.75\" y=\"-474.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"102.75\" y=\"-474.4\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"53.75\" y=\"-460.4\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M117.5,-414.6C117.5,-414.6 24.5,-414.6 24.5,-414.6 18.5,-414.6 12.5,-408.6 12.5,-402.6 12.5,-402.6 12.5,-390.6 12.5,-390.6 12.5,-384.6 18.5,-378.6 24.5,-378.6 24.5,-378.6 117.5,-378.6 117.5,-378.6 123.5,-378.6 129.5,-384.6 129.5,-390.6 129.5,-390.6 129.5,-402.6 129.5,-402.6 129.5,-408.6 123.5,-414.6 117.5,-414.6\"/>\n",
"<text text-anchor=\"start\" x=\"20.5\" y=\"-392.9\" font-family=\"Lato\" font-size=\"14.00\">(FG(a) &amp;&amp; GF(b))</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M71,-451.45C71,-449.81 71,-435.45 71,-421.97\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"71,-414.66 74.15,-421.66 71,-418.16 71,-421.66 71,-421.66 71,-421.66 71,-418.16 67.85,-421.66 71,-414.66 71,-414.66\"/>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"71\" cy=\"-325.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 0&#45;&gt;&#45;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M71,-378.59C71,-364.81 71,-345.96 71,-335.21\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"73.45,-335.19 71,-328.19 68.55,-335.19 73.45,-335.19\"/>\n",
"<text text-anchor=\"start\" x=\"71\" y=\"-349.4\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>1</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M38,-286C38,-286 12,-286 12,-286 6,-286 0,-280 0,-274 0,-274 0,-262 0,-262 0,-256 6,-250 12,-250 12,-250 38,-250 38,-250 44,-250 50,-256 50,-262 50,-262 50,-274 50,-274 50,-280 44,-286 38,-286\"/>\n",
"<text text-anchor=\"start\" x=\"8\" y=\"-264.3\" font-family=\"Lato\" font-size=\"14.00\">GF(b)</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M70.2,-323.83C66.99,-319.93 54.63,-304.95 43.65,-291.62\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"39.06,-286.05 45.94,-289.45 41.29,-288.76 43.51,-291.46 43.51,-291.46 43.51,-291.46 41.29,-288.76 41.08,-293.46 39.06,-286.05 39.06,-286.05\"/>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>3</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M131.5,-287C131.5,-287 106.5,-287 106.5,-287 100.5,-287 94.5,-281 94.5,-275 94.5,-275 94.5,-261 94.5,-261 94.5,-255 100.5,-249 106.5,-249 106.5,-249 131.5,-249 131.5,-249 137.5,-249 143.5,-255 143.5,-261 143.5,-261 143.5,-275 143.5,-275 143.5,-281 137.5,-287 131.5,-287\"/>\n",
"<text text-anchor=\"start\" x=\"102.5\" y=\"-271.8\" font-family=\"Lato\" font-size=\"14.00\">FG(a)</text>\n",
"<text text-anchor=\"start\" x=\"111\" y=\"-256.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;3 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M71.83,-323.83C75.1,-320.03 87.42,-305.72 98.64,-292.67\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"103.36,-287.18 101.18,-294.55 101.08,-289.84 98.79,-292.49 98.79,-292.49 98.79,-292.49 101.08,-289.84 96.4,-290.44 103.36,-287.18 103.36,-287.18\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M50.18,-274.72C59.91,-275.02 68,-272.78 68,-268 68,-264.49 63.64,-262.35 57.46,-261.58\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"50.18,-261.28 57.3,-258.42 53.67,-261.42 57.17,-261.56 57.17,-261.56 57.17,-261.56 53.67,-261.42 57.04,-264.71 50.18,-261.28 50.18,-261.28\"/>\n",
"<text text-anchor=\"start\" x=\"68\" y=\"-264.3\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
"</g>\n",
"<!-- &#45;4 -->\n",
"<g id=\"node6\" class=\"node\">\n",
"<title>&#45;4</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"26\" cy=\"-180\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;&#45;4 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>1&#45;&gt;&#45;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M17.29,-249.63C13.85,-239.81 10.97,-227.28 13,-216 14.77,-206.18 19.11,-195.51 22.29,-188.56\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"24.71,-189.2 25.56,-181.83 20.3,-187.06 24.71,-189.2\"/>\n",
"<text text-anchor=\"start\" x=\"13\" y=\"-219.8\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;3 -->\n",
"<g id=\"edge12\" class=\"edge\">\n",
"<title>3&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M143.88,-274.72C153.5,-275.02 161.5,-272.78 161.5,-268 161.5,-264.49 157.19,-262.35 151.09,-261.58\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"143.88,-261.28 151.01,-258.42 147.38,-261.42 150.88,-261.57 150.88,-261.57 150.88,-261.57 147.38,-261.42 150.75,-264.71 143.88,-261.28 143.88,-261.28\"/>\n",
"<text text-anchor=\"start\" x=\"161.5\" y=\"-264.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 4 -->\n",
"<g id=\"node9\" class=\"node\">\n",
"<title>4</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M127.5,-198C127.5,-198 110.5,-198 110.5,-198 104.5,-198 98.5,-192 98.5,-186 98.5,-186 98.5,-174 98.5,-174 98.5,-168 104.5,-162 110.5,-162 110.5,-162 127.5,-162 127.5,-162 133.5,-162 139.5,-168 139.5,-174 139.5,-174 139.5,-186 139.5,-186 139.5,-192 133.5,-198 127.5,-198\"/>\n",
"<text text-anchor=\"start\" x=\"106.5\" y=\"-176.3\" font-family=\"Lato\" font-size=\"14.00\">G(a)</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;4 -->\n",
"<g id=\"edge11\" class=\"edge\">\n",
"<title>3&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M119,-248.76C119,-236.11 119,-219.13 119,-205.33\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"119,-198.04 122.15,-205.04 119,-201.54 119,-205.04 119,-205.04 119,-205.04 119,-201.54 115.85,-205.04 119,-198.04 119,-198.04\"/>\n",
"<text text-anchor=\"start\" x=\"119\" y=\"-219.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- &#45;4&#45;&gt;1 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>&#45;4&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M25.99,-182.1C25.91,-188.32 25.55,-219.73 25.28,-242.54\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"25.2,-249.6 22.13,-242.56 25.24,-246.1 25.28,-242.6 25.28,-242.6 25.28,-242.6 25.24,-246.1 28.43,-242.63 25.2,-249.6 25.2,-249.6\"/>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node7\" class=\"node\">\n",
"<title>2</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M34,-125C34,-125 18,-125 18,-125 12,-125 6,-119 6,-113 6,-113 6,-99 6,-99 6,-93 12,-87 18,-87 18,-87 34,-87 34,-87 40,-87 46,-93 46,-99 46,-99 46,-113 46,-113 46,-119 40,-125 34,-125\"/>\n",
"<text text-anchor=\"start\" x=\"14\" y=\"-109.8\" font-family=\"Lato\" font-size=\"14.00\">F(b)</text>\n",
"<text text-anchor=\"start\" x=\"18\" y=\"-94.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- &#45;4&#45;&gt;2 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>&#45;4&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M26,-178.19C26,-173.66 26,-150.99 26,-132.43\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"26,-125.31 29.15,-132.31 26,-128.81 26,-132.31 26,-132.31 26,-132.31 26,-128.81 22.85,-132.31 26,-125.31 26,-125.31\"/>\n",
"</g>\n",
"<!-- 2&#45;&gt;2 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>2&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M46.33,-112.62C55.76,-113.34 64,-111.13 64,-106 64,-102.23 59.56,-100.04 53.46,-99.43\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"46.33,-99.38 53.35,-96.28 49.83,-99.41 53.33,-99.43 53.33,-99.43 53.33,-99.43 49.83,-99.41 53.31,-102.58 46.33,-99.38 46.33,-99.38\"/>\n",
"<text text-anchor=\"start\" x=\"64\" y=\"-102.3\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
"</g>\n",
"<!-- 5 -->\n",
"<g id=\"node8\" class=\"node\">\n",
"<title>5</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M32,-36C32,-36 20,-36 20,-36 14,-36 8,-30 8,-24 8,-24 8,-12 8,-12 8,-6 14,0 20,0 20,0 32,0 32,0 38,0 44,-6 44,-12 44,-12 44,-24 44,-24 44,-30 38,-36 32,-36\"/>\n",
"<text text-anchor=\"middle\" x=\"26\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">t</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;5 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>2&#45;&gt;5</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M26,-86.76C26,-74.11 26,-57.13 26,-43.33\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"26,-36.04 29.15,-43.04 26,-39.54 26,-43.04 26,-43.04 26,-43.04 26,-39.54 22.85,-43.04 26,-36.04 26,-36.04\"/>\n",
"<text text-anchor=\"start\" x=\"26\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
"</g>\n",
"<!-- 5&#45;&gt;5 -->\n",
"<g id=\"edge14\" class=\"edge\">\n",
"<title>5&#45;&gt;5</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M44.15,-25.6C53.54,-26.77 62,-24.23 62,-18 62,-13.42 57.44,-10.84 51.3,-10.25\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"44.15,-10.4 51.09,-7.11 47.65,-10.33 51.15,-10.26 51.15,-10.26 51.15,-10.26 47.65,-10.33 51.22,-13.41 44.15,-10.4 44.15,-10.4\"/>\n",
"<text text-anchor=\"start\" x=\"62\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 4&#45;&gt;4 -->\n",
"<g id=\"edge13\" class=\"edge\">\n",
"<title>4&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M139.6,-186.62C149.15,-187.34 157.5,-185.13 157.5,-180 157.5,-176.23 153,-174.04 146.82,-173.43\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"139.6,-173.38 146.62,-170.28 143.1,-173.41 146.6,-173.43 146.6,-173.43 146.6,-173.43 143.1,-173.41 146.58,-176.58 139.6,-173.38 139.6,-173.38\"/>\n",
"<text text-anchor=\"start\" x=\"157.5\" y=\"-176.3\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Pages: 1 -->\n",
"<svg width=\"201pt\" height=\"296pt\"\n",
" viewBox=\"0.00 0.00 200.64 296.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1.0 1.0) rotate(0) translate(4 292)\">\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-292 196.64,-292 196.64,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"74.82\" y=\"-273.8\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"97.82\" y=\"-273.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"113.82\" y=\"-273.8\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"64.82\" y=\"-259.8\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M96.5,-214C96.5,-214 55.5,-214 55.5,-214 49.5,-214 43.5,-208 43.5,-202 43.5,-202 43.5,-188 43.5,-188 43.5,-182 49.5,-176 55.5,-176 55.5,-176 96.5,-176 96.5,-176 102.5,-176 108.5,-182 108.5,-188 108.5,-188 108.5,-202 108.5,-202 108.5,-208 102.5,-214 96.5,-214\"/>\n",
"<text text-anchor=\"start\" x=\"51.5\" y=\"-198.8\" font-family=\"Lato\" font-size=\"14.00\">(a;a*;b)*</text>\n",
"<text text-anchor=\"start\" x=\"68\" y=\"-183.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M76,-250.84C76,-249.2 76,-235.1 76,-221.61\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"76,-214.26 79.15,-221.26 76,-217.76 76,-221.26 76,-221.26 76,-221.26 76,-217.76 72.85,-221.26 76,-214.26 76,-214.26\"/>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>1</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M110,-125C110,-125 42,-125 42,-125 36,-125 30,-119 30,-113 30,-113 30,-99 30,-99 30,-93 36,-87 42,-87 42,-87 110,-87 110,-87 116,-87 122,-93 122,-99 122,-99 122,-113 122,-113 122,-119 116,-125 110,-125\"/>\n",
"<text text-anchor=\"start\" x=\"38\" y=\"-109.8\" font-family=\"Lato\" font-size=\"14.00\">a*;b;(a;a*;b)*</text>\n",
"<text text-anchor=\"start\" x=\"68\" y=\"-94.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M68.12,-175.71C64.86,-166.05 62.22,-153.95 64,-143 64.59,-139.35 65.5,-135.58 66.56,-131.91\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"68.73,-125.03 69.62,-132.65 67.68,-128.36 66.62,-131.7 66.62,-131.7 66.62,-131.7 67.68,-128.36 63.62,-130.75 68.73,-125.03 68.73,-125.03\"/>\n",
"<text text-anchor=\"start\" x=\"64\" y=\"-146.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>2</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M24,-36C24,-36 12,-36 12,-36 6,-36 0,-30 0,-24 0,-24 0,-12 0,-12 0,-6 6,0 12,0 12,0 24,0 24,0 30,0 36,-6 36,-12 36,-12 36,-24 36,-24 36,-30 30,-36 24,-36\"/>\n",
"<text text-anchor=\"middle\" x=\"18\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>0&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M50.95,-175.97C35.97,-163.55 18.27,-145.62 10,-125 -0.67,-98.42 4.54,-65.11 10.3,-43\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"12.16,-36.23 13.34,-43.82 11.23,-39.61 10.3,-42.98 10.3,-42.98 10.3,-42.98 11.23,-39.61 7.26,-42.14 12.16,-36.23 12.16,-36.23\"/>\n",
"<text text-anchor=\"start\" x=\"10\" y=\"-102.3\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M76,-125C76,-137.71 76,-154.91 76,-168.96\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"76,-175.97 72.85,-168.97 76,-172.47 76,-168.97 76,-168.97 76,-168.97 76,-172.47 79.15,-168.97 76,-175.97 76,-175.97\"/>\n",
"<text text-anchor=\"start\" x=\"76\" y=\"-146.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M122.02,-114.05C132.41,-113.32 140,-110.64 140,-106 140,-102.52 135.73,-100.14 129.21,-98.86\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"122.02,-97.95 129.36,-95.71 125.5,-98.39 128.97,-98.83 128.97,-98.83 128.97,-98.83 125.5,-98.39 128.57,-101.96 122.02,-97.95 122.02,-97.95\"/>\n",
"<text text-anchor=\"start\" x=\"140\" y=\"-102.3\" font-family=\"Lato\" font-size=\"14.00\">!b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>1&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M50.91,-86.67C45.07,-81.47 39.32,-75.46 35,-69 29.83,-61.26 26.08,-51.79 23.45,-43.18\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"21.49,-36.21 26.42,-42.1 22.44,-39.58 23.38,-42.95 23.38,-42.95 23.38,-42.95 22.44,-39.58 20.35,-43.8 21.49,-36.21 21.49,-36.21\"/>\n",
"<text text-anchor=\"start\" x=\"35\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"169\" cy=\"-18\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;&#45;1 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>1&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M80.47,-86.7C83.83,-76.1 89.36,-63.09 98,-54 115.88,-35.19 146.01,-25.09 160.59,-21.08\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"161.23,-23.45 167.41,-19.35 160.02,-18.7 161.23,-23.45\"/>\n",
"<text text-anchor=\"start\" x=\"98\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;2 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>2&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M36.15,-25.6C45.54,-26.77 54,-24.23 54,-18 54,-13.42 49.44,-10.84 43.3,-10.25\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"36.15,-10.4 43.09,-7.11 39.65,-10.33 43.15,-10.26 43.15,-10.26 43.15,-10.26 39.65,-10.33 43.22,-13.41 36.15,-10.4 36.15,-10.4\"/>\n",
"<text text-anchor=\"middle\" x=\"58.5\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;0 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M169.66,-20.12C174.66,-28.78 205.88,-85.76 186,-125 171.88,-152.87 140.8,-170.79 115.27,-181.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"108.57,-184.02 113.91,-178.51 111.82,-182.73 115.08,-181.44 115.08,-181.44 115.08,-181.44 111.82,-182.73 116.24,-184.37 108.57,-184.02 108.57,-184.02\"/>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M169.01,-19.82C169.05,-24.96 168.6,-53.11 155,-69 147.92,-77.26 138.56,-83.73 128.75,-88.76\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"122.27,-91.85 127.23,-85.99 125.43,-90.35 128.58,-88.84 128.58,-88.84 128.58,-88.84 125.43,-90.35 129.94,-91.68 122.27,-91.85 122.27,-91.85\"/>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Pages: 1 -->\n",
"<svg width=\"166pt\" height=\"360pt\"\n",
" viewBox=\"0.00 0.00 166.05 360.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(0.8264462809917356 0.8264462809917356) rotate(0) translate(4 431)\">\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-431 196.64,-431 196.64,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"74.82\" y=\"-412.8\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"97.82\" y=\"-412.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"113.82\" y=\"-412.8\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"64.82\" y=\"-398.8\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 3 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>3</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M132,-353C132,-353 120,-353 120,-353 114,-353 108,-347 108,-341 108,-341 108,-329 108,-329 108,-323 114,-317 120,-317 120,-317 132,-317 132,-317 138,-317 144,-323 144,-329 144,-329 144,-341 144,-341 144,-347 138,-353 132,-353\"/>\n",
"<text text-anchor=\"middle\" x=\"126\" y=\"-331.3\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
"</g>\n",
"<!-- I&#45;&gt;3 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M126,-389.85C126,-388.21 126,-373.85 126,-360.37\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"126,-353.06 129.15,-360.06 126,-356.56 126,-360.06 126,-360.06 126,-360.06 126,-356.56 122.85,-360.06 126,-353.06 126,-353.06\"/>\n",
"</g>\n",
"<!-- &#45;4 -->\n",
"<g id=\"node7\" class=\"node\">\n",
"<title>&#45;4</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"107\" cy=\"-258.5\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 3&#45;&gt;&#45;4 -->\n",
"<g id=\"edge11\" class=\"edge\">\n",
"<title>3&#45;&gt;&#45;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M121.59,-316.72C117.62,-301.14 111.96,-278.94 108.99,-267.3\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"111.33,-266.57 107.23,-260.39 106.58,-267.78 111.33,-266.57\"/>\n",
"<text text-anchor=\"start\" x=\"118\" y=\"-287.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- 0 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>0</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M96.5,-214C96.5,-214 55.5,-214 55.5,-214 49.5,-214 43.5,-208 43.5,-202 43.5,-202 43.5,-188 43.5,-188 43.5,-182 49.5,-176 55.5,-176 55.5,-176 96.5,-176 96.5,-176 102.5,-176 108.5,-182 108.5,-188 108.5,-188 108.5,-202 108.5,-202 108.5,-208 102.5,-214 96.5,-214\"/>\n",
"<text text-anchor=\"start\" x=\"51.5\" y=\"-198.8\" font-family=\"Lato\" font-size=\"14.00\">(a;a*;b)*</text>\n",
"<text text-anchor=\"start\" x=\"68\" y=\"-183.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>1</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M110,-125C110,-125 42,-125 42,-125 36,-125 30,-119 30,-113 30,-113 30,-99 30,-99 30,-93 36,-87 42,-87 42,-87 110,-87 110,-87 116,-87 122,-93 122,-99 122,-99 122,-113 122,-113 122,-119 116,-125 110,-125\"/>\n",
"<text text-anchor=\"start\" x=\"38\" y=\"-109.8\" font-family=\"Lato\" font-size=\"14.00\">a*;b;(a;a*;b)*</text>\n",
"<text text-anchor=\"start\" x=\"68\" y=\"-94.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M68.12,-175.71C64.86,-166.05 62.22,-153.95 64,-143 64.59,-139.35 65.5,-135.58 66.56,-131.91\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"68.73,-125.03 69.62,-132.65 67.68,-128.36 66.62,-131.7 66.62,-131.7 66.62,-131.7 67.68,-128.36 63.62,-130.75 68.73,-125.03 68.73,-125.03\"/>\n",
"<text text-anchor=\"start\" x=\"64\" y=\"-146.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>2</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M24,-36C24,-36 12,-36 12,-36 6,-36 0,-30 0,-24 0,-24 0,-12 0,-12 0,-6 6,0 12,0 12,0 24,0 24,0 30,0 36,-6 36,-12 36,-12 36,-24 36,-24 36,-30 30,-36 24,-36\"/>\n",
"<text text-anchor=\"middle\" x=\"18\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>0&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M50.95,-175.97C35.97,-163.55 18.27,-145.62 10,-125 -0.67,-98.42 4.54,-65.11 10.3,-43\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"12.16,-36.23 13.34,-43.82 11.23,-39.61 10.3,-42.98 10.3,-42.98 10.3,-42.98 11.23,-39.61 7.26,-42.14 12.16,-36.23 12.16,-36.23\"/>\n",
"<text text-anchor=\"start\" x=\"10\" y=\"-102.3\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M76,-125C76,-137.71 76,-154.91 76,-168.96\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"76,-175.97 72.85,-168.97 76,-172.47 76,-168.97 76,-168.97 76,-168.97 76,-172.47 79.15,-168.97 76,-175.97 76,-175.97\"/>\n",
"<text text-anchor=\"start\" x=\"76\" y=\"-146.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M122.02,-114.05C132.41,-113.32 140,-110.64 140,-106 140,-102.52 135.73,-100.14 129.21,-98.86\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"122.02,-97.95 129.36,-95.71 125.5,-98.39 128.97,-98.83 128.97,-98.83 128.97,-98.83 125.5,-98.39 128.57,-101.96 122.02,-97.95 122.02,-97.95\"/>\n",
"<text text-anchor=\"start\" x=\"140\" y=\"-102.3\" font-family=\"Lato\" font-size=\"14.00\">!b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>1&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M50.91,-86.67C45.07,-81.47 39.32,-75.46 35,-69 29.83,-61.26 26.08,-51.79 23.45,-43.18\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"21.49,-36.21 26.42,-42.1 22.44,-39.58 23.38,-42.95 23.38,-42.95 23.38,-42.95 22.44,-39.58 20.35,-43.8 21.49,-36.21 21.49,-36.21\"/>\n",
"<text text-anchor=\"start\" x=\"35\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node6\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"169\" cy=\"-18\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;&#45;1 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>1&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M80.47,-86.7C83.83,-76.1 89.36,-63.09 98,-54 115.88,-35.19 146.01,-25.09 160.59,-21.08\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"161.23,-23.45 167.41,-19.35 160.02,-18.7 161.23,-23.45\"/>\n",
"<text text-anchor=\"start\" x=\"98\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;2 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>2&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M36.15,-25.6C45.54,-26.77 54,-24.23 54,-18 54,-13.42 49.44,-10.84 43.3,-10.25\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"36.15,-10.4 43.09,-7.11 39.65,-10.33 43.15,-10.26 43.15,-10.26 43.15,-10.26 39.65,-10.33 43.22,-13.41 36.15,-10.4 36.15,-10.4\"/>\n",
"<text text-anchor=\"middle\" x=\"58.5\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;0 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M169.66,-20.12C174.66,-28.78 205.88,-85.76 186,-125 178.54,-139.72 143.63,-160.18 115.11,-174.99\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"108.76,-178.25 113.55,-172.25 111.87,-176.65 114.99,-175.05 114.99,-175.05 114.99,-175.05 111.87,-176.65 116.42,-177.85 108.76,-178.25 108.76,-178.25\"/>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M169.01,-19.82C169.05,-24.96 168.6,-53.11 155,-69 147.92,-77.26 138.56,-83.73 128.75,-88.76\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"122.27,-91.85 127.23,-85.99 125.43,-90.35 128.58,-88.84 128.58,-88.84 128.58,-88.84 125.43,-90.35 129.94,-91.68 122.27,-91.85 122.27,-91.85\"/>\n",
"</g>\n",
"<!-- &#45;4&#45;&gt;0 -->\n",
"<g id=\"edge12\" class=\"edge\">\n",
"<title>&#45;4&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M106.46,-256.43C104.29,-252.12 95.9,-235.49 88.48,-220.76\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"85.16,-214.18 91.13,-219.01 86.74,-217.31 88.32,-220.43 88.32,-220.43 88.32,-220.43 86.74,-217.31 85.5,-221.85 85.16,-214.18 85.16,-214.18\"/>\n",
"</g>\n",
"<!-- 4 -->\n",
"<g id=\"node8\" class=\"node\">\n",
"<title>4</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M151,-213C151,-213 139,-213 139,-213 133,-213 127,-207 127,-201 127,-201 127,-189 127,-189 127,-183 133,-177 139,-177 139,-177 151,-177 151,-177 157,-177 163,-183 163,-189 163,-189 163,-201 163,-201 163,-207 157,-213 151,-213\"/>\n",
"<text text-anchor=\"middle\" x=\"145\" y=\"-191.3\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
"</g>\n",
"<!-- &#45;4&#45;&gt;4 -->\n",
"<g id=\"edge13\" class=\"edge\">\n",
"<title>&#45;4&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M107.66,-256.43C110.4,-251.99 121.19,-234.53 130.47,-219.51\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"134.33,-213.27 133.33,-220.88 132.49,-216.25 130.65,-219.22 130.65,-219.22 130.65,-219.22 132.49,-216.25 127.97,-217.57 134.33,-213.27 134.33,-213.27\"/>\n",
"</g>\n",
"<!-- 4&#45;&gt;3 -->\n",
"<g id=\"edge14\" class=\"edge\">\n",
"<title>4&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M142.6,-213.42C139.24,-237.81 133.12,-282.25 129.33,-309.84\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"128.37,-316.8 126.2,-309.44 128.85,-313.33 129.32,-309.87 129.32,-309.87 129.32,-309.87 128.85,-313.33 132.44,-310.3 128.37,-316.8 128.37,-316.8\"/>\n",
"<text text-anchor=\"middle\" x=\"142.5\" y=\"-254.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Pages: 1 -->\n",
"<svg width=\"201pt\" height=\"296pt\"\n",
" viewBox=\"0.00 0.00 200.64 296.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1.0 1.0) rotate(0) translate(4 292)\">\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-292 196.64,-292 196.64,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"74.82\" y=\"-273.8\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"97.82\" y=\"-273.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"113.82\" y=\"-273.8\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"64.82\" y=\"-259.8\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M96.5,-214C96.5,-214 55.5,-214 55.5,-214 49.5,-214 43.5,-208 43.5,-202 43.5,-202 43.5,-188 43.5,-188 43.5,-182 49.5,-176 55.5,-176 55.5,-176 96.5,-176 96.5,-176 102.5,-176 108.5,-182 108.5,-188 108.5,-188 108.5,-202 108.5,-202 108.5,-208 102.5,-214 96.5,-214\"/>\n",
"<text text-anchor=\"start\" x=\"51.5\" y=\"-198.8\" font-family=\"Lato\" font-size=\"14.00\">(a;a*;b)*</text>\n",
"<text text-anchor=\"start\" x=\"68\" y=\"-183.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M76,-250.84C76,-249.2 76,-235.1 76,-221.61\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"76,-214.26 79.15,-221.26 76,-217.76 76,-221.26 76,-221.26 76,-221.26 76,-217.76 72.85,-221.26 76,-214.26 76,-214.26\"/>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>1</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M110,-125C110,-125 42,-125 42,-125 36,-125 30,-119 30,-113 30,-113 30,-99 30,-99 30,-93 36,-87 42,-87 42,-87 110,-87 110,-87 116,-87 122,-93 122,-99 122,-99 122,-113 122,-113 122,-119 116,-125 110,-125\"/>\n",
"<text text-anchor=\"start\" x=\"38\" y=\"-109.8\" font-family=\"Lato\" font-size=\"14.00\">a*;b;(a;a*;b)*</text>\n",
"<text text-anchor=\"start\" x=\"68\" y=\"-94.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M68.12,-175.71C64.86,-166.05 62.22,-153.95 64,-143 64.59,-139.35 65.5,-135.58 66.56,-131.91\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"68.73,-125.03 69.62,-132.65 67.68,-128.36 66.62,-131.7 66.62,-131.7 66.62,-131.7 67.68,-128.36 63.62,-130.75 68.73,-125.03 68.73,-125.03\"/>\n",
"<text text-anchor=\"start\" x=\"64\" y=\"-146.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>2</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M24,-36C24,-36 12,-36 12,-36 6,-36 0,-30 0,-24 0,-24 0,-12 0,-12 0,-6 6,0 12,0 12,0 24,0 24,0 30,0 36,-6 36,-12 36,-12 36,-24 36,-24 36,-30 30,-36 24,-36\"/>\n",
"<text text-anchor=\"middle\" x=\"18\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>0&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M50.95,-175.97C35.97,-163.55 18.27,-145.62 10,-125 -0.67,-98.42 4.54,-65.11 10.3,-43\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"12.16,-36.23 13.34,-43.82 11.23,-39.61 10.3,-42.98 10.3,-42.98 10.3,-42.98 11.23,-39.61 7.26,-42.14 12.16,-36.23 12.16,-36.23\"/>\n",
"<text text-anchor=\"start\" x=\"10\" y=\"-102.3\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M76,-125C76,-137.71 76,-154.91 76,-168.96\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"76,-175.97 72.85,-168.97 76,-172.47 76,-168.97 76,-168.97 76,-168.97 76,-172.47 79.15,-168.97 76,-175.97 76,-175.97\"/>\n",
"<text text-anchor=\"start\" x=\"76\" y=\"-146.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M122.02,-114.05C132.41,-113.32 140,-110.64 140,-106 140,-102.52 135.73,-100.14 129.21,-98.86\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"122.02,-97.95 129.36,-95.71 125.5,-98.39 128.97,-98.83 128.97,-98.83 128.97,-98.83 125.5,-98.39 128.57,-101.96 122.02,-97.95 122.02,-97.95\"/>\n",
"<text text-anchor=\"start\" x=\"140\" y=\"-102.3\" font-family=\"Lato\" font-size=\"14.00\">!b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>1&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M50.91,-86.67C45.07,-81.47 39.32,-75.46 35,-69 29.83,-61.26 26.08,-51.79 23.45,-43.18\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"21.49,-36.21 26.42,-42.1 22.44,-39.58 23.38,-42.95 23.38,-42.95 23.38,-42.95 22.44,-39.58 20.35,-43.8 21.49,-36.21 21.49,-36.21\"/>\n",
"<text text-anchor=\"start\" x=\"35\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"169\" cy=\"-18\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;&#45;1 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>1&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M80.47,-86.7C83.83,-76.1 89.36,-63.09 98,-54 115.88,-35.19 146.01,-25.09 160.59,-21.08\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"161.23,-23.45 167.41,-19.35 160.02,-18.7 161.23,-23.45\"/>\n",
"<text text-anchor=\"start\" x=\"98\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;2 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>2&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M36.15,-25.6C45.54,-26.77 54,-24.23 54,-18 54,-13.42 49.44,-10.84 43.3,-10.25\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"36.15,-10.4 43.09,-7.11 39.65,-10.33 43.15,-10.26 43.15,-10.26 43.15,-10.26 39.65,-10.33 43.22,-13.41 36.15,-10.4 36.15,-10.4\"/>\n",
"<text text-anchor=\"middle\" x=\"58.5\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;0 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M169.66,-20.12C174.66,-28.78 205.88,-85.76 186,-125 171.88,-152.87 140.8,-170.79 115.27,-181.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"108.57,-184.02 113.91,-178.51 111.82,-182.73 115.08,-181.44 115.08,-181.44 115.08,-181.44 111.82,-182.73 116.24,-184.37 108.57,-184.02 108.57,-184.02\"/>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M169.01,-19.82C169.05,-24.96 168.6,-53.11 155,-69 147.92,-77.26 138.56,-83.73 128.75,-88.76\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"122.27,-91.85 127.23,-85.99 125.43,-90.35 128.58,-88.84 128.58,-88.84 128.58,-88.84 125.43,-90.35 129.94,-91.68 122.27,-91.85 122.27,-91.85\"/>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Title: VWAA for GFa Pages: 1 -->\n",
"<svg width=\"87pt\" height=\"335pt\"\n",
" viewBox=\"0.00 0.00 87.00 334.60\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1.0 1.0) rotate(0) translate(4 330.6)\">\n",
"<title>VWAA for GFa</title>\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-330.6 83,-330.6 83,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"18\" y=\"-312.4\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"41\" y=\"-312.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"57\" y=\"-312.4\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"8\" y=\"-298.4\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M41.75,-252.6C41.75,-252.6 15.75,-252.6 15.75,-252.6 9.75,-252.6 3.75,-246.6 3.75,-240.6 3.75,-240.6 3.75,-228.6 3.75,-228.6 3.75,-222.6 9.75,-216.6 15.75,-216.6 15.75,-216.6 41.75,-216.6 41.75,-216.6 47.75,-216.6 53.75,-222.6 53.75,-228.6 53.75,-228.6 53.75,-240.6 53.75,-240.6 53.75,-246.6 47.75,-252.6 41.75,-252.6\"/>\n",
"<text text-anchor=\"start\" x=\"11.75\" y=\"-230.9\" font-family=\"Lato\" font-size=\"14.00\">GF(a)</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M28.75,-289.45C28.75,-287.81 28.75,-273.45 28.75,-259.97\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"28.75,-252.66 31.9,-259.66 28.75,-256.16 28.75,-259.66 28.75,-259.66 28.75,-259.66 28.75,-256.16 25.6,-259.66 28.75,-252.66 28.75,-252.66\"/>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"28.75\" cy=\"-163.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 0&#45;&gt;&#45;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M20.85,-216.38C17.44,-206.69 14.82,-194.41 17.75,-183.6 18.94,-179.21 21.44,-174.8 23.75,-171.35\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"25.72,-172.81 27.95,-165.73 21.8,-169.87 25.72,-172.81\"/>\n",
"<text text-anchor=\"start\" x=\"17.75\" y=\"-187.4\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;0 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M28.75,-166.19C28.75,-171.7 28.75,-192.51 28.75,-209.57\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"28.75,-216.59 25.6,-209.59 28.75,-213.09 28.75,-209.59 28.75,-209.59 28.75,-209.59 28.75,-213.09 31.9,-209.59 28.75,-216.59 28.75,-216.59\"/>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>1</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M36.25,-125C36.25,-125 21.25,-125 21.25,-125 15.25,-125 9.25,-119 9.25,-113 9.25,-113 9.25,-99 9.25,-99 9.25,-93 15.25,-87 21.25,-87 21.25,-87 36.25,-87 36.25,-87 42.25,-87 48.25,-93 48.25,-99 48.25,-99 48.25,-113 48.25,-113 48.25,-119 42.25,-125 36.25,-125\"/>\n",
"<text text-anchor=\"start\" x=\"17.25\" y=\"-109.8\" font-family=\"Lato\" font-size=\"14.00\">F(a)</text>\n",
"<text text-anchor=\"start\" x=\"20.75\" y=\"-94.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M28.75,-161.83C28.75,-158.2 28.75,-144.97 28.75,-132.42\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"28.75,-125.18 31.9,-132.18 28.75,-128.68 28.75,-132.18 28.75,-132.18 28.75,-132.18 28.75,-128.68 25.6,-132.18 28.75,-125.18 28.75,-125.18\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M48.43,-112.59C57.89,-113.4 66.25,-111.2 66.25,-106 66.25,-102.18 61.74,-99.98 55.6,-99.4\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"48.43,-99.41 55.42,-96.25 51.93,-99.41 55.43,-99.4 55.43,-99.4 55.43,-99.4 51.93,-99.41 55.43,-102.55 48.43,-99.41 48.43,-99.41\"/>\n",
"<text text-anchor=\"start\" x=\"66.25\" y=\"-102.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>2</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M34.75,-36C34.75,-36 22.75,-36 22.75,-36 16.75,-36 10.75,-30 10.75,-24 10.75,-24 10.75,-12 10.75,-12 10.75,-6 16.75,0 22.75,0 22.75,0 34.75,0 34.75,0 40.75,0 46.75,-6 46.75,-12 46.75,-12 46.75,-24 46.75,-24 46.75,-30 40.75,-36 34.75,-36\"/>\n",
"<text text-anchor=\"middle\" x=\"28.75\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">t</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>1&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M28.75,-86.76C28.75,-74.11 28.75,-57.13 28.75,-43.33\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"28.75,-36.04 31.9,-43.04 28.75,-39.54 28.75,-43.04 28.75,-43.04 28.75,-43.04 28.75,-39.54 25.6,-43.04 28.75,-36.04 28.75,-36.04\"/>\n",
"<text text-anchor=\"start\" x=\"28.75\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;2 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>2&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M46.9,-25.6C56.29,-26.77 64.75,-24.23 64.75,-18 64.75,-13.42 60.19,-10.84 54.05,-10.25\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"46.9,-10.4 53.84,-7.11 50.4,-10.33 53.9,-10.26 53.9,-10.26 53.9,-10.26 50.4,-10.33 53.97,-13.41 46.9,-10.4 46.9,-10.4\"/>\n",
"<text text-anchor=\"start\" x=\"64.75\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"display_inline(aut1, aut2, aut3, aut4, aut5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If the state labels take too much space, you can reduce the size of the automaton by forcing states to be numbered with option `1`. The original label is still displayed as a tooltip when the mouse is over the state.\n",
"\n",
"Note that passing option `show=...` to `display_inline` is similar to calling `aut.show(...)` on each argument."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Title: VWAA for FGa &amp;&amp; GFb Pages: 1 -->\n",
"<svg width=\"109pt\" height=\"360pt\"\n",
" viewBox=\"0.00 0.00 109.46 360.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(0.7246376811594204 0.7246376811594204) rotate(0) translate(4 492.6)\">\n",
"<title>VWAA for FGa &amp;&amp; GFb</title>\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-492.6 147,-492.6 147,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"50\" y=\"-474.4\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"73\" y=\"-474.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"89\" y=\"-474.4\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"40\" y=\"-460.4\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<g id=\"a_node2\"><a xlink:title=\"(FG(a) &amp;&amp; GF(b))\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M63,-414.6C63,-414.6 51,-414.6 51,-414.6 45,-414.6 39,-408.6 39,-402.6 39,-402.6 39,-390.6 39,-390.6 39,-384.6 45,-378.6 51,-378.6 51,-378.6 63,-378.6 63,-378.6 69,-378.6 75,-384.6 75,-390.6 75,-390.6 75,-402.6 75,-402.6 75,-408.6 69,-414.6 63,-414.6\"/>\n",
"<text text-anchor=\"middle\" x=\"57\" y=\"-392.9\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M57,-451.45C57,-449.81 57,-435.45 57,-421.97\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"57,-414.66 60.15,-421.66 57,-418.16 57,-421.66 57,-421.66 57,-421.66 57,-418.16 53.85,-421.66 57,-414.66 57,-414.66\"/>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"57\" cy=\"-325.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 0&#45;&gt;&#45;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M57,-378.59C57,-364.81 57,-345.96 57,-335.21\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"59.45,-335.19 57,-328.19 54.55,-335.19 59.45,-335.19\"/>\n",
"<text text-anchor=\"start\" x=\"57\" y=\"-349.4\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>1</title>\n",
"<g id=\"a_node4\"><a xlink:title=\"GF(b)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M24,-286C24,-286 12,-286 12,-286 6,-286 0,-280 0,-274 0,-274 0,-262 0,-262 0,-256 6,-250 12,-250 12,-250 24,-250 24,-250 30,-250 36,-256 36,-262 36,-262 36,-274 36,-274 36,-280 30,-286 24,-286\"/>\n",
"<text text-anchor=\"start\" x=\"13.5\" y=\"-264.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M56.32,-323.83C53.62,-319.97 43.31,-305.21 34.06,-291.98\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"29.92,-286.05 36.51,-289.99 31.92,-288.92 33.93,-291.79 33.93,-291.79 33.93,-291.79 31.92,-288.92 31.35,-293.6 29.92,-286.05 29.92,-286.05\"/>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>3</title>\n",
"<g id=\"a_node5\"><a xlink:title=\"FG(a)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M104,-287C104,-287 92,-287 92,-287 86,-287 80,-281 80,-275 80,-275 80,-261 80,-261 80,-255 86,-249 92,-249 92,-249 104,-249 104,-249 110,-249 116,-255 116,-261 116,-261 116,-275 116,-275 116,-281 110,-287 104,-287\"/>\n",
"<text text-anchor=\"start\" x=\"93.5\" y=\"-271.8\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
"<text text-anchor=\"start\" x=\"90\" y=\"-256.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;3 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M57.71,-323.83C60.48,-320.07 70.83,-305.97 80.35,-293.02\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"84.64,-287.18 83.03,-294.69 82.57,-290 80.49,-292.83 80.49,-292.83 80.49,-292.83 82.57,-290 77.96,-290.96 84.64,-287.18 84.64,-287.18\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M36.15,-274.51C45.54,-275.51 54,-273.34 54,-268 54,-264.08 49.44,-261.86 43.3,-261.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"36.15,-261.49 43.1,-258.21 39.65,-261.43 43.15,-261.36 43.15,-261.36 43.15,-261.36 39.65,-261.43 43.21,-264.51 36.15,-261.49 36.15,-261.49\"/>\n",
"<text text-anchor=\"start\" x=\"54\" y=\"-264.3\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
"</g>\n",
"<!-- &#45;4 -->\n",
"<g id=\"node6\" class=\"node\">\n",
"<title>&#45;4</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"19\" cy=\"-180\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;&#45;4 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>1&#45;&gt;&#45;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M10.29,-249.63C6.85,-239.81 3.97,-227.28 6,-216 7.77,-206.18 12.11,-195.51 15.29,-188.56\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"17.71,-189.2 18.56,-181.83 13.3,-187.06 17.71,-189.2\"/>\n",
"<text text-anchor=\"start\" x=\"6\" y=\"-219.8\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;3 -->\n",
"<g id=\"edge12\" class=\"edge\">\n",
"<title>3&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M116.15,-274.51C125.54,-275.51 134,-273.34 134,-268 134,-264.08 129.44,-261.86 123.3,-261.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"116.15,-261.49 123.1,-258.21 119.65,-261.43 123.15,-261.36 123.15,-261.36 123.15,-261.36 119.65,-261.43 123.21,-264.51 116.15,-261.49 116.15,-261.49\"/>\n",
"<text text-anchor=\"start\" x=\"134\" y=\"-264.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 4 -->\n",
"<g id=\"node9\" class=\"node\">\n",
"<title>4</title>\n",
"<g id=\"a_node9\"><a xlink:title=\"G(a)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M104,-198C104,-198 92,-198 92,-198 86,-198 80,-192 80,-186 80,-186 80,-174 80,-174 80,-168 86,-162 92,-162 92,-162 104,-162 104,-162 110,-162 116,-168 116,-174 116,-174 116,-186 116,-186 116,-192 110,-198 104,-198\"/>\n",
"<text text-anchor=\"middle\" x=\"98\" y=\"-176.3\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 3&#45;&gt;4 -->\n",
"<g id=\"edge11\" class=\"edge\">\n",
"<title>3&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M98,-248.76C98,-236.11 98,-219.13 98,-205.33\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"98,-198.04 101.15,-205.04 98,-201.54 98,-205.04 98,-205.04 98,-205.04 98,-201.54 94.85,-205.04 98,-198.04 98,-198.04\"/>\n",
"<text text-anchor=\"start\" x=\"98\" y=\"-219.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- &#45;4&#45;&gt;1 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>&#45;4&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M18.99,-182.1C18.91,-188.32 18.55,-219.73 18.28,-242.54\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"18.2,-249.6 15.13,-242.56 18.24,-246.1 18.28,-242.6 18.28,-242.6 18.28,-242.6 18.24,-246.1 21.43,-242.63 18.2,-249.6 18.2,-249.6\"/>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node7\" class=\"node\">\n",
"<title>2</title>\n",
"<g id=\"a_node7\"><a xlink:title=\"F(b)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M25,-125C25,-125 13,-125 13,-125 7,-125 1,-119 1,-113 1,-113 1,-99 1,-99 1,-93 7,-87 13,-87 13,-87 25,-87 25,-87 31,-87 37,-93 37,-99 37,-99 37,-113 37,-113 37,-119 31,-125 25,-125\"/>\n",
"<text text-anchor=\"start\" x=\"14.5\" y=\"-109.8\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
"<text text-anchor=\"start\" x=\"11\" y=\"-94.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- &#45;4&#45;&gt;2 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>&#45;4&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M19,-178.19C19,-173.66 19,-150.99 19,-132.43\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"19,-125.31 22.15,-132.31 19,-128.81 19,-132.31 19,-132.31 19,-132.31 19,-128.81 15.85,-132.31 19,-125.31 19,-125.31\"/>\n",
"</g>\n",
"<!-- 2&#45;&gt;2 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>2&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M37.15,-112.51C46.54,-113.51 55,-111.34 55,-106 55,-102.08 50.44,-99.86 44.3,-99.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"37.15,-99.49 44.1,-96.21 40.65,-99.43 44.15,-99.36 44.15,-99.36 44.15,-99.36 40.65,-99.43 44.21,-102.51 37.15,-99.49 37.15,-99.49\"/>\n",
"<text text-anchor=\"start\" x=\"55\" y=\"-102.3\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
"</g>\n",
"<!-- 5 -->\n",
"<g id=\"node8\" class=\"node\">\n",
"<title>5</title>\n",
"<g id=\"a_node8\"><a xlink:title=\"t\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M25,-36C25,-36 13,-36 13,-36 7,-36 1,-30 1,-24 1,-24 1,-12 1,-12 1,-6 7,0 13,0 13,0 25,0 25,0 31,0 37,-6 37,-12 37,-12 37,-24 37,-24 37,-30 31,-36 25,-36\"/>\n",
"<text text-anchor=\"middle\" x=\"19\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">5</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 2&#45;&gt;5 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>2&#45;&gt;5</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M19,-86.76C19,-74.11 19,-57.13 19,-43.33\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"19,-36.04 22.15,-43.04 19,-39.54 19,-43.04 19,-43.04 19,-43.04 19,-39.54 15.85,-43.04 19,-36.04 19,-36.04\"/>\n",
"<text text-anchor=\"start\" x=\"19\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
"</g>\n",
"<!-- 5&#45;&gt;5 -->\n",
"<g id=\"edge14\" class=\"edge\">\n",
"<title>5&#45;&gt;5</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M37.15,-25.6C46.54,-26.77 55,-24.23 55,-18 55,-13.42 50.44,-10.84 44.3,-10.25\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"37.15,-10.4 44.09,-7.11 40.65,-10.33 44.15,-10.26 44.15,-10.26 44.15,-10.26 40.65,-10.33 44.22,-13.41 37.15,-10.4 37.15,-10.4\"/>\n",
"<text text-anchor=\"start\" x=\"55\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 4&#45;&gt;4 -->\n",
"<g id=\"edge13\" class=\"edge\">\n",
"<title>4&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M116.15,-186.51C125.54,-187.51 134,-185.34 134,-180 134,-176.08 129.44,-173.86 123.3,-173.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"116.15,-173.49 123.1,-170.21 119.65,-173.43 123.15,-173.36 123.15,-173.36 123.15,-173.36 119.65,-173.43 123.21,-176.51 116.15,-173.49 116.15,-173.49\"/>\n",
"<text text-anchor=\"start\" x=\"134\" y=\"-176.3\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Pages: 1 -->\n",
"<svg width=\"187pt\" height=\"296pt\"\n",
" viewBox=\"0.00 0.00 187.11 296.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1.0 1.0) rotate(0) translate(4 292)\">\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-292 183.11,-292 183.11,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"68.06\" y=\"-273.8\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"91.06\" y=\"-273.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"107.06\" y=\"-273.8\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"58.06\" y=\"-259.8\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<g id=\"a_node2\"><a xlink:title=\"(a;a*;b)*\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M96,-214C96,-214 84,-214 84,-214 78,-214 72,-208 72,-202 72,-202 72,-188 72,-188 72,-182 78,-176 84,-176 84,-176 96,-176 96,-176 102,-176 108,-182 108,-188 108,-188 108,-202 108,-202 108,-208 102,-214 96,-214\"/>\n",
"<text text-anchor=\"start\" x=\"85.5\" y=\"-198.8\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"<text text-anchor=\"start\" x=\"82\" y=\"-183.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M90,-250.84C90,-249.2 90,-235.1 90,-221.61\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"90,-214.26 93.15,-221.26 90,-217.76 90,-221.26 90,-221.26 90,-221.26 90,-217.76 86.85,-221.26 90,-214.26 90,-214.26\"/>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>1</title>\n",
"<g id=\"a_node3\"><a xlink:title=\"a*;b;(a;a*;b)*\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M99,-125C99,-125 87,-125 87,-125 81,-125 75,-119 75,-113 75,-113 75,-99 75,-99 75,-93 81,-87 87,-87 87,-87 99,-87 99,-87 105,-87 111,-93 111,-99 111,-99 111,-113 111,-113 111,-119 105,-125 99,-125\"/>\n",
"<text text-anchor=\"start\" x=\"88.5\" y=\"-109.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"<text text-anchor=\"start\" x=\"85\" y=\"-94.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M81.79,-175.65C78.45,-165.97 75.82,-153.88 78,-143 78.73,-139.36 79.83,-135.63 81.12,-132.01\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"83.77,-125.24 84.15,-132.91 82.49,-128.5 81.22,-131.76 81.22,-131.76 81.22,-131.76 82.49,-128.5 78.28,-130.61 83.77,-125.24 83.77,-125.24\"/>\n",
"<text text-anchor=\"start\" x=\"78\" y=\"-146.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>2</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M24,-36C24,-36 12,-36 12,-36 6,-36 0,-30 0,-24 0,-24 0,-12 0,-12 0,-6 6,0 12,0 12,0 24,0 24,0 30,0 36,-6 36,-12 36,-12 36,-24 36,-24 36,-30 30,-36 24,-36\"/>\n",
"<text text-anchor=\"middle\" x=\"18\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>0&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M77.35,-175.95C61.65,-152.51 35.42,-109.75 23,-69 20.55,-60.95 19.23,-51.87 18.55,-43.67\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"18.08,-36.45 21.67,-43.23 18.31,-39.94 18.53,-43.44 18.53,-43.44 18.53,-43.44 18.31,-39.94 15.39,-43.64 18.08,-36.45 18.08,-36.45\"/>\n",
"<text text-anchor=\"start\" x=\"47\" y=\"-102.3\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M92.38,-125C91.94,-137.71 91.35,-154.91 90.86,-168.96\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"90.62,-175.97 87.71,-168.87 90.74,-172.48 90.86,-168.98 90.86,-168.98 90.86,-168.98 90.74,-172.48 94.01,-169.09 90.62,-175.97 90.62,-175.97\"/>\n",
"<text text-anchor=\"start\" x=\"92\" y=\"-146.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M111.15,-113.96C120.54,-115.18 129,-112.53 129,-106 129,-101.2 124.44,-98.5 118.3,-97.89\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"111.15,-98.04 118.08,-94.74 114.65,-97.96 118.15,-97.89 118.15,-97.89 118.15,-97.89 114.65,-97.96 118.22,-101.04 111.15,-98.04 111.15,-98.04\"/>\n",
"<text text-anchor=\"start\" x=\"129\" y=\"-102.3\" font-family=\"Lato\" font-size=\"14.00\">!b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>1&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M74.97,-97.78C62.17,-91.81 45.47,-82.18 35,-69 29.06,-61.52 25.14,-51.85 22.58,-43.01\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"20.8,-36.16 25.61,-42.15 21.68,-39.55 22.56,-42.94 22.56,-42.94 22.56,-42.94 21.68,-39.55 19.51,-43.73 20.8,-36.16 20.8,-36.16\"/>\n",
"<text text-anchor=\"start\" x=\"35\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"169\" cy=\"-18\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;&#45;1 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>1&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M90.64,-86.52C90.27,-76.11 91.52,-63.36 98,-54 112.9,-32.46 144.97,-23.59 160.38,-20.47\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"160.82,-22.88 167.28,-19.24 159.96,-18.06 160.82,-22.88\"/>\n",
"<text text-anchor=\"start\" x=\"98\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;2 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>2&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M36.15,-25.6C45.54,-26.77 54,-24.23 54,-18 54,-13.42 49.44,-10.84 43.3,-10.25\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"36.15,-10.4 43.09,-7.11 39.65,-10.33 43.15,-10.26 43.15,-10.26 43.15,-10.26 39.65,-10.33 43.22,-13.41 36.15,-10.4 36.15,-10.4\"/>\n",
"<text text-anchor=\"middle\" x=\"58.5\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;0 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M169.3,-20.07C171.58,-28.33 185.75,-82.85 175,-125 170.87,-141.19 168.85,-146.22 157,-158 145.01,-169.92 128.25,-178.92 114.49,-184.94\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"108.02,-187.66 113.25,-182.05 111.24,-186.3 114.47,-184.95 114.47,-184.95 114.47,-184.95 111.24,-186.3 115.69,-187.86 108.02,-187.66 108.02,-187.66\"/>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M168.98,-20.4C168.81,-26.73 167.36,-53.03 155,-69 145.46,-81.32 130.43,-90.2 117.55,-96.06\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"111.06,-98.85 116.24,-93.19 114.27,-97.47 117.49,-96.08 117.49,-96.08 117.49,-96.08 114.27,-97.47 118.73,-98.98 111.06,-98.85 111.06,-98.85\"/>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Pages: 1 -->\n",
"<svg width=\"155pt\" height=\"360pt\"\n",
" viewBox=\"0.00 0.00 154.85 360.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(0.8264462809917356 0.8264462809917356) rotate(0) translate(4 431)\">\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-431 183.11,-431 183.11,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"68.06\" y=\"-412.8\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"91.06\" y=\"-412.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"107.06\" y=\"-412.8\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"58.06\" y=\"-398.8\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 3 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>3</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M131,-353C131,-353 119,-353 119,-353 113,-353 107,-347 107,-341 107,-341 107,-329 107,-329 107,-323 113,-317 119,-317 119,-317 131,-317 131,-317 137,-317 143,-323 143,-329 143,-329 143,-341 143,-341 143,-347 137,-353 131,-353\"/>\n",
"<text text-anchor=\"middle\" x=\"125\" y=\"-331.3\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
"</g>\n",
"<!-- I&#45;&gt;3 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M125,-389.85C125,-388.21 125,-373.85 125,-360.37\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"125,-353.06 128.15,-360.06 125,-356.56 125,-360.06 125,-360.06 125,-360.06 125,-356.56 121.85,-360.06 125,-353.06 125,-353.06\"/>\n",
"</g>\n",
"<!-- &#45;4 -->\n",
"<g id=\"node7\" class=\"node\">\n",
"<title>&#45;4</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"106\" cy=\"-258.5\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 3&#45;&gt;&#45;4 -->\n",
"<g id=\"edge11\" class=\"edge\">\n",
"<title>3&#45;&gt;&#45;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M120.59,-316.72C116.62,-301.14 110.96,-278.94 107.99,-267.3\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"110.33,-266.57 106.23,-260.39 105.58,-267.78 110.33,-266.57\"/>\n",
"<text text-anchor=\"start\" x=\"117\" y=\"-287.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- 0 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>0</title>\n",
"<g id=\"a_node3\"><a xlink:title=\"(a;a*;b)*\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M96,-214C96,-214 84,-214 84,-214 78,-214 72,-208 72,-202 72,-202 72,-188 72,-188 72,-182 78,-176 84,-176 84,-176 96,-176 96,-176 102,-176 108,-182 108,-188 108,-188 108,-202 108,-202 108,-208 102,-214 96,-214\"/>\n",
"<text text-anchor=\"start\" x=\"85.5\" y=\"-198.8\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"<text text-anchor=\"start\" x=\"82\" y=\"-183.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>1</title>\n",
"<g id=\"a_node4\"><a xlink:title=\"a*;b;(a;a*;b)*\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M99,-125C99,-125 87,-125 87,-125 81,-125 75,-119 75,-113 75,-113 75,-99 75,-99 75,-93 81,-87 87,-87 87,-87 99,-87 99,-87 105,-87 111,-93 111,-99 111,-99 111,-113 111,-113 111,-119 105,-125 99,-125\"/>\n",
"<text text-anchor=\"start\" x=\"88.5\" y=\"-109.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"<text text-anchor=\"start\" x=\"85\" y=\"-94.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M81.79,-175.65C78.45,-165.97 75.82,-153.88 78,-143 78.73,-139.36 79.83,-135.63 81.12,-132.01\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"83.77,-125.24 84.15,-132.91 82.49,-128.5 81.22,-131.76 81.22,-131.76 81.22,-131.76 82.49,-128.5 78.28,-130.61 83.77,-125.24 83.77,-125.24\"/>\n",
"<text text-anchor=\"start\" x=\"78\" y=\"-146.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>2</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M24,-36C24,-36 12,-36 12,-36 6,-36 0,-30 0,-24 0,-24 0,-12 0,-12 0,-6 6,0 12,0 12,0 24,0 24,0 30,0 36,-6 36,-12 36,-12 36,-24 36,-24 36,-30 30,-36 24,-36\"/>\n",
"<text text-anchor=\"middle\" x=\"18\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>0&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M77.35,-175.95C61.65,-152.51 35.42,-109.75 23,-69 20.55,-60.95 19.23,-51.87 18.55,-43.67\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"18.08,-36.45 21.67,-43.23 18.31,-39.94 18.53,-43.44 18.53,-43.44 18.53,-43.44 18.31,-39.94 15.39,-43.64 18.08,-36.45 18.08,-36.45\"/>\n",
"<text text-anchor=\"start\" x=\"47\" y=\"-102.3\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M92.38,-125C91.94,-137.71 91.35,-154.91 90.86,-168.96\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"90.62,-175.97 87.71,-168.87 90.74,-172.48 90.86,-168.98 90.86,-168.98 90.86,-168.98 90.74,-172.48 94.01,-169.09 90.62,-175.97 90.62,-175.97\"/>\n",
"<text text-anchor=\"start\" x=\"92\" y=\"-146.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M111.15,-113.96C120.54,-115.18 129,-112.53 129,-106 129,-101.2 124.44,-98.5 118.3,-97.89\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"111.15,-98.04 118.08,-94.74 114.65,-97.96 118.15,-97.89 118.15,-97.89 118.15,-97.89 114.65,-97.96 118.22,-101.04 111.15,-98.04 111.15,-98.04\"/>\n",
"<text text-anchor=\"start\" x=\"129\" y=\"-102.3\" font-family=\"Lato\" font-size=\"14.00\">!b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>1&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M74.97,-97.78C62.17,-91.81 45.47,-82.18 35,-69 29.06,-61.52 25.14,-51.85 22.58,-43.01\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"20.8,-36.16 25.61,-42.15 21.68,-39.55 22.56,-42.94 22.56,-42.94 22.56,-42.94 21.68,-39.55 19.51,-43.73 20.8,-36.16 20.8,-36.16\"/>\n",
"<text text-anchor=\"start\" x=\"35\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node6\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"169\" cy=\"-18\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;&#45;1 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>1&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M90.64,-86.52C90.27,-76.11 91.52,-63.36 98,-54 112.9,-32.46 144.97,-23.59 160.38,-20.47\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"160.82,-22.88 167.28,-19.24 159.96,-18.06 160.82,-22.88\"/>\n",
"<text text-anchor=\"start\" x=\"98\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;2 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>2&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M36.15,-25.6C45.54,-26.77 54,-24.23 54,-18 54,-13.42 49.44,-10.84 43.3,-10.25\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"36.15,-10.4 43.09,-7.11 39.65,-10.33 43.15,-10.26 43.15,-10.26 43.15,-10.26 39.65,-10.33 43.22,-13.41 36.15,-10.4 36.15,-10.4\"/>\n",
"<text text-anchor=\"middle\" x=\"58.5\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;0 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M169.3,-20.07C171.58,-28.33 185.75,-82.85 175,-125 170.87,-141.19 169.26,-146.65 157,-158 142.7,-171.25 134.06,-166.56 117,-176 116.08,-176.51 115.14,-177.04 114.21,-177.59\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"108.04,-181.38 112.36,-175.03 111.03,-179.55 114.01,-177.71 114.01,-177.71 114.01,-177.71 111.03,-179.55 115.66,-180.4 108.04,-181.38 108.04,-181.38\"/>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M168.98,-20.4C168.81,-26.73 167.36,-53.03 155,-69 145.46,-81.32 130.43,-90.2 117.55,-96.06\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"111.06,-98.85 116.24,-93.19 114.27,-97.47 117.49,-96.08 117.49,-96.08 117.49,-96.08 114.27,-97.47 118.73,-98.98 111.06,-98.85 111.06,-98.85\"/>\n",
"</g>\n",
"<!-- &#45;4&#45;&gt;0 -->\n",
"<g id=\"edge12\" class=\"edge\">\n",
"<title>&#45;4&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M105.72,-256.43C104.61,-252.16 100.35,-235.79 96.55,-221.16\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"94.73,-214.18 99.54,-220.16 95.61,-217.57 96.49,-220.96 96.49,-220.96 96.49,-220.96 95.61,-217.57 93.44,-221.75 94.73,-214.18 94.73,-214.18\"/>\n",
"</g>\n",
"<!-- 4 -->\n",
"<g id=\"node8\" class=\"node\">\n",
"<title>4</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M150,-213C150,-213 138,-213 138,-213 132,-213 126,-207 126,-201 126,-201 126,-189 126,-189 126,-183 132,-177 138,-177 138,-177 150,-177 150,-177 156,-177 162,-183 162,-189 162,-189 162,-201 162,-201 162,-207 156,-213 150,-213\"/>\n",
"<text text-anchor=\"middle\" x=\"144\" y=\"-191.3\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
"</g>\n",
"<!-- &#45;4&#45;&gt;4 -->\n",
"<g id=\"edge13\" class=\"edge\">\n",
"<title>&#45;4&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M106.66,-256.43C109.4,-251.99 120.19,-234.53 129.47,-219.51\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"133.33,-213.27 132.33,-220.88 131.49,-216.25 129.65,-219.22 129.65,-219.22 129.65,-219.22 131.49,-216.25 126.97,-217.57 133.33,-213.27 133.33,-213.27\"/>\n",
"</g>\n",
"<!-- 4&#45;&gt;3 -->\n",
"<g id=\"edge14\" class=\"edge\">\n",
"<title>4&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M141.6,-213.42C138.24,-237.81 132.12,-282.25 128.33,-309.84\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"127.37,-316.8 125.2,-309.44 127.85,-313.33 128.32,-309.87 128.32,-309.87 128.32,-309.87 127.85,-313.33 131.44,-310.3 127.37,-316.8 127.37,-316.8\"/>\n",
"<text text-anchor=\"middle\" x=\"141.5\" y=\"-254.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Pages: 1 -->\n",
"<svg width=\"187pt\" height=\"296pt\"\n",
" viewBox=\"0.00 0.00 187.11 296.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1.0 1.0) rotate(0) translate(4 292)\">\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-292 183.11,-292 183.11,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"68.06\" y=\"-273.8\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"91.06\" y=\"-273.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"107.06\" y=\"-273.8\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"58.06\" y=\"-259.8\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<g id=\"a_node2\"><a xlink:title=\"(a;a*;b)*\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M96,-214C96,-214 84,-214 84,-214 78,-214 72,-208 72,-202 72,-202 72,-188 72,-188 72,-182 78,-176 84,-176 84,-176 96,-176 96,-176 102,-176 108,-182 108,-188 108,-188 108,-202 108,-202 108,-208 102,-214 96,-214\"/>\n",
"<text text-anchor=\"start\" x=\"85.5\" y=\"-198.8\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"<text text-anchor=\"start\" x=\"82\" y=\"-183.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M90,-250.84C90,-249.2 90,-235.1 90,-221.61\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"90,-214.26 93.15,-221.26 90,-217.76 90,-221.26 90,-221.26 90,-221.26 90,-217.76 86.85,-221.26 90,-214.26 90,-214.26\"/>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>1</title>\n",
"<g id=\"a_node3\"><a xlink:title=\"a*;b;(a;a*;b)*\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M99,-125C99,-125 87,-125 87,-125 81,-125 75,-119 75,-113 75,-113 75,-99 75,-99 75,-93 81,-87 87,-87 87,-87 99,-87 99,-87 105,-87 111,-93 111,-99 111,-99 111,-113 111,-113 111,-119 105,-125 99,-125\"/>\n",
"<text text-anchor=\"start\" x=\"88.5\" y=\"-109.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"<text text-anchor=\"start\" x=\"85\" y=\"-94.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M81.79,-175.65C78.45,-165.97 75.82,-153.88 78,-143 78.73,-139.36 79.83,-135.63 81.12,-132.01\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"83.77,-125.24 84.15,-132.91 82.49,-128.5 81.22,-131.76 81.22,-131.76 81.22,-131.76 82.49,-128.5 78.28,-130.61 83.77,-125.24 83.77,-125.24\"/>\n",
"<text text-anchor=\"start\" x=\"78\" y=\"-146.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>2</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M24,-36C24,-36 12,-36 12,-36 6,-36 0,-30 0,-24 0,-24 0,-12 0,-12 0,-6 6,0 12,0 12,0 24,0 24,0 30,0 36,-6 36,-12 36,-12 36,-24 36,-24 36,-30 30,-36 24,-36\"/>\n",
"<text text-anchor=\"middle\" x=\"18\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>0&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M77.35,-175.95C61.65,-152.51 35.42,-109.75 23,-69 20.55,-60.95 19.23,-51.87 18.55,-43.67\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"18.08,-36.45 21.67,-43.23 18.31,-39.94 18.53,-43.44 18.53,-43.44 18.53,-43.44 18.31,-39.94 15.39,-43.64 18.08,-36.45 18.08,-36.45\"/>\n",
"<text text-anchor=\"start\" x=\"47\" y=\"-102.3\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M92.38,-125C91.94,-137.71 91.35,-154.91 90.86,-168.96\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"90.62,-175.97 87.71,-168.87 90.74,-172.48 90.86,-168.98 90.86,-168.98 90.86,-168.98 90.74,-172.48 94.01,-169.09 90.62,-175.97 90.62,-175.97\"/>\n",
"<text text-anchor=\"start\" x=\"92\" y=\"-146.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M111.15,-113.96C120.54,-115.18 129,-112.53 129,-106 129,-101.2 124.44,-98.5 118.3,-97.89\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"111.15,-98.04 118.08,-94.74 114.65,-97.96 118.15,-97.89 118.15,-97.89 118.15,-97.89 114.65,-97.96 118.22,-101.04 111.15,-98.04 111.15,-98.04\"/>\n",
"<text text-anchor=\"start\" x=\"129\" y=\"-102.3\" font-family=\"Lato\" font-size=\"14.00\">!b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>1&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M74.97,-97.78C62.17,-91.81 45.47,-82.18 35,-69 29.06,-61.52 25.14,-51.85 22.58,-43.01\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"20.8,-36.16 25.61,-42.15 21.68,-39.55 22.56,-42.94 22.56,-42.94 22.56,-42.94 21.68,-39.55 19.51,-43.73 20.8,-36.16 20.8,-36.16\"/>\n",
"<text text-anchor=\"start\" x=\"35\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"169\" cy=\"-18\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;&#45;1 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>1&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M90.64,-86.52C90.27,-76.11 91.52,-63.36 98,-54 112.9,-32.46 144.97,-23.59 160.38,-20.47\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"160.82,-22.88 167.28,-19.24 159.96,-18.06 160.82,-22.88\"/>\n",
"<text text-anchor=\"start\" x=\"98\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;2 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>2&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M36.15,-25.6C45.54,-26.77 54,-24.23 54,-18 54,-13.42 49.44,-10.84 43.3,-10.25\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"36.15,-10.4 43.09,-7.11 39.65,-10.33 43.15,-10.26 43.15,-10.26 43.15,-10.26 39.65,-10.33 43.22,-13.41 36.15,-10.4 36.15,-10.4\"/>\n",
"<text text-anchor=\"middle\" x=\"58.5\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;0 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M169.3,-20.07C171.58,-28.33 185.75,-82.85 175,-125 170.87,-141.19 168.85,-146.22 157,-158 145.01,-169.92 128.25,-178.92 114.49,-184.94\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"108.02,-187.66 113.25,-182.05 111.24,-186.3 114.47,-184.95 114.47,-184.95 114.47,-184.95 111.24,-186.3 115.69,-187.86 108.02,-187.66 108.02,-187.66\"/>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M168.98,-20.4C168.81,-26.73 167.36,-53.03 155,-69 145.46,-81.32 130.43,-90.2 117.55,-96.06\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"111.06,-98.85 116.24,-93.19 114.27,-97.47 117.49,-96.08 117.49,-96.08 117.49,-96.08 114.27,-97.47 118.73,-98.98 111.06,-98.85 111.06,-98.85\"/>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Title: VWAA for GFa Pages: 1 -->\n",
"<svg width=\"87pt\" height=\"335pt\"\n",
" viewBox=\"0.00 0.00 87.00 334.60\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1.0 1.0) rotate(0) translate(4 330.6)\">\n",
"<title>VWAA for GFa</title>\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-330.6 83,-330.6 83,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"18\" y=\"-312.4\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"41\" y=\"-312.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"57\" y=\"-312.4\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"8\" y=\"-298.4\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<g id=\"a_node2\"><a xlink:title=\"GF(a)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M32,-252.6C32,-252.6 20,-252.6 20,-252.6 14,-252.6 8,-246.6 8,-240.6 8,-240.6 8,-228.6 8,-228.6 8,-222.6 14,-216.6 20,-216.6 20,-216.6 32,-216.6 32,-216.6 38,-216.6 44,-222.6 44,-228.6 44,-228.6 44,-240.6 44,-240.6 44,-246.6 38,-252.6 32,-252.6\"/>\n",
"<text text-anchor=\"middle\" x=\"26\" y=\"-230.9\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M26,-289.45C26,-287.81 26,-273.45 26,-259.97\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"26,-252.66 29.15,-259.66 26,-256.16 26,-259.66 26,-259.66 26,-259.66 26,-256.16 22.85,-259.66 26,-252.66 26,-252.66\"/>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"26\" cy=\"-163.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 0&#45;&gt;&#45;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M18.1,-216.38C14.69,-206.69 12.07,-194.41 15,-183.6 16.19,-179.21 18.69,-174.8 21,-171.35\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"22.97,-172.81 25.2,-165.73 19.05,-169.87 22.97,-172.81\"/>\n",
"<text text-anchor=\"start\" x=\"15\" y=\"-187.4\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;0 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M26,-166.19C26,-171.7 26,-192.51 26,-209.57\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"26,-216.59 22.85,-209.59 26,-213.09 26,-209.59 26,-209.59 26,-209.59 26,-213.09 29.15,-209.59 26,-216.59 26,-216.59\"/>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>1</title>\n",
"<g id=\"a_node4\"><a xlink:title=\"F(a)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M32,-125C32,-125 20,-125 20,-125 14,-125 8,-119 8,-113 8,-113 8,-99 8,-99 8,-93 14,-87 20,-87 20,-87 32,-87 32,-87 38,-87 44,-93 44,-99 44,-99 44,-113 44,-113 44,-119 38,-125 32,-125\"/>\n",
"<text text-anchor=\"start\" x=\"21.5\" y=\"-109.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"<text text-anchor=\"start\" x=\"18\" y=\"-94.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M26,-161.83C26,-158.2 26,-144.97 26,-132.42\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"26,-125.18 29.15,-132.18 26,-128.68 26,-132.18 26,-132.18 26,-132.18 26,-128.68 22.85,-132.18 26,-125.18 26,-125.18\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M44.15,-112.51C53.54,-113.51 62,-111.34 62,-106 62,-102.08 57.44,-99.86 51.3,-99.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"44.15,-99.49 51.1,-96.21 47.65,-99.43 51.15,-99.36 51.15,-99.36 51.15,-99.36 47.65,-99.43 51.21,-102.51 44.15,-99.49 44.15,-99.49\"/>\n",
"<text text-anchor=\"start\" x=\"62\" y=\"-102.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>2</title>\n",
"<g id=\"a_node5\"><a xlink:title=\"t\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M32,-36C32,-36 20,-36 20,-36 14,-36 8,-30 8,-24 8,-24 8,-12 8,-12 8,-6 14,0 20,0 20,0 32,0 32,0 38,0 44,-6 44,-12 44,-12 44,-24 44,-24 44,-30 38,-36 32,-36\"/>\n",
"<text text-anchor=\"middle\" x=\"26\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>1&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M26,-86.76C26,-74.11 26,-57.13 26,-43.33\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"26,-36.04 29.15,-43.04 26,-39.54 26,-43.04 26,-43.04 26,-43.04 26,-39.54 22.85,-43.04 26,-36.04 26,-36.04\"/>\n",
"<text text-anchor=\"start\" x=\"26\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;2 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>2&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M44.15,-25.6C53.54,-26.77 62,-24.23 62,-18 62,-13.42 57.44,-10.84 51.3,-10.25\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"44.15,-10.4 51.09,-7.11 47.65,-10.33 51.15,-10.26 51.15,-10.26 51.15,-10.26 47.65,-10.33 51.22,-13.41 44.15,-10.4 44.15,-10.4\"/>\n",
"<text text-anchor=\"start\" x=\"62\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"display_inline(aut1, aut2, aut3, aut4, aut5, show='.bav1')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"When working with alternating automata, it is quite common to hide \"true states\", and display \"exiting transitions instead\". You can do that with option `u`."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Title: VWAA for FGa &amp;&amp; GFb Pages: 1 -->\n",
"<svg width=\"118pt\" height=\"360pt\"\n",
" viewBox=\"0.00 0.00 117.76 360.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(0.78125 0.78125) rotate(0) translate(4 457.6)\">\n",
"<title>VWAA for FGa &amp;&amp; GFb</title>\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-457.6 147,-457.6 147,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"50\" y=\"-439.4\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"73\" y=\"-439.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"89\" y=\"-439.4\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"40\" y=\"-425.4\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<g id=\"a_node2\"><a xlink:title=\"(FG(a) &amp;&amp; GF(b))\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M63,-379.6C63,-379.6 51,-379.6 51,-379.6 45,-379.6 39,-373.6 39,-367.6 39,-367.6 39,-355.6 39,-355.6 39,-349.6 45,-343.6 51,-343.6 51,-343.6 63,-343.6 63,-343.6 69,-343.6 75,-349.6 75,-355.6 75,-355.6 75,-367.6 75,-367.6 75,-373.6 69,-379.6 63,-379.6\"/>\n",
"<text text-anchor=\"middle\" x=\"57\" y=\"-357.9\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M57,-416.45C57,-414.81 57,-400.45 57,-386.97\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"57,-379.66 60.15,-386.66 57,-383.16 57,-386.66 57,-386.66 57,-386.66 57,-383.16 53.85,-386.66 57,-379.66 57,-379.66\"/>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"57\" cy=\"-290.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 0&#45;&gt;&#45;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M57,-343.59C57,-329.81 57,-310.96 57,-300.21\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"59.45,-300.19 57,-293.19 54.55,-300.19 59.45,-300.19\"/>\n",
"<text text-anchor=\"start\" x=\"57\" y=\"-314.4\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>1</title>\n",
"<g id=\"a_node4\"><a xlink:title=\"GF(b)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M24,-251C24,-251 12,-251 12,-251 6,-251 0,-245 0,-239 0,-239 0,-227 0,-227 0,-221 6,-215 12,-215 12,-215 24,-215 24,-215 30,-215 36,-221 36,-227 36,-227 36,-239 36,-239 36,-245 30,-251 24,-251\"/>\n",
"<text text-anchor=\"start\" x=\"13.5\" y=\"-229.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M56.32,-288.83C53.62,-284.97 43.31,-270.21 34.06,-256.98\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"29.92,-251.05 36.51,-254.99 31.92,-253.92 33.93,-256.79 33.93,-256.79 33.93,-256.79 31.92,-253.92 31.35,-258.6 29.92,-251.05 29.92,-251.05\"/>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>3</title>\n",
"<g id=\"a_node5\"><a xlink:title=\"FG(a)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M104,-252C104,-252 92,-252 92,-252 86,-252 80,-246 80,-240 80,-240 80,-226 80,-226 80,-220 86,-214 92,-214 92,-214 104,-214 104,-214 110,-214 116,-220 116,-226 116,-226 116,-240 116,-240 116,-246 110,-252 104,-252\"/>\n",
"<text text-anchor=\"start\" x=\"93.5\" y=\"-236.8\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
"<text text-anchor=\"start\" x=\"90\" y=\"-221.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;3 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M57.71,-288.83C60.48,-285.07 70.83,-270.97 80.35,-258.02\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"84.64,-252.18 83.03,-259.69 82.57,-255 80.49,-257.83 80.49,-257.83 80.49,-257.83 82.57,-255 77.96,-255.96 84.64,-252.18 84.64,-252.18\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M36.15,-239.51C45.54,-240.51 54,-238.34 54,-233 54,-229.08 49.44,-226.86 43.3,-226.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"36.15,-226.49 43.1,-223.21 39.65,-226.43 43.15,-226.36 43.15,-226.36 43.15,-226.36 39.65,-226.43 43.21,-229.51 36.15,-226.49 36.15,-226.49\"/>\n",
"<text text-anchor=\"start\" x=\"54\" y=\"-229.3\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
"</g>\n",
"<!-- &#45;4 -->\n",
"<g id=\"node6\" class=\"node\">\n",
"<title>&#45;4</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"19\" cy=\"-145\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;&#45;4 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>1&#45;&gt;&#45;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M10.29,-214.63C6.85,-204.81 3.97,-192.28 6,-181 7.77,-171.18 12.11,-160.51 15.29,-153.56\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"17.71,-154.2 18.56,-146.83 13.3,-152.06 17.71,-154.2\"/>\n",
"<text text-anchor=\"start\" x=\"6\" y=\"-184.8\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;3 -->\n",
"<g id=\"edge12\" class=\"edge\">\n",
"<title>3&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M116.15,-239.51C125.54,-240.51 134,-238.34 134,-233 134,-229.08 129.44,-226.86 123.3,-226.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"116.15,-226.49 123.1,-223.21 119.65,-226.43 123.15,-226.36 123.15,-226.36 123.15,-226.36 119.65,-226.43 123.21,-229.51 116.15,-226.49 116.15,-226.49\"/>\n",
"<text text-anchor=\"start\" x=\"134\" y=\"-229.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 4 -->\n",
"<g id=\"node9\" class=\"node\">\n",
"<title>4</title>\n",
"<g id=\"a_node9\"><a xlink:title=\"G(a)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M104,-163C104,-163 92,-163 92,-163 86,-163 80,-157 80,-151 80,-151 80,-139 80,-139 80,-133 86,-127 92,-127 92,-127 104,-127 104,-127 110,-127 116,-133 116,-139 116,-139 116,-151 116,-151 116,-157 110,-163 104,-163\"/>\n",
"<text text-anchor=\"middle\" x=\"98\" y=\"-141.3\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 3&#45;&gt;4 -->\n",
"<g id=\"edge11\" class=\"edge\">\n",
"<title>3&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M98,-213.76C98,-201.11 98,-184.13 98,-170.33\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"98,-163.04 101.15,-170.04 98,-166.54 98,-170.04 98,-170.04 98,-170.04 98,-166.54 94.85,-170.04 98,-163.04 98,-163.04\"/>\n",
"<text text-anchor=\"start\" x=\"98\" y=\"-184.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- &#45;4&#45;&gt;1 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>&#45;4&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M18.99,-147.1C18.91,-153.32 18.55,-184.73 18.28,-207.54\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"18.2,-214.6 15.13,-207.56 18.24,-211.1 18.28,-207.6 18.28,-207.6 18.28,-207.6 18.24,-211.1 21.43,-207.63 18.2,-214.6 18.2,-214.6\"/>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node7\" class=\"node\">\n",
"<title>2</title>\n",
"<g id=\"a_node7\"><a xlink:title=\"F(b)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M25,-90C25,-90 13,-90 13,-90 7,-90 1,-84 1,-78 1,-78 1,-64 1,-64 1,-58 7,-52 13,-52 13,-52 25,-52 25,-52 31,-52 37,-58 37,-64 37,-64 37,-78 37,-78 37,-84 31,-90 25,-90\"/>\n",
"<text text-anchor=\"start\" x=\"14.5\" y=\"-74.8\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
"<text text-anchor=\"start\" x=\"11\" y=\"-59.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- &#45;4&#45;&gt;2 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>&#45;4&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M19,-143.19C19,-138.66 19,-115.99 19,-97.43\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"19,-90.31 22.15,-97.31 19,-93.81 19,-97.31 19,-97.31 19,-97.31 19,-93.81 15.85,-97.31 19,-90.31 19,-90.31\"/>\n",
"</g>\n",
"<!-- 2&#45;&gt;2 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>2&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M37.15,-77.51C46.54,-78.51 55,-76.34 55,-71 55,-67.08 50.44,-64.86 44.3,-64.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"37.15,-64.49 44.1,-61.21 40.65,-64.43 44.15,-64.36 44.15,-64.36 44.15,-64.36 40.65,-64.43 44.21,-67.51 37.15,-64.49 37.15,-64.49\"/>\n",
"<text text-anchor=\"start\" x=\"55\" y=\"-67.3\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
"</g>\n",
"<!-- T5T2 -->\n",
"<!-- 2&#45;&gt;T5T2 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>2&#45;&gt;T5T2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M19,-51.87C19,-37.64 19,-18.56 19,-8.29\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"19,-1.09 22.15,-8.09 19,-4.59 19,-8.09 19,-8.09 19,-8.09 19,-4.59 15.85,-8.09 19,-1.09 19,-1.09\"/>\n",
"<text text-anchor=\"start\" x=\"19\" y=\"-22.8\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
"</g>\n",
"<!-- 4&#45;&gt;4 -->\n",
"<g id=\"edge13\" class=\"edge\">\n",
"<title>4&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M116.15,-151.51C125.54,-152.51 134,-150.34 134,-145 134,-141.08 129.44,-138.86 123.3,-138.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"116.15,-138.49 123.1,-135.21 119.65,-138.43 123.15,-138.36 123.15,-138.36 123.15,-138.36 119.65,-138.43 123.21,-141.51 116.15,-138.49 116.15,-138.49\"/>\n",
"<text text-anchor=\"start\" x=\"134\" y=\"-141.3\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Pages: 1 -->\n",
"<svg width=\"196pt\" height=\"264pt\"\n",
" viewBox=\"0.00 0.00 196.43 263.60\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1.0 1.0) rotate(0) translate(4 259.6)\">\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-259.6 192.43,-259.6 192.43,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"72.72\" y=\"-241.4\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"95.72\" y=\"-241.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"111.72\" y=\"-241.4\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"62.72\" y=\"-227.4\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<g id=\"a_node2\"><a xlink:title=\"(a;a*;b)*\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M121,-181.6C121,-181.6 109,-181.6 109,-181.6 103,-181.6 97,-175.6 97,-169.6 97,-169.6 97,-155.6 97,-155.6 97,-149.6 103,-143.6 109,-143.6 109,-143.6 121,-143.6 121,-143.6 127,-143.6 133,-149.6 133,-155.6 133,-155.6 133,-169.6 133,-169.6 133,-175.6 127,-181.6 121,-181.6\"/>\n",
"<text text-anchor=\"start\" x=\"110.5\" y=\"-166.4\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"<text text-anchor=\"start\" x=\"107\" y=\"-151.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M115,-218.44C115,-216.8 115,-202.7 115,-189.21\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"115,-181.86 118.15,-188.86 115,-185.36 115,-188.86 115,-188.86 115,-188.86 115,-185.36 111.85,-188.86 115,-181.86 115,-181.86\"/>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>1</title>\n",
"<g id=\"a_node3\"><a xlink:title=\"a*;b;(a;a*;b)*\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M54,-92.6C54,-92.6 42,-92.6 42,-92.6 36,-92.6 30,-86.6 30,-80.6 30,-80.6 30,-66.6 30,-66.6 30,-60.6 36,-54.6 42,-54.6 42,-54.6 54,-54.6 54,-54.6 60,-54.6 66,-60.6 66,-66.6 66,-66.6 66,-80.6 66,-80.6 66,-86.6 60,-92.6 54,-92.6\"/>\n",
"<text text-anchor=\"start\" x=\"43.5\" y=\"-77.4\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"<text text-anchor=\"start\" x=\"40\" y=\"-62.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M96.96,-157.75C80.46,-153.17 57,-143.74 46,-125.6 41.41,-118.02 40.71,-108.58 41.56,-99.89\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"42.59,-92.83 44.7,-100.21 42.09,-96.29 41.58,-99.75 41.58,-99.75 41.58,-99.75 42.09,-96.29 38.46,-99.3 42.59,-92.83 42.59,-92.83\"/>\n",
"<text text-anchor=\"start\" x=\"46\" y=\"-114.4\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- T2T0 -->\n",
"<!-- 0&#45;&gt;T2T0 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>0&#45;&gt;T2T0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M125.53,-143.47C128.7,-137.81 132.1,-131.5 135,-125.6 142.67,-110.01 150.44,-91.1 154.37,-81.27\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"156.97,-74.68 157.33,-82.35 155.68,-77.94 154.4,-81.2 154.4,-81.2 154.4,-81.2 155.68,-77.94 151.47,-80.04 156.97,-74.68 156.97,-74.68\"/>\n",
"<text text-anchor=\"start\" x=\"141\" y=\"-114.4\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M53.39,-92.74C57.01,-103.04 62.51,-115.79 70,-125.6 75.69,-133.06 83.25,-139.88 90.54,-145.53\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"96.56,-150 89.06,-148.36 93.75,-147.91 90.94,-145.83 90.94,-145.83 90.94,-145.83 93.75,-147.91 92.81,-143.3 96.56,-150 96.56,-150\"/>\n",
"<text text-anchor=\"start\" x=\"70\" y=\"-114.4\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M66.15,-81.56C75.54,-82.78 84,-80.13 84,-73.6 84,-68.8 79.44,-66.1 73.3,-65.49\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"66.15,-65.64 73.08,-62.34 69.65,-65.56 73.15,-65.49 73.15,-65.49 73.15,-65.49 69.65,-65.56 73.22,-68.64 66.15,-65.64 66.15,-65.64\"/>\n",
"<text text-anchor=\"start\" x=\"84\" y=\"-69.9\" font-family=\"Lato\" font-size=\"14.00\">!b &amp; p</text>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"106\" cy=\"-1.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;&#45;1 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>1&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M66.35,-55.72C72.26,-49.9 78.66,-43.19 84,-36.6 90.94,-28.03 97.67,-17.21 101.82,-10.16\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"104.17,-10.97 105.52,-3.68 99.92,-8.54 104.17,-10.97\"/>\n",
"<text text-anchor=\"start\" x=\"94\" y=\"-25.4\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- T2T1 -->\n",
"<!-- 1&#45;&gt;T2T1 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>1&#45;&gt;T2T1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M29.78,-54.62C25.45,-49.26 21.39,-43.07 19,-36.6 15.77,-27.85 16.16,-16.94 16.93,-9.93\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"17.99,-2.86 20.06,-10.25 17.47,-6.32 16.95,-9.78 16.95,-9.78 16.95,-9.78 17.47,-6.32 13.83,-9.31 17.99,-2.86 17.99,-2.86\"/>\n",
"<text text-anchor=\"start\" x=\"19\" y=\"-25.4\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;0 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M107.32,-3.06C113.3,-4.29 138.25,-9.94 155,-21.6 171.03,-32.75 177.11,-36.33 184,-54.6 189.96,-70.4 189.82,-76.75 184,-92.6 175.73,-115.12 155.5,-133.84 139.07,-146.07\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"133.21,-150.28 137.06,-143.64 136.06,-148.24 138.9,-146.19 138.9,-146.19 138.9,-146.19 136.06,-148.24 140.74,-148.75 133.21,-150.28 133.21,-150.28\"/>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M105.24,-3.48C102.6,-5.86 93.62,-14.08 87,-21.6 79.58,-30.03 71.96,-39.72 65.45,-48.38\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"61.13,-54.18 62.78,-46.68 63.22,-51.37 65.31,-48.56 65.31,-48.56 65.31,-48.56 63.22,-51.37 67.84,-50.45 61.13,-54.18 61.13,-54.18\"/>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Pages: 1 -->\n",
"<svg width=\"176pt\" height=\"360pt\"\n",
" viewBox=\"0.00 0.00 175.56 360.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(0.8928571428571428 0.8928571428571428) rotate(0) translate(4 398.6)\">\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-398.6 192.33,-398.6 192.33,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"72.66\" y=\"-380.4\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"95.66\" y=\"-380.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"111.66\" y=\"-380.4\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"62.66\" y=\"-366.4\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 3 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>3</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M156,-320.6C156,-320.6 144,-320.6 144,-320.6 138,-320.6 132,-314.6 132,-308.6 132,-308.6 132,-296.6 132,-296.6 132,-290.6 138,-284.6 144,-284.6 144,-284.6 156,-284.6 156,-284.6 162,-284.6 168,-290.6 168,-296.6 168,-296.6 168,-308.6 168,-308.6 168,-314.6 162,-320.6 156,-320.6\"/>\n",
"<text text-anchor=\"middle\" x=\"150\" y=\"-298.9\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
"</g>\n",
"<!-- I&#45;&gt;3 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M150,-357.45C150,-355.81 150,-341.45 150,-327.97\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"150,-320.66 153.15,-327.66 150,-324.16 150,-327.66 150,-327.66 150,-327.66 150,-324.16 146.85,-327.66 150,-320.66 150,-320.66\"/>\n",
"</g>\n",
"<!-- &#45;4 -->\n",
"<g id=\"node8\" class=\"node\">\n",
"<title>&#45;4</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"131\" cy=\"-226.1\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 3&#45;&gt;&#45;4 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>3&#45;&gt;&#45;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M145.59,-284.32C141.62,-268.74 135.96,-246.54 132.99,-234.9\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"135.33,-234.17 131.23,-227.99 130.58,-235.38 135.33,-234.17\"/>\n",
"<text text-anchor=\"start\" x=\"142\" y=\"-255.4\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- 0 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>0</title>\n",
"<g id=\"a_node3\"><a xlink:title=\"(a;a*;b)*\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M121,-181.6C121,-181.6 109,-181.6 109,-181.6 103,-181.6 97,-175.6 97,-169.6 97,-169.6 97,-155.6 97,-155.6 97,-149.6 103,-143.6 109,-143.6 109,-143.6 121,-143.6 121,-143.6 127,-143.6 133,-149.6 133,-155.6 133,-155.6 133,-169.6 133,-169.6 133,-175.6 127,-181.6 121,-181.6\"/>\n",
"<text text-anchor=\"start\" x=\"110.5\" y=\"-166.4\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"<text text-anchor=\"start\" x=\"107\" y=\"-151.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>1</title>\n",
"<g id=\"a_node4\"><a xlink:title=\"a*;b;(a;a*;b)*\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M54,-92.6C54,-92.6 42,-92.6 42,-92.6 36,-92.6 30,-86.6 30,-80.6 30,-80.6 30,-66.6 30,-66.6 30,-60.6 36,-54.6 42,-54.6 42,-54.6 54,-54.6 54,-54.6 60,-54.6 66,-60.6 66,-66.6 66,-66.6 66,-80.6 66,-80.6 66,-86.6 60,-92.6 54,-92.6\"/>\n",
"<text text-anchor=\"start\" x=\"43.5\" y=\"-77.4\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"<text text-anchor=\"start\" x=\"40\" y=\"-62.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M96.96,-157.75C80.46,-153.17 57,-143.74 46,-125.6 41.41,-118.02 40.71,-108.58 41.56,-99.89\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"42.59,-92.83 44.7,-100.21 42.09,-96.29 41.58,-99.75 41.58,-99.75 41.58,-99.75 42.09,-96.29 38.46,-99.3 42.59,-92.83 42.59,-92.83\"/>\n",
"<text text-anchor=\"start\" x=\"46\" y=\"-114.4\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- T2T0 -->\n",
"<!-- 0&#45;&gt;T2T0 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>0&#45;&gt;T2T0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M125.53,-143.47C128.7,-137.81 132.1,-131.5 135,-125.6 142.67,-110.01 150.44,-91.1 154.37,-81.27\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"156.97,-74.68 157.33,-82.35 155.68,-77.94 154.4,-81.2 154.4,-81.2 154.4,-81.2 155.68,-77.94 151.47,-80.04 156.97,-74.68 156.97,-74.68\"/>\n",
"<text text-anchor=\"start\" x=\"142\" y=\"-114.4\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M53.39,-92.74C57.01,-103.04 62.51,-115.79 70,-125.6 75.69,-133.06 83.25,-139.88 90.54,-145.53\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"96.56,-150 89.06,-148.36 93.75,-147.91 90.94,-145.83 90.94,-145.83 90.94,-145.83 93.75,-147.91 92.81,-143.3 96.56,-150 96.56,-150\"/>\n",
"<text text-anchor=\"start\" x=\"70\" y=\"-114.4\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M66.15,-81.56C75.54,-82.78 84,-80.13 84,-73.6 84,-68.8 79.44,-66.1 73.3,-65.49\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"66.15,-65.64 73.08,-62.34 69.65,-65.56 73.15,-65.49 73.15,-65.49 73.15,-65.49 69.65,-65.56 73.22,-68.64 66.15,-65.64 66.15,-65.64\"/>\n",
"<text text-anchor=\"start\" x=\"84\" y=\"-69.9\" font-family=\"Lato\" font-size=\"14.00\">!b &amp; p</text>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node6\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"106\" cy=\"-1.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;&#45;1 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>1&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M66.35,-55.72C72.26,-49.9 78.66,-43.19 84,-36.6 90.94,-28.03 97.67,-17.21 101.82,-10.16\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"104.17,-10.97 105.52,-3.68 99.92,-8.54 104.17,-10.97\"/>\n",
"<text text-anchor=\"start\" x=\"95\" y=\"-25.4\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- T2T1 -->\n",
"<!-- 1&#45;&gt;T2T1 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>1&#45;&gt;T2T1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M29.78,-54.62C25.45,-49.26 21.39,-43.07 19,-36.6 15.77,-27.85 16.16,-16.94 16.93,-9.93\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"17.99,-2.86 20.06,-10.25 17.47,-6.32 16.95,-9.78 16.95,-9.78 16.95,-9.78 17.47,-6.32 13.83,-9.31 17.99,-2.86 17.99,-2.86\"/>\n",
"<text text-anchor=\"start\" x=\"19\" y=\"-25.4\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;0 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M107.35,-3.05C113.47,-4.22 139.01,-9.64 156,-21.6 171.73,-32.67 177.37,-36.54 184,-54.6 189.82,-70.45 189.68,-76.69 184,-92.6 177.63,-110.45 170.25,-112.05 157,-125.6 151.35,-131.38 144.87,-137.26 138.72,-142.54\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"133.2,-147.2 136.51,-140.28 135.87,-144.94 138.54,-142.68 138.54,-142.68 138.54,-142.68 135.87,-144.94 140.58,-145.09 133.2,-147.2 133.2,-147.2\"/>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M105.24,-3.48C102.6,-5.86 93.62,-14.08 87,-21.6 79.58,-30.03 71.96,-39.72 65.45,-48.38\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"61.13,-54.18 62.78,-46.68 63.22,-51.37 65.31,-48.56 65.31,-48.56 65.31,-48.56 63.22,-51.37 67.84,-50.45 61.13,-54.18 61.13,-54.18\"/>\n",
"</g>\n",
"<!-- &#45;4&#45;&gt;0 -->\n",
"<g id=\"edge11\" class=\"edge\">\n",
"<title>&#45;4&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M130.72,-224.03C129.61,-219.76 125.35,-203.39 121.55,-188.76\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"119.73,-181.78 124.54,-187.76 120.61,-185.17 121.49,-188.56 121.49,-188.56 121.49,-188.56 120.61,-185.17 118.44,-189.35 119.73,-181.78 119.73,-181.78\"/>\n",
"</g>\n",
"<!-- 4 -->\n",
"<g id=\"node9\" class=\"node\">\n",
"<title>4</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M175,-180.6C175,-180.6 163,-180.6 163,-180.6 157,-180.6 151,-174.6 151,-168.6 151,-168.6 151,-156.6 151,-156.6 151,-150.6 157,-144.6 163,-144.6 163,-144.6 175,-144.6 175,-144.6 181,-144.6 187,-150.6 187,-156.6 187,-156.6 187,-168.6 187,-168.6 187,-174.6 181,-180.6 175,-180.6\"/>\n",
"<text text-anchor=\"middle\" x=\"169\" y=\"-158.9\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
"</g>\n",
"<!-- &#45;4&#45;&gt;4 -->\n",
"<g id=\"edge12\" class=\"edge\">\n",
"<title>&#45;4&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M131.66,-224.03C134.4,-219.59 145.19,-202.13 154.47,-187.11\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"158.33,-180.87 157.33,-188.48 156.49,-183.85 154.65,-186.82 154.65,-186.82 154.65,-186.82 156.49,-183.85 151.97,-185.17 158.33,-180.87 158.33,-180.87\"/>\n",
"</g>\n",
"<!-- 4&#45;&gt;3 -->\n",
"<g id=\"edge13\" class=\"edge\">\n",
"<title>4&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M166.6,-181.02C163.24,-205.41 157.12,-249.85 153.33,-277.44\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"152.37,-284.4 150.2,-277.04 152.85,-280.93 153.32,-277.47 153.32,-277.47 153.32,-277.47 152.85,-280.93 156.44,-277.9 152.37,-284.4 152.37,-284.4\"/>\n",
"<text text-anchor=\"middle\" x=\"166.5\" y=\"-222.4\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Pages: 1 -->\n",
"<svg width=\"196pt\" height=\"264pt\"\n",
" viewBox=\"0.00 0.00 196.43 263.60\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1.0 1.0) rotate(0) translate(4 259.6)\">\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-259.6 192.43,-259.6 192.43,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"72.72\" y=\"-241.4\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"95.72\" y=\"-241.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"111.72\" y=\"-241.4\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"62.72\" y=\"-227.4\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<g id=\"a_node2\"><a xlink:title=\"(a;a*;b)*\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M121,-181.6C121,-181.6 109,-181.6 109,-181.6 103,-181.6 97,-175.6 97,-169.6 97,-169.6 97,-155.6 97,-155.6 97,-149.6 103,-143.6 109,-143.6 109,-143.6 121,-143.6 121,-143.6 127,-143.6 133,-149.6 133,-155.6 133,-155.6 133,-169.6 133,-169.6 133,-175.6 127,-181.6 121,-181.6\"/>\n",
"<text text-anchor=\"start\" x=\"110.5\" y=\"-166.4\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"<text text-anchor=\"start\" x=\"107\" y=\"-151.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M115,-218.44C115,-216.8 115,-202.7 115,-189.21\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"115,-181.86 118.15,-188.86 115,-185.36 115,-188.86 115,-188.86 115,-188.86 115,-185.36 111.85,-188.86 115,-181.86 115,-181.86\"/>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>1</title>\n",
"<g id=\"a_node3\"><a xlink:title=\"a*;b;(a;a*;b)*\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M54,-92.6C54,-92.6 42,-92.6 42,-92.6 36,-92.6 30,-86.6 30,-80.6 30,-80.6 30,-66.6 30,-66.6 30,-60.6 36,-54.6 42,-54.6 42,-54.6 54,-54.6 54,-54.6 60,-54.6 66,-60.6 66,-66.6 66,-66.6 66,-80.6 66,-80.6 66,-86.6 60,-92.6 54,-92.6\"/>\n",
"<text text-anchor=\"start\" x=\"43.5\" y=\"-77.4\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"<text text-anchor=\"start\" x=\"40\" y=\"-62.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M96.96,-157.75C80.46,-153.17 57,-143.74 46,-125.6 41.41,-118.02 40.71,-108.58 41.56,-99.89\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"42.59,-92.83 44.7,-100.21 42.09,-96.29 41.58,-99.75 41.58,-99.75 41.58,-99.75 42.09,-96.29 38.46,-99.3 42.59,-92.83 42.59,-92.83\"/>\n",
"<text text-anchor=\"start\" x=\"46\" y=\"-114.4\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- T2T0 -->\n",
"<!-- 0&#45;&gt;T2T0 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>0&#45;&gt;T2T0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M125.53,-143.47C128.7,-137.81 132.1,-131.5 135,-125.6 142.67,-110.01 150.44,-91.1 154.37,-81.27\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"156.97,-74.68 157.33,-82.35 155.68,-77.94 154.4,-81.2 154.4,-81.2 154.4,-81.2 155.68,-77.94 151.47,-80.04 156.97,-74.68 156.97,-74.68\"/>\n",
"<text text-anchor=\"start\" x=\"141\" y=\"-114.4\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M53.39,-92.74C57.01,-103.04 62.51,-115.79 70,-125.6 75.69,-133.06 83.25,-139.88 90.54,-145.53\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"96.56,-150 89.06,-148.36 93.75,-147.91 90.94,-145.83 90.94,-145.83 90.94,-145.83 93.75,-147.91 92.81,-143.3 96.56,-150 96.56,-150\"/>\n",
"<text text-anchor=\"start\" x=\"70\" y=\"-114.4\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M66.15,-81.56C75.54,-82.78 84,-80.13 84,-73.6 84,-68.8 79.44,-66.1 73.3,-65.49\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"66.15,-65.64 73.08,-62.34 69.65,-65.56 73.15,-65.49 73.15,-65.49 73.15,-65.49 69.65,-65.56 73.22,-68.64 66.15,-65.64 66.15,-65.64\"/>\n",
"<text text-anchor=\"start\" x=\"84\" y=\"-69.9\" font-family=\"Lato\" font-size=\"14.00\">!b &amp; p</text>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"106\" cy=\"-1.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;&#45;1 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>1&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M66.35,-55.72C72.26,-49.9 78.66,-43.19 84,-36.6 90.94,-28.03 97.67,-17.21 101.82,-10.16\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"104.17,-10.97 105.52,-3.68 99.92,-8.54 104.17,-10.97\"/>\n",
"<text text-anchor=\"start\" x=\"94\" y=\"-25.4\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- T2T1 -->\n",
"<!-- 1&#45;&gt;T2T1 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>1&#45;&gt;T2T1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M29.78,-54.62C25.45,-49.26 21.39,-43.07 19,-36.6 15.77,-27.85 16.16,-16.94 16.93,-9.93\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"17.99,-2.86 20.06,-10.25 17.47,-6.32 16.95,-9.78 16.95,-9.78 16.95,-9.78 17.47,-6.32 13.83,-9.31 17.99,-2.86 17.99,-2.86\"/>\n",
"<text text-anchor=\"start\" x=\"19\" y=\"-25.4\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;0 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M107.32,-3.06C113.3,-4.29 138.25,-9.94 155,-21.6 171.03,-32.75 177.11,-36.33 184,-54.6 189.96,-70.4 189.82,-76.75 184,-92.6 175.73,-115.12 155.5,-133.84 139.07,-146.07\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"133.21,-150.28 137.06,-143.64 136.06,-148.24 138.9,-146.19 138.9,-146.19 138.9,-146.19 136.06,-148.24 140.74,-148.75 133.21,-150.28 133.21,-150.28\"/>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M105.24,-3.48C102.6,-5.86 93.62,-14.08 87,-21.6 79.58,-30.03 71.96,-39.72 65.45,-48.38\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"61.13,-54.18 62.78,-46.68 63.22,-51.37 65.31,-48.56 65.31,-48.56 65.31,-48.56 63.22,-51.37 67.84,-50.45 61.13,-54.18 61.13,-54.18\"/>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Title: VWAA for GFa Pages: 1 -->\n",
"<svg width=\"87pt\" height=\"300pt\"\n",
" viewBox=\"0.00 0.00 87.00 299.60\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1.0 1.0) rotate(0) translate(4 295.6)\">\n",
"<title>VWAA for GFa</title>\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-295.6 83,-295.6 83,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"18\" y=\"-277.4\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"41\" y=\"-277.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"57\" y=\"-277.4\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"8\" y=\"-263.4\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<g id=\"a_node2\"><a xlink:title=\"GF(a)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M32,-217.6C32,-217.6 20,-217.6 20,-217.6 14,-217.6 8,-211.6 8,-205.6 8,-205.6 8,-193.6 8,-193.6 8,-187.6 14,-181.6 20,-181.6 20,-181.6 32,-181.6 32,-181.6 38,-181.6 44,-187.6 44,-193.6 44,-193.6 44,-205.6 44,-205.6 44,-211.6 38,-217.6 32,-217.6\"/>\n",
"<text text-anchor=\"middle\" x=\"26\" y=\"-195.9\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M26,-254.45C26,-252.81 26,-238.45 26,-224.97\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"26,-217.66 29.15,-224.66 26,-221.16 26,-224.66 26,-224.66 26,-224.66 26,-221.16 22.85,-224.66 26,-217.66 26,-217.66\"/>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"26\" cy=\"-128.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 0&#45;&gt;&#45;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M18.1,-181.38C14.69,-171.69 12.07,-159.41 15,-148.6 16.19,-144.21 18.69,-139.8 21,-136.35\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"22.97,-137.81 25.2,-130.73 19.05,-134.87 22.97,-137.81\"/>\n",
"<text text-anchor=\"start\" x=\"15\" y=\"-152.4\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;0 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M26,-131.19C26,-136.7 26,-157.51 26,-174.57\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"26,-181.59 22.85,-174.59 26,-178.09 26,-174.59 26,-174.59 26,-174.59 26,-178.09 29.15,-174.59 26,-181.59 26,-181.59\"/>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>1</title>\n",
"<g id=\"a_node4\"><a xlink:title=\"F(a)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M32,-90C32,-90 20,-90 20,-90 14,-90 8,-84 8,-78 8,-78 8,-64 8,-64 8,-58 14,-52 20,-52 20,-52 32,-52 32,-52 38,-52 44,-58 44,-64 44,-64 44,-78 44,-78 44,-84 38,-90 32,-90\"/>\n",
"<text text-anchor=\"start\" x=\"21.5\" y=\"-74.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"<text text-anchor=\"start\" x=\"18\" y=\"-59.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M26,-126.83C26,-123.2 26,-109.97 26,-97.42\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"26,-90.18 29.15,-97.18 26,-93.68 26,-97.18 26,-97.18 26,-97.18 26,-93.68 22.85,-97.18 26,-90.18 26,-90.18\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M44.15,-77.51C53.54,-78.51 62,-76.34 62,-71 62,-67.08 57.44,-64.86 51.3,-64.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"44.15,-64.49 51.1,-61.21 47.65,-64.43 51.15,-64.36 51.15,-64.36 51.15,-64.36 47.65,-64.43 51.21,-67.51 44.15,-64.49 44.15,-64.49\"/>\n",
"<text text-anchor=\"start\" x=\"62\" y=\"-67.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- T2T1 -->\n",
"<!-- 1&#45;&gt;T2T1 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>1&#45;&gt;T2T1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M26,-51.87C26,-37.64 26,-18.56 26,-8.29\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"26,-1.09 29.15,-8.09 26,-4.59 26,-8.09 26,-8.09 26,-8.09 26,-4.59 22.85,-8.09 26,-1.09 26,-1.09\"/>\n",
"<text text-anchor=\"start\" x=\"26\" y=\"-22.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"display_inline(aut1, aut2, aut3, aut4, aut5, show='.bav1u')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's make sure that option `u` and `s` (to display SCCs) work well together:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Title: VWAA for FGa &amp;&amp; GFb Pages: 1 -->\n",
"<svg width=\"147pt\" height=\"360pt\"\n",
" viewBox=\"0.00 0.00 147.40 360.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(0.78125 0.78125) rotate(0) translate(4 457.6)\">\n",
"<title>VWAA for FGa &amp;&amp; GFb</title>\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-457.6 185,-457.6 185,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"69\" y=\"-439.4\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"92\" y=\"-439.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"108\" y=\"-439.4\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"59\" y=\"-425.4\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<g id=\"clust2\" class=\"cluster\">\n",
"<title>cluster_1</title>\n",
"<polygon fill=\"none\" stroke=\"red\" points=\"17,-44 17,-98 99,-98 99,-44 17,-44\"/>\n",
"</g>\n",
"<g id=\"clust3\" class=\"cluster\">\n",
"<title>cluster_2</title>\n",
"<polygon fill=\"none\" stroke=\"green\" points=\"8,-135.2 8,-259 86,-259 86,-135.2 8,-135.2\"/>\n",
"</g>\n",
"<g id=\"clust4\" class=\"cluster\">\n",
"<title>cluster_3</title>\n",
"<polygon fill=\"none\" stroke=\"green\" points=\"94,-119 94,-171 171,-171 171,-119 94,-119\"/>\n",
"</g>\n",
"<g id=\"clust5\" class=\"cluster\">\n",
"<title>cluster_4</title>\n",
"<polygon fill=\"none\" stroke=\"red\" points=\"94,-206 94,-260 173,-260 173,-206 94,-206\"/>\n",
"</g>\n",
"<g id=\"clust6\" class=\"cluster\">\n",
"<title>cluster_5</title>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"50,-335.6 50,-387.6 102,-387.6 102,-335.6 50,-335.6\"/>\n",
"</g>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<g id=\"a_node2\"><a xlink:title=\"(FG(a) &amp;&amp; GF(b))\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M82,-379.6C82,-379.6 70,-379.6 70,-379.6 64,-379.6 58,-373.6 58,-367.6 58,-367.6 58,-355.6 58,-355.6 58,-349.6 64,-343.6 70,-343.6 70,-343.6 82,-343.6 82,-343.6 88,-343.6 94,-349.6 94,-355.6 94,-355.6 94,-367.6 94,-367.6 94,-373.6 88,-379.6 82,-379.6\"/>\n",
"<text text-anchor=\"middle\" x=\"76\" y=\"-357.9\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M76,-416.45C76,-414.81 76,-400.45 76,-386.97\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"76,-379.66 79.15,-386.66 76,-383.16 76,-386.66 76,-386.66 76,-386.66 76,-383.16 72.85,-386.66 76,-379.66 76,-379.66\"/>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node8\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"76\" cy=\"-290.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 0&#45;&gt;&#45;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M76,-343.59C76,-329.81 76,-310.96 76,-300.21\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"78.45,-300.19 76,-293.19 73.55,-300.19 78.45,-300.19\"/>\n",
"<text text-anchor=\"middle\" x=\"80.5\" y=\"-314.4\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>2</title>\n",
"<g id=\"a_node3\"><a xlink:title=\"F(b)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M49,-90C49,-90 37,-90 37,-90 31,-90 25,-84 25,-78 25,-78 25,-64 25,-64 25,-58 31,-52 37,-52 37,-52 49,-52 49,-52 55,-52 61,-58 61,-64 61,-64 61,-78 61,-78 61,-84 55,-90 49,-90\"/>\n",
"<text text-anchor=\"start\" x=\"38.5\" y=\"-74.8\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
"<text text-anchor=\"start\" x=\"35\" y=\"-59.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 2&#45;&gt;2 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>2&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M61.15,-77.51C70.54,-78.51 79,-76.34 79,-71 79,-67.08 74.44,-64.86 68.3,-64.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"61.15,-64.49 68.1,-61.21 64.65,-64.43 68.15,-64.36 68.15,-64.36 68.15,-64.36 64.65,-64.43 68.21,-67.51 61.15,-64.49 61.15,-64.49\"/>\n",
"<text text-anchor=\"start\" x=\"79\" y=\"-67.3\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
"</g>\n",
"<!-- T5T2 -->\n",
"<!-- 2&#45;&gt;T5T2 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>2&#45;&gt;T5T2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M43,-51.87C43,-37.64 43,-18.56 43,-8.29\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"43,-1.09 46.15,-8.09 43,-4.59 43,-8.09 43,-8.09 43,-8.09 43,-4.59 39.85,-8.09 43,-1.09 43,-1.09\"/>\n",
"<text text-anchor=\"start\" x=\"43\" y=\"-22.8\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>1</title>\n",
"<g id=\"a_node4\"><a xlink:title=\"GF(b)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M40,-251C40,-251 28,-251 28,-251 22,-251 16,-245 16,-239 16,-239 16,-227 16,-227 16,-221 22,-215 28,-215 28,-215 40,-215 40,-215 46,-215 52,-221 52,-227 52,-227 52,-239 52,-239 52,-245 46,-251 40,-251\"/>\n",
"<text text-anchor=\"middle\" x=\"34\" y=\"-229.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M52.15,-239.51C61.54,-240.51 70,-238.34 70,-233 70,-229.08 65.44,-226.86 59.3,-226.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"52.15,-226.49 59.1,-223.21 55.65,-226.43 59.15,-226.36 59.15,-226.36 59.15,-226.36 55.65,-226.43 59.21,-229.51 52.15,-226.49 52.15,-226.49\"/>\n",
"<text text-anchor=\"start\" x=\"70\" y=\"-229.3\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
"</g>\n",
"<!-- &#45;4 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>&#45;4</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"43\" cy=\"-145\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;&#45;4 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>1&#45;&gt;&#45;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M33.46,-214.94C33.37,-205 33.62,-192.25 35,-181 36.17,-171.47 38.83,-160.74 40.76,-153.7\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"43.15,-154.26 42.74,-146.85 38.44,-152.9 43.15,-154.26\"/>\n",
"<text text-anchor=\"start\" x=\"35\" y=\"-184.8\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
"</g>\n",
"<!-- &#45;4&#45;&gt;2 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>&#45;4&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M43,-143.19C43,-138.66 43,-115.99 43,-97.43\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"43,-90.31 46.15,-97.31 43,-93.81 43,-97.31 43,-97.31 43,-97.31 43,-93.81 39.85,-97.31 43,-90.31 43,-90.31\"/>\n",
"</g>\n",
"<!-- &#45;4&#45;&gt;1 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>&#45;4&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M43.33,-147.25C44.78,-152.92 50.36,-176.79 47,-196 46.31,-199.93 45.23,-203.99 43.98,-207.91\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"41.6,-214.75 40.93,-207.11 42.75,-211.45 43.9,-208.14 43.9,-208.14 43.9,-208.14 42.75,-211.45 46.88,-209.18 41.6,-214.75 41.6,-214.75\"/>\n",
"</g>\n",
"<!-- 4 -->\n",
"<g id=\"node6\" class=\"node\">\n",
"<title>4</title>\n",
"<g id=\"a_node6\"><a xlink:title=\"G(a)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M126,-163C126,-163 114,-163 114,-163 108,-163 102,-157 102,-151 102,-151 102,-139 102,-139 102,-133 108,-127 114,-127 114,-127 126,-127 126,-127 132,-127 138,-133 138,-139 138,-139 138,-151 138,-151 138,-157 132,-163 126,-163\"/>\n",
"<text text-anchor=\"middle\" x=\"120\" y=\"-141.3\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 4&#45;&gt;4 -->\n",
"<g id=\"edge13\" class=\"edge\">\n",
"<title>4&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M138.15,-151.51C147.54,-152.51 156,-150.34 156,-145 156,-141.08 151.44,-138.86 145.3,-138.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"138.15,-138.49 145.1,-135.21 141.65,-138.43 145.15,-138.36 145.15,-138.36 145.15,-138.36 141.65,-138.43 145.21,-141.51 138.15,-138.49 138.15,-138.49\"/>\n",
"<text text-anchor=\"start\" x=\"156\" y=\"-141.3\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g id=\"node7\" class=\"node\">\n",
"<title>3</title>\n",
"<g id=\"a_node7\"><a xlink:title=\"FG(a)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M126,-252C126,-252 114,-252 114,-252 108,-252 102,-246 102,-240 102,-240 102,-226 102,-226 102,-220 108,-214 114,-214 114,-214 126,-214 126,-214 132,-214 138,-220 138,-226 138,-226 138,-240 138,-240 138,-246 132,-252 126,-252\"/>\n",
"<text text-anchor=\"start\" x=\"115.5\" y=\"-236.8\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
"<text text-anchor=\"start\" x=\"112\" y=\"-221.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 3&#45;&gt;4 -->\n",
"<g id=\"edge11\" class=\"edge\">\n",
"<title>3&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M120,-213.76C120,-201.11 120,-184.13 120,-170.33\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"120,-163.04 123.15,-170.04 120,-166.54 120,-170.04 120,-170.04 120,-170.04 120,-166.54 116.85,-170.04 120,-163.04 120,-163.04\"/>\n",
"<text text-anchor=\"start\" x=\"120\" y=\"-184.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;3 -->\n",
"<g id=\"edge12\" class=\"edge\">\n",
"<title>3&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M138.15,-239.51C147.54,-240.51 156,-238.34 156,-233 156,-229.08 151.44,-226.86 145.3,-226.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"138.15,-226.49 145.1,-223.21 141.65,-226.43 145.15,-226.36 145.15,-226.36 145.15,-226.36 141.65,-226.43 145.21,-229.51 138.15,-226.49 138.15,-226.49\"/>\n",
"<text text-anchor=\"middle\" x=\"160.5\" y=\"-229.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M75.27,-288.83C72.36,-284.97 61.26,-270.21 51.3,-256.98\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"46.84,-251.05 53.56,-254.75 48.94,-253.85 51.05,-256.65 51.05,-256.65 51.05,-256.65 48.94,-253.85 48.53,-258.54 46.84,-251.05 46.84,-251.05\"/>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;3 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M76.76,-288.83C79.73,-285.07 90.85,-270.97 101.06,-258.02\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"105.66,-252.18 103.8,-259.63 103.49,-254.93 101.33,-257.68 101.33,-257.68 101.33,-257.68 103.49,-254.93 98.85,-255.73 105.66,-252.18 105.66,-252.18\"/>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Pages: 1 -->\n",
"<svg width=\"193pt\" height=\"280pt\"\n",
" viewBox=\"0.00 0.00 193.00 279.60\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1.0 1.0) rotate(0) translate(4 275.6)\">\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-275.6 189,-275.6 189,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"71\" y=\"-257.4\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"94\" y=\"-257.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"110\" y=\"-257.4\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"61\" y=\"-243.4\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<g id=\"clust2\" class=\"cluster\">\n",
"<title>cluster_1</title>\n",
"<polygon fill=\"none\" stroke=\"red\" points=\"8,-8 8,-205.6 140,-205.6 140,-8 8,-8\"/>\n",
"</g>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<g id=\"a_node2\"><a xlink:title=\"(a;a*;b)*\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M83,-197.6C83,-197.6 71,-197.6 71,-197.6 65,-197.6 59,-191.6 59,-185.6 59,-185.6 59,-171.6 59,-171.6 59,-165.6 65,-159.6 71,-159.6 71,-159.6 83,-159.6 83,-159.6 89,-159.6 95,-165.6 95,-171.6 95,-171.6 95,-185.6 95,-185.6 95,-191.6 89,-197.6 83,-197.6\"/>\n",
"<text text-anchor=\"start\" x=\"72.5\" y=\"-182.4\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"<text text-anchor=\"start\" x=\"69\" y=\"-167.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M77,-234.44C77,-232.8 77,-218.7 77,-205.21\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"77,-197.86 80.15,-204.86 77,-201.36 77,-204.86 77,-204.86 77,-204.86 77,-201.36 73.85,-204.86 77,-197.86 77,-197.86\"/>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>1</title>\n",
"<g id=\"a_node3\"><a xlink:title=\"a*;b;(a;a*;b)*\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M64,-108.6C64,-108.6 52,-108.6 52,-108.6 46,-108.6 40,-102.6 40,-96.6 40,-96.6 40,-82.6 40,-82.6 40,-76.6 46,-70.6 52,-70.6 52,-70.6 64,-70.6 64,-70.6 70,-70.6 76,-76.6 76,-82.6 76,-82.6 76,-96.6 76,-96.6 76,-102.6 70,-108.6 64,-108.6\"/>\n",
"<text text-anchor=\"start\" x=\"53.5\" y=\"-93.4\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"<text text-anchor=\"start\" x=\"50\" y=\"-78.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M95.23,-159.29C102.59,-149.62 108.25,-137.53 103,-126.6 98.58,-117.4 90.54,-109.82 82.46,-104.02\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"76.34,-99.94 83.91,-101.2 79.25,-101.88 82.16,-103.83 82.16,-103.83 82.16,-103.83 79.25,-101.88 80.42,-106.45 76.34,-99.94 76.34,-99.94\"/>\n",
"<text text-anchor=\"start\" x=\"106\" y=\"-130.4\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- T2T0 -->\n",
"<!-- 0&#45;&gt;T2T0 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>0&#45;&gt;T2T0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M95.14,-161.71C102.07,-155.52 109.98,-148.32 117,-141.6 134,-125.31 153.29,-105.13 162.12,-95.79\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"166.92,-90.68 164.42,-97.94 164.52,-93.23 162.13,-95.78 162.13,-95.78 162.13,-95.78 164.52,-93.23 159.83,-93.62 166.92,-90.68 166.92,-90.68\"/>\n",
"<text text-anchor=\"start\" x=\"132\" y=\"-130.4\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M43.76,-108.68C37.81,-118.49 33.27,-130.8 38,-141.6 41.28,-149.1 46.98,-155.72 53.02,-161.18\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"58.61,-165.86 51.22,-163.78 55.93,-163.61 53.24,-161.37 53.24,-161.37 53.24,-161.37 55.93,-163.61 55.27,-158.95 58.61,-165.86 58.61,-165.86\"/>\n",
"<text text-anchor=\"start\" x=\"38\" y=\"-130.4\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M76.15,-97.56C85.54,-98.78 94,-96.13 94,-89.6 94,-84.8 89.44,-82.1 83.3,-81.49\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"76.15,-81.64 83.08,-78.34 79.65,-81.56 83.15,-81.49 83.15,-81.49 83.15,-81.49 79.65,-81.56 83.22,-84.64 76.15,-81.64 76.15,-81.64\"/>\n",
"<text text-anchor=\"start\" x=\"94\" y=\"-85.9\" font-family=\"Lato\" font-size=\"14.00\">!b &amp; p</text>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"41\" cy=\"-17.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;&#45;1 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>1&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M48.27,-70.39C45.75,-64.83 43.37,-58.6 42,-52.6 40.04,-43.99 40.04,-33.82 40.37,-26.9\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"42.83,-26.81 40.91,-19.65 37.95,-26.45 42.83,-26.81\"/>\n",
"<text text-anchor=\"start\" x=\"42\" y=\"-41.4\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- T2T1 -->\n",
"<!-- 1&#45;&gt;T2T1 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>1&#45;&gt;T2T1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M76.32,-76.76C101.04,-60.78 143.81,-33.14 159.77,-22.83\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"165.83,-18.91 161.66,-25.35 162.89,-20.81 159.95,-22.71 159.95,-22.71 159.95,-22.71 162.89,-20.81 158.24,-20.06 165.83,-18.91 165.83,-18.91\"/>\n",
"<text text-anchor=\"start\" x=\"135\" y=\"-41.4\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;0 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M40.64,-19.64C37.11,-27.96 9.65,-95.95 33,-141.6 37.51,-150.42 45.25,-157.86 53,-163.65\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"58.87,-167.74 51.32,-166.32 56,-165.74 53.13,-163.74 53.13,-163.74 53.13,-163.74 56,-165.74 54.93,-161.15 58.87,-167.74 58.87,-167.74\"/>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M42.84,-18.71C51.11,-18.41 85.06,-18.42 99,-37.6 108.24,-50.3 95.54,-64.16 81.91,-74.22\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"76.07,-78.28 80.01,-71.7 78.94,-76.28 81.81,-74.28 81.81,-74.28 81.81,-74.28 78.94,-76.28 83.61,-76.87 76.07,-78.28 76.07,-78.28\"/>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Pages: 1 -->\n",
"<svg width=\"229pt\" height=\"360pt\"\n",
" viewBox=\"0.00 0.00 228.76 360.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(0.8620689655172414 0.8620689655172414) rotate(0) translate(4 414.6)\">\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-414.6 262,-414.6 262,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"107.5\" y=\"-396.4\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"130.5\" y=\"-396.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"146.5\" y=\"-396.4\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"97.5\" y=\"-382.4\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<g id=\"clust2\" class=\"cluster\">\n",
"<title>cluster_1</title>\n",
"<polygon fill=\"none\" stroke=\"red\" points=\"81,-8 81,-205.6 213,-205.6 213,-8 81,-8\"/>\n",
"</g>\n",
"<g id=\"clust3\" class=\"cluster\">\n",
"<title>cluster_2</title>\n",
"<polygon fill=\"none\" stroke=\"green\" points=\"8,-152.6 8,-344.6 73,-344.6 73,-152.6 8,-152.6\"/>\n",
"</g>\n",
"<!-- I -->\n",
"<!-- 3 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>3</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M46,-336.6C46,-336.6 34,-336.6 34,-336.6 28,-336.6 22,-330.6 22,-324.6 22,-324.6 22,-312.6 22,-312.6 22,-306.6 28,-300.6 34,-300.6 34,-300.6 46,-300.6 46,-300.6 52,-300.6 58,-306.6 58,-312.6 58,-312.6 58,-324.6 58,-324.6 58,-330.6 52,-336.6 46,-336.6\"/>\n",
"<text text-anchor=\"middle\" x=\"40\" y=\"-314.9\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
"</g>\n",
"<!-- I&#45;&gt;3 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M40,-373.45C40,-371.81 40,-357.45 40,-343.97\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"40,-336.66 43.15,-343.66 40,-340.16 40,-343.66 40,-343.66 40,-343.66 40,-340.16 36.85,-343.66 40,-336.66 40,-336.66\"/>\n",
"</g>\n",
"<!-- &#45;4 -->\n",
"<g id=\"node6\" class=\"node\">\n",
"<title>&#45;4</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"63\" cy=\"-242.1\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 3&#45;&gt;&#45;4 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>3&#45;&gt;&#45;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M45.33,-300.32C50.14,-284.74 57,-262.54 60.59,-250.9\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"63,-251.4 62.73,-243.99 58.32,-249.95 63,-251.4\"/>\n",
"<text text-anchor=\"start\" x=\"55\" y=\"-271.4\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- 0 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>0</title>\n",
"<g id=\"a_node3\"><a xlink:title=\"(a;a*;b)*\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M120,-197.6C120,-197.6 108,-197.6 108,-197.6 102,-197.6 96,-191.6 96,-185.6 96,-185.6 96,-171.6 96,-171.6 96,-165.6 102,-159.6 108,-159.6 108,-159.6 120,-159.6 120,-159.6 126,-159.6 132,-165.6 132,-171.6 132,-171.6 132,-185.6 132,-185.6 132,-191.6 126,-197.6 120,-197.6\"/>\n",
"<text text-anchor=\"start\" x=\"109.5\" y=\"-182.4\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"<text text-anchor=\"start\" x=\"106\" y=\"-167.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>1</title>\n",
"<g id=\"a_node4\"><a xlink:title=\"a*;b;(a;a*;b)*\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M137,-108.6C137,-108.6 125,-108.6 125,-108.6 119,-108.6 113,-102.6 113,-96.6 113,-96.6 113,-82.6 113,-82.6 113,-76.6 119,-70.6 125,-70.6 125,-70.6 137,-70.6 137,-70.6 143,-70.6 149,-76.6 149,-82.6 149,-82.6 149,-96.6 149,-96.6 149,-102.6 143,-108.6 137,-108.6\"/>\n",
"<text text-anchor=\"start\" x=\"126.5\" y=\"-93.4\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"<text text-anchor=\"start\" x=\"123\" y=\"-78.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M132,-172.62C146.74,-167.49 166.62,-157.89 176,-141.6 184.25,-127.27 170.02,-113.36 155.43,-103.7\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"149.21,-99.83 156.82,-100.86 152.19,-101.68 155.16,-103.53 155.16,-103.53 155.16,-103.53 152.19,-101.68 153.49,-106.2 149.21,-99.83 149.21,-99.83\"/>\n",
"<text text-anchor=\"start\" x=\"179\" y=\"-130.4\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- T2T0 -->\n",
"<!-- 0&#45;&gt;T2T0 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>0&#45;&gt;T2T0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M132.17,-171.1C148.21,-164.89 171.8,-154.56 190,-141.6 209.18,-127.94 227.41,-106.49 235.55,-96.32\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"239.93,-90.69 238.12,-98.15 237.78,-93.46 235.63,-96.22 235.63,-96.22 235.63,-96.22 237.78,-93.46 233.14,-94.28 239.93,-90.69 239.93,-90.69\"/>\n",
"<text text-anchor=\"start\" x=\"207\" y=\"-130.4\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M118.5,-108.89C115.43,-114.35 112.58,-120.51 111,-126.6 108.87,-134.83 108.75,-144.06 109.44,-152.37\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"110.23,-159.4 106.32,-152.79 109.84,-155.92 109.45,-152.44 109.45,-152.44 109.45,-152.44 109.84,-155.92 112.58,-152.09 110.23,-159.4 110.23,-159.4\"/>\n",
"<text text-anchor=\"start\" x=\"111\" y=\"-130.4\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M149.15,-97.56C158.54,-98.78 167,-96.13 167,-89.6 167,-84.8 162.44,-82.1 156.3,-81.49\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"149.15,-81.64 156.08,-78.34 152.65,-81.56 156.15,-81.49 156.15,-81.49 156.15,-81.49 152.65,-81.56 156.22,-84.64 149.15,-81.64 149.15,-81.64\"/>\n",
"<text text-anchor=\"start\" x=\"167\" y=\"-85.9\" font-family=\"Lato\" font-size=\"14.00\">!b &amp; p</text>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"114\" cy=\"-17.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;&#45;1 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>1&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M121.27,-70.39C118.75,-64.83 116.37,-58.6 115,-52.6 113.04,-43.99 113.04,-33.82 113.37,-26.9\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"115.83,-26.81 113.91,-19.65 110.95,-26.45 115.83,-26.81\"/>\n",
"<text text-anchor=\"start\" x=\"115\" y=\"-41.4\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- T2T1 -->\n",
"<!-- 1&#45;&gt;T2T1 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>1&#45;&gt;T2T1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M149.32,-76.76C174.04,-60.78 216.81,-33.14 232.77,-22.83\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"238.83,-18.91 234.66,-25.35 235.89,-20.81 232.95,-22.71 232.95,-22.71 232.95,-22.71 235.89,-20.81 231.24,-20.06 238.83,-18.91 238.83,-18.91\"/>\n",
"<text text-anchor=\"start\" x=\"208\" y=\"-41.4\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;0 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M113.77,-19.82C113.14,-22.64 111.34,-30.79 110,-37.6 107.12,-52.23 105.34,-55.75 104,-70.6 101.17,-102.04 101.61,-110.34 106,-141.6 106.5,-145.15 107.16,-148.88 107.9,-152.53\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"109.37,-159.39 104.82,-153.2 108.63,-155.97 107.9,-152.54 107.9,-152.54 107.9,-152.54 108.63,-155.97 110.98,-151.88 109.37,-159.39 109.37,-159.39\"/>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M115.84,-18.71C124.11,-18.41 158.06,-18.42 172,-37.6 181.24,-50.3 168.54,-64.16 154.91,-74.22\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"149.07,-78.28 153.01,-71.7 151.94,-76.28 154.81,-74.28 154.81,-74.28 154.81,-74.28 151.94,-76.28 156.61,-76.87 149.07,-78.28 149.07,-78.28\"/>\n",
"</g>\n",
"<!-- &#45;4&#45;&gt;0 -->\n",
"<g id=\"edge11\" class=\"edge\">\n",
"<title>&#45;4&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M63.89,-240.03C67.56,-235.6 82.01,-218.18 94.45,-203.17\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"98.92,-197.78 96.88,-205.18 96.69,-200.48 94.45,-203.17 94.45,-203.17 94.45,-203.17 96.69,-200.48 92.03,-201.16 98.92,-197.78 98.92,-197.78\"/>\n",
"</g>\n",
"<!-- 4 -->\n",
"<g id=\"node7\" class=\"node\">\n",
"<title>4</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M49,-196.6C49,-196.6 37,-196.6 37,-196.6 31,-196.6 25,-190.6 25,-184.6 25,-184.6 25,-172.6 25,-172.6 25,-166.6 31,-160.6 37,-160.6 37,-160.6 49,-160.6 49,-160.6 55,-160.6 61,-166.6 61,-172.6 61,-172.6 61,-184.6 61,-184.6 61,-190.6 55,-196.6 49,-196.6\"/>\n",
"<text text-anchor=\"middle\" x=\"43\" y=\"-174.9\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
"</g>\n",
"<!-- &#45;4&#45;&gt;4 -->\n",
"<g id=\"edge12\" class=\"edge\">\n",
"<title>&#45;4&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M62.58,-240.18C61.11,-236.98 56.18,-226 53,-216.6 51.61,-212.48 50.28,-208.05 49.06,-203.74\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"47.14,-196.68 52.02,-202.61 48.06,-200.06 48.98,-203.43 48.98,-203.43 48.98,-203.43 48.06,-200.06 45.94,-204.26 47.14,-196.68 47.14,-196.68\"/>\n",
"</g>\n",
"<!-- 4&#45;&gt;3 -->\n",
"<g id=\"edge13\" class=\"edge\">\n",
"<title>4&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M42.62,-197.02C42.09,-221.31 41.13,-265.48 40.53,-293.08\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"40.37,-300.4 37.38,-293.33 40.45,-296.9 40.53,-293.4 40.53,-293.4 40.53,-293.4 40.45,-296.9 43.68,-293.47 40.37,-300.4 40.37,-300.4\"/>\n",
"<text text-anchor=\"middle\" x=\"46.5\" y=\"-238.4\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Pages: 1 -->\n",
"<svg width=\"193pt\" height=\"280pt\"\n",
" viewBox=\"0.00 0.00 193.00 279.60\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1.0 1.0) rotate(0) translate(4 275.6)\">\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-275.6 189,-275.6 189,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"71\" y=\"-257.4\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"94\" y=\"-257.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"110\" y=\"-257.4\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"61\" y=\"-243.4\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<g id=\"clust2\" class=\"cluster\">\n",
"<title>cluster_1</title>\n",
"<polygon fill=\"none\" stroke=\"red\" points=\"8,-8 8,-205.6 140,-205.6 140,-8 8,-8\"/>\n",
"</g>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<g id=\"a_node2\"><a xlink:title=\"(a;a*;b)*\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M83,-197.6C83,-197.6 71,-197.6 71,-197.6 65,-197.6 59,-191.6 59,-185.6 59,-185.6 59,-171.6 59,-171.6 59,-165.6 65,-159.6 71,-159.6 71,-159.6 83,-159.6 83,-159.6 89,-159.6 95,-165.6 95,-171.6 95,-171.6 95,-185.6 95,-185.6 95,-191.6 89,-197.6 83,-197.6\"/>\n",
"<text text-anchor=\"start\" x=\"72.5\" y=\"-182.4\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"<text text-anchor=\"start\" x=\"69\" y=\"-167.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M77,-234.44C77,-232.8 77,-218.7 77,-205.21\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"77,-197.86 80.15,-204.86 77,-201.36 77,-204.86 77,-204.86 77,-204.86 77,-201.36 73.85,-204.86 77,-197.86 77,-197.86\"/>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>1</title>\n",
"<g id=\"a_node3\"><a xlink:title=\"a*;b;(a;a*;b)*\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M64,-108.6C64,-108.6 52,-108.6 52,-108.6 46,-108.6 40,-102.6 40,-96.6 40,-96.6 40,-82.6 40,-82.6 40,-76.6 46,-70.6 52,-70.6 52,-70.6 64,-70.6 64,-70.6 70,-70.6 76,-76.6 76,-82.6 76,-82.6 76,-96.6 76,-96.6 76,-102.6 70,-108.6 64,-108.6\"/>\n",
"<text text-anchor=\"start\" x=\"53.5\" y=\"-93.4\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"<text text-anchor=\"start\" x=\"50\" y=\"-78.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M95.23,-159.29C102.59,-149.62 108.25,-137.53 103,-126.6 98.58,-117.4 90.54,-109.82 82.46,-104.02\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"76.34,-99.94 83.91,-101.2 79.25,-101.88 82.16,-103.83 82.16,-103.83 82.16,-103.83 79.25,-101.88 80.42,-106.45 76.34,-99.94 76.34,-99.94\"/>\n",
"<text text-anchor=\"start\" x=\"106\" y=\"-130.4\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- T2T0 -->\n",
"<!-- 0&#45;&gt;T2T0 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>0&#45;&gt;T2T0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M95.14,-161.71C102.07,-155.52 109.98,-148.32 117,-141.6 134,-125.31 153.29,-105.13 162.12,-95.79\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"166.92,-90.68 164.42,-97.94 164.52,-93.23 162.13,-95.78 162.13,-95.78 162.13,-95.78 164.52,-93.23 159.83,-93.62 166.92,-90.68 166.92,-90.68\"/>\n",
"<text text-anchor=\"start\" x=\"132\" y=\"-130.4\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M43.76,-108.68C37.81,-118.49 33.27,-130.8 38,-141.6 41.28,-149.1 46.98,-155.72 53.02,-161.18\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"58.61,-165.86 51.22,-163.78 55.93,-163.61 53.24,-161.37 53.24,-161.37 53.24,-161.37 55.93,-163.61 55.27,-158.95 58.61,-165.86 58.61,-165.86\"/>\n",
"<text text-anchor=\"start\" x=\"38\" y=\"-130.4\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M76.15,-97.56C85.54,-98.78 94,-96.13 94,-89.6 94,-84.8 89.44,-82.1 83.3,-81.49\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"76.15,-81.64 83.08,-78.34 79.65,-81.56 83.15,-81.49 83.15,-81.49 83.15,-81.49 79.65,-81.56 83.22,-84.64 76.15,-81.64 76.15,-81.64\"/>\n",
"<text text-anchor=\"start\" x=\"94\" y=\"-85.9\" font-family=\"Lato\" font-size=\"14.00\">!b &amp; p</text>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"41\" cy=\"-17.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;&#45;1 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>1&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M48.27,-70.39C45.75,-64.83 43.37,-58.6 42,-52.6 40.04,-43.99 40.04,-33.82 40.37,-26.9\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"42.83,-26.81 40.91,-19.65 37.95,-26.45 42.83,-26.81\"/>\n",
"<text text-anchor=\"start\" x=\"42\" y=\"-41.4\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- T2T1 -->\n",
"<!-- 1&#45;&gt;T2T1 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>1&#45;&gt;T2T1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M76.32,-76.76C101.04,-60.78 143.81,-33.14 159.77,-22.83\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"165.83,-18.91 161.66,-25.35 162.89,-20.81 159.95,-22.71 159.95,-22.71 159.95,-22.71 162.89,-20.81 158.24,-20.06 165.83,-18.91 165.83,-18.91\"/>\n",
"<text text-anchor=\"start\" x=\"135\" y=\"-41.4\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;0 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M40.64,-19.64C37.11,-27.96 9.65,-95.95 33,-141.6 37.51,-150.42 45.25,-157.86 53,-163.65\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"58.87,-167.74 51.32,-166.32 56,-165.74 53.13,-163.74 53.13,-163.74 53.13,-163.74 56,-165.74 54.93,-161.15 58.87,-167.74 58.87,-167.74\"/>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M42.84,-18.71C51.11,-18.41 85.06,-18.42 99,-37.6 108.24,-50.3 95.54,-64.16 81.91,-74.22\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"76.07,-78.28 80.01,-71.7 78.94,-76.28 81.81,-74.28 81.81,-74.28 81.81,-74.28 78.94,-76.28 83.61,-76.87 76.07,-78.28 76.07,-78.28\"/>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Title: VWAA for GFa Pages: 1 -->\n",
"<svg width=\"110pt\" height=\"300pt\"\n",
" viewBox=\"0.00 0.00 110.00 299.60\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1.0 1.0) rotate(0) translate(4 295.6)\">\n",
"<title>VWAA for GFa</title>\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-295.6 106,-295.6 106,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"29.5\" y=\"-277.4\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"52.5\" y=\"-277.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"68.5\" y=\"-277.4\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"19.5\" y=\"-263.4\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<g id=\"clust2\" class=\"cluster\">\n",
"<title>cluster_1</title>\n",
"<polygon fill=\"none\" stroke=\"red\" points=\"15,-44 15,-98 94,-98 94,-44 15,-44\"/>\n",
"</g>\n",
"<g id=\"clust3\" class=\"cluster\">\n",
"<title>cluster_2</title>\n",
"<polygon fill=\"none\" stroke=\"green\" points=\"8,-119 8,-225.6 60,-225.6 60,-119 8,-119\"/>\n",
"</g>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<g id=\"a_node2\"><a xlink:title=\"GF(a)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M40,-217.6C40,-217.6 28,-217.6 28,-217.6 22,-217.6 16,-211.6 16,-205.6 16,-205.6 16,-193.6 16,-193.6 16,-187.6 22,-181.6 28,-181.6 28,-181.6 40,-181.6 40,-181.6 46,-181.6 52,-187.6 52,-193.6 52,-193.6 52,-205.6 52,-205.6 52,-211.6 46,-217.6 40,-217.6\"/>\n",
"<text text-anchor=\"middle\" x=\"34\" y=\"-195.9\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M34,-254.45C34,-252.81 34,-238.45 34,-224.97\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"34,-217.66 37.15,-224.66 34,-221.16 34,-224.66 34,-224.66 34,-224.66 34,-221.16 30.85,-224.66 34,-217.66 34,-217.66\"/>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"41\" cy=\"-128.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 0&#45;&gt;&#45;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M33.13,-181.36C32.94,-171.67 33.21,-159.39 35,-148.6 35.62,-144.87 36.82,-140.85 37.99,-137.5\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"40.34,-138.21 40.57,-130.79 35.77,-136.45 40.34,-138.21\"/>\n",
"<text text-anchor=\"middle\" x=\"39.5\" y=\"-152.4\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>1</title>\n",
"<g id=\"a_node3\"><a xlink:title=\"F(a)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M47,-90C47,-90 35,-90 35,-90 29,-90 23,-84 23,-78 23,-78 23,-64 23,-64 23,-58 29,-52 35,-52 35,-52 47,-52 47,-52 53,-52 59,-58 59,-64 59,-64 59,-78 59,-78 59,-84 53,-90 47,-90\"/>\n",
"<text text-anchor=\"start\" x=\"36.5\" y=\"-74.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"<text text-anchor=\"start\" x=\"33\" y=\"-59.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M59.15,-77.51C68.54,-78.51 77,-76.34 77,-71 77,-67.08 72.44,-64.86 66.3,-64.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"59.15,-64.49 66.1,-61.21 62.65,-64.43 66.15,-64.36 66.15,-64.36 66.15,-64.36 62.65,-64.43 66.21,-67.51 59.15,-64.49 59.15,-64.49\"/>\n",
"<text text-anchor=\"middle\" x=\"81.5\" y=\"-67.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- T2T1 -->\n",
"<!-- 1&#45;&gt;T2T1 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>1&#45;&gt;T2T1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M41,-51.87C41,-37.64 41,-18.56 41,-8.29\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"41,-1.09 44.15,-8.09 41,-4.59 41,-8.09 41,-8.09 41,-8.09 41,-4.59 37.85,-8.09 41,-1.09 41,-1.09\"/>\n",
"<text text-anchor=\"start\" x=\"41\" y=\"-22.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;0 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M41.22,-130.81C41.82,-133.62 43.46,-141.75 44,-148.6 44.53,-155.25 44.92,-157 44,-163.6 43.5,-167.18 42.72,-170.92 41.81,-174.55\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"39.96,-181.36 38.76,-173.78 40.88,-177.98 41.8,-174.61 41.8,-174.61 41.8,-174.61 40.88,-177.98 44.84,-175.44 39.96,-181.36 39.96,-181.36\"/>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M41,-126.83C41,-123.2 41,-109.97 41,-97.42\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"41,-90.18 44.15,-97.18 41,-93.68 41,-97.18 41,-97.18 41,-97.18 41,-93.68 37.85,-97.18 41,-90.18 41,-90.18\"/>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"display_inline(aut1, aut2, aut3, aut4, aut5, show='.bav1us')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Alternation removal"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `remove_alternation()` function works on any alternating automaton that is weak (not necessarily very weak), i.e., in each SCC all transition should belong to the same accepting sets.\n",
"\n",
"The second argument of `remove_alternation()`, set to `True` below, simply asks for states to be labeled to help debugging. As the function builds Transition-based Generalized Büchi acceptance, it can be worthwhile to apply `scc_filter()` in an attempt to reduce the number of acceptance sets.\n",
"\n",
"The next cell shows this two-step process on our first example automaton."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Title: VWAA for FGa &amp;&amp; GFb Pages: 1 -->\n",
"<svg width=\"118pt\" height=\"360pt\"\n",
" viewBox=\"0.00 0.00 117.76 360.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(0.78125 0.78125) rotate(0) translate(4 457.6)\">\n",
"<title>VWAA for FGa &amp;&amp; GFb</title>\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-457.6 147,-457.6 147,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"50\" y=\"-439.4\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"73\" y=\"-439.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"89\" y=\"-439.4\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"40\" y=\"-425.4\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<g id=\"a_node2\"><a xlink:title=\"(FG(a) &amp;&amp; GF(b))\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M63,-379.6C63,-379.6 51,-379.6 51,-379.6 45,-379.6 39,-373.6 39,-367.6 39,-367.6 39,-355.6 39,-355.6 39,-349.6 45,-343.6 51,-343.6 51,-343.6 63,-343.6 63,-343.6 69,-343.6 75,-349.6 75,-355.6 75,-355.6 75,-367.6 75,-367.6 75,-373.6 69,-379.6 63,-379.6\"/>\n",
"<text text-anchor=\"middle\" x=\"57\" y=\"-357.9\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M57,-416.45C57,-414.81 57,-400.45 57,-386.97\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"57,-379.66 60.15,-386.66 57,-383.16 57,-386.66 57,-386.66 57,-386.66 57,-383.16 53.85,-386.66 57,-379.66 57,-379.66\"/>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"57\" cy=\"-290.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 0&#45;&gt;&#45;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M57,-343.59C57,-329.81 57,-310.96 57,-300.21\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"59.45,-300.19 57,-293.19 54.55,-300.19 59.45,-300.19\"/>\n",
"<text text-anchor=\"start\" x=\"57\" y=\"-314.4\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>1</title>\n",
"<g id=\"a_node4\"><a xlink:title=\"GF(b)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M24,-251C24,-251 12,-251 12,-251 6,-251 0,-245 0,-239 0,-239 0,-227 0,-227 0,-221 6,-215 12,-215 12,-215 24,-215 24,-215 30,-215 36,-221 36,-227 36,-227 36,-239 36,-239 36,-245 30,-251 24,-251\"/>\n",
"<text text-anchor=\"start\" x=\"13.5\" y=\"-229.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;1 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M56.32,-288.83C53.62,-284.97 43.31,-270.21 34.06,-256.98\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"29.92,-251.05 36.51,-254.99 31.92,-253.92 33.93,-256.79 33.93,-256.79 33.93,-256.79 31.92,-253.92 31.35,-258.6 29.92,-251.05 29.92,-251.05\"/>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>3</title>\n",
"<g id=\"a_node5\"><a xlink:title=\"FG(a)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M104,-252C104,-252 92,-252 92,-252 86,-252 80,-246 80,-240 80,-240 80,-226 80,-226 80,-220 86,-214 92,-214 92,-214 104,-214 104,-214 110,-214 116,-220 116,-226 116,-226 116,-240 116,-240 116,-246 110,-252 104,-252\"/>\n",
"<text text-anchor=\"start\" x=\"93.5\" y=\"-236.8\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
"<text text-anchor=\"start\" x=\"90\" y=\"-221.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;3 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M57.71,-288.83C60.48,-285.07 70.83,-270.97 80.35,-258.02\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"84.64,-252.18 83.03,-259.69 82.57,-255 80.49,-257.83 80.49,-257.83 80.49,-257.83 82.57,-255 77.96,-255.96 84.64,-252.18 84.64,-252.18\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M36.15,-239.51C45.54,-240.51 54,-238.34 54,-233 54,-229.08 49.44,-226.86 43.3,-226.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"36.15,-226.49 43.1,-223.21 39.65,-226.43 43.15,-226.36 43.15,-226.36 43.15,-226.36 39.65,-226.43 43.21,-229.51 36.15,-226.49 36.15,-226.49\"/>\n",
"<text text-anchor=\"start\" x=\"54\" y=\"-229.3\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
"</g>\n",
"<!-- &#45;4 -->\n",
"<g id=\"node6\" class=\"node\">\n",
"<title>&#45;4</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"19\" cy=\"-145\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 1&#45;&gt;&#45;4 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>1&#45;&gt;&#45;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M10.29,-214.63C6.85,-204.81 3.97,-192.28 6,-181 7.77,-171.18 12.11,-160.51 15.29,-153.56\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"17.71,-154.2 18.56,-146.83 13.3,-152.06 17.71,-154.2\"/>\n",
"<text text-anchor=\"start\" x=\"6\" y=\"-184.8\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;3 -->\n",
"<g id=\"edge12\" class=\"edge\">\n",
"<title>3&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M116.15,-239.51C125.54,-240.51 134,-238.34 134,-233 134,-229.08 129.44,-226.86 123.3,-226.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"116.15,-226.49 123.1,-223.21 119.65,-226.43 123.15,-226.36 123.15,-226.36 123.15,-226.36 119.65,-226.43 123.21,-229.51 116.15,-226.49 116.15,-226.49\"/>\n",
"<text text-anchor=\"start\" x=\"134\" y=\"-229.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 4 -->\n",
"<g id=\"node9\" class=\"node\">\n",
"<title>4</title>\n",
"<g id=\"a_node9\"><a xlink:title=\"G(a)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M104,-163C104,-163 92,-163 92,-163 86,-163 80,-157 80,-151 80,-151 80,-139 80,-139 80,-133 86,-127 92,-127 92,-127 104,-127 104,-127 110,-127 116,-133 116,-139 116,-139 116,-151 116,-151 116,-157 110,-163 104,-163\"/>\n",
"<text text-anchor=\"middle\" x=\"98\" y=\"-141.3\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- 3&#45;&gt;4 -->\n",
"<g id=\"edge11\" class=\"edge\">\n",
"<title>3&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M98,-213.76C98,-201.11 98,-184.13 98,-170.33\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"98,-163.04 101.15,-170.04 98,-166.54 98,-170.04 98,-170.04 98,-170.04 98,-166.54 94.85,-170.04 98,-163.04 98,-163.04\"/>\n",
"<text text-anchor=\"start\" x=\"98\" y=\"-184.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- &#45;4&#45;&gt;1 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>&#45;4&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M18.99,-147.1C18.91,-153.32 18.55,-184.73 18.28,-207.54\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"18.2,-214.6 15.13,-207.56 18.24,-211.1 18.28,-207.6 18.28,-207.6 18.28,-207.6 18.24,-211.1 21.43,-207.63 18.2,-214.6 18.2,-214.6\"/>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node7\" class=\"node\">\n",
"<title>2</title>\n",
"<g id=\"a_node7\"><a xlink:title=\"F(b)\">\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M25,-90C25,-90 13,-90 13,-90 7,-90 1,-84 1,-78 1,-78 1,-64 1,-64 1,-58 7,-52 13,-52 13,-52 25,-52 25,-52 31,-52 37,-58 37,-64 37,-64 37,-78 37,-78 37,-84 31,-90 25,-90\"/>\n",
"<text text-anchor=\"start\" x=\"14.5\" y=\"-74.8\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
"<text text-anchor=\"start\" x=\"11\" y=\"-59.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- &#45;4&#45;&gt;2 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>&#45;4&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M19,-143.19C19,-138.66 19,-115.99 19,-97.43\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"19,-90.31 22.15,-97.31 19,-93.81 19,-97.31 19,-97.31 19,-97.31 19,-93.81 15.85,-97.31 19,-90.31 19,-90.31\"/>\n",
"</g>\n",
"<!-- 2&#45;&gt;2 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>2&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M37.15,-77.51C46.54,-78.51 55,-76.34 55,-71 55,-67.08 50.44,-64.86 44.3,-64.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"37.15,-64.49 44.1,-61.21 40.65,-64.43 44.15,-64.36 44.15,-64.36 44.15,-64.36 40.65,-64.43 44.21,-67.51 37.15,-64.49 37.15,-64.49\"/>\n",
"<text text-anchor=\"start\" x=\"55\" y=\"-67.3\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
"</g>\n",
"<!-- T5T2 -->\n",
"<!-- 2&#45;&gt;T5T2 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>2&#45;&gt;T5T2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M19,-51.87C19,-37.64 19,-18.56 19,-8.29\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"19,-1.09 22.15,-8.09 19,-4.59 19,-8.09 19,-8.09 19,-8.09 19,-4.59 15.85,-8.09 19,-1.09 19,-1.09\"/>\n",
"<text text-anchor=\"start\" x=\"19\" y=\"-22.8\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
"</g>\n",
"<!-- 4&#45;&gt;4 -->\n",
"<g id=\"edge13\" class=\"edge\">\n",
"<title>4&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M116.15,-151.51C125.54,-152.51 134,-150.34 134,-145 134,-141.08 129.44,-138.86 123.3,-138.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"116.15,-138.49 123.1,-135.21 119.65,-138.43 123.15,-138.36 123.15,-138.36 123.15,-138.36 119.65,-138.43 123.21,-141.51 116.15,-138.49 116.15,-138.49\"/>\n",
"<text text-anchor=\"start\" x=\"134\" y=\"-141.3\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Pages: 1 -->\n",
"<svg width=\"144pt\" height=\"360pt\"\n",
" viewBox=\"0.00 0.00 144.41 360.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(0.684931506849315 0.684931506849315) rotate(0) translate(4 522)\">\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-522 207,-522 207,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"56\" y=\"-503.8\" font-family=\"Lato\" font-size=\"14.00\">Inf(</text>\n",
"<text text-anchor=\"start\" x=\"77\" y=\"-503.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"93\" y=\"-503.8\" font-family=\"Lato\" font-size=\"14.00\">)&amp;Inf(</text>\n",
"<text text-anchor=\"start\" x=\"127\" y=\"-503.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"<text text-anchor=\"start\" x=\"143\" y=\"-503.8\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"59\" y=\"-489.8\" font-family=\"Lato\" font-size=\"14.00\">[gen. Büchi 2]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M106,-444C106,-444 94,-444 94,-444 88,-444 82,-438 82,-432 82,-432 82,-420 82,-420 82,-414 88,-408 94,-408 94,-408 106,-408 106,-408 112,-408 118,-414 118,-420 118,-420 118,-432 118,-432 118,-438 112,-444 106,-444\"/>\n",
"<text text-anchor=\"middle\" x=\"100\" y=\"-422.3\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M100,-480.85C100,-479.21 100,-464.85 100,-451.37\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"100,-444.06 103.15,-451.06 100,-447.56 100,-451.06 100,-451.06 100,-451.06 100,-447.56 96.85,-451.06 100,-444.06 100,-444.06\"/>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>1</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M106,-342C106,-342 94,-342 94,-342 88,-342 82,-336 82,-330 82,-330 82,-318 82,-318 82,-312 88,-306 94,-306 94,-306 106,-306 106,-306 112,-306 118,-312 118,-318 118,-318 118,-330 118,-330 118,-336 112,-342 106,-342\"/>\n",
"<text text-anchor=\"start\" x=\"90\" y=\"-320.3\" font-family=\"Lato\" font-size=\"14.00\">1,3</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M100,-407.58C100,-391.52 100,-367.52 100,-349.52\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"100,-342.22 103.15,-349.22 100,-345.72 100,-349.22 100,-349.22 100,-349.22 100,-345.72 96.85,-349.22 100,-342.22 100,-342.22\"/>\n",
"<text text-anchor=\"start\" x=\"103.5\" y=\"-378.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"<text text-anchor=\"start\" x=\"100\" y=\"-363.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M118.15,-333.05C127.54,-334.44 136,-331.42 136,-324 136,-318.55 131.44,-315.48 125.3,-314.78\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"118.15,-314.95 125.07,-311.63 121.65,-314.87 125.15,-314.78 125.15,-314.78 125.15,-314.78 121.65,-314.87 125.23,-317.93 118.15,-314.95 118.15,-314.95\"/>\n",
"<text text-anchor=\"start\" x=\"140\" y=\"-327.8\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
"<text text-anchor=\"start\" x=\"136\" y=\"-312.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>2</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M24,-138C24,-138 12,-138 12,-138 6,-138 0,-132 0,-126 0,-126 0,-114 0,-114 0,-108 6,-102 12,-102 12,-102 24,-102 24,-102 30,-102 36,-108 36,-114 36,-114 36,-126 36,-126 36,-132 30,-138 24,-138\"/>\n",
"<text text-anchor=\"start\" x=\"8\" y=\"-116.3\" font-family=\"Lato\" font-size=\"14.00\">1,4</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>1&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M82.56,-305.94C67.66,-290.25 46.93,-265.6 36,-240 22.84,-209.18 19.11,-170.26 18.15,-145.49\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"17.94,-138.29 21.29,-145.19 18.04,-141.78 18.14,-145.28 18.14,-145.28 18.14,-145.28 18.04,-141.78 15,-145.38 17.94,-138.29 17.94,-138.29\"/>\n",
"<text text-anchor=\"start\" x=\"36\" y=\"-225.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b</text>\n",
"<text text-anchor=\"start\" x=\"36\" y=\"-211.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"52\" y=\"-211.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>3</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M112.5,-240C112.5,-240 89.5,-240 89.5,-240 83.5,-240 77.5,-234 77.5,-228 77.5,-228 77.5,-216 77.5,-216 77.5,-210 83.5,-204 89.5,-204 89.5,-204 112.5,-204 112.5,-204 118.5,-204 124.5,-210 124.5,-216 124.5,-216 124.5,-228 124.5,-228 124.5,-234 118.5,-240 112.5,-240\"/>\n",
"<text text-anchor=\"start\" x=\"85.5\" y=\"-218.3\" font-family=\"Lato\" font-size=\"14.00\">1,2,3</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;3 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>1&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M90.32,-305.71C87.74,-300.22 85.31,-294.01 84,-288 81.16,-274.97 81.01,-270.99 84,-258 84.87,-254.21 86.21,-250.36 87.76,-246.67\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"90.72,-240.23 90.66,-247.91 89.26,-243.41 87.79,-246.59 87.79,-246.59 87.79,-246.59 89.26,-243.41 84.93,-245.27 90.72,-240.23 90.72,-240.23\"/>\n",
"<text text-anchor=\"start\" x=\"84\" y=\"-269.3\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
"</g>\n",
"<!-- 4 -->\n",
"<g id=\"node6\" class=\"node\">\n",
"<title>4</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M109.5,-36C109.5,-36 86.5,-36 86.5,-36 80.5,-36 74.5,-30 74.5,-24 74.5,-24 74.5,-12 74.5,-12 74.5,-6 80.5,0 86.5,0 86.5,0 109.5,0 109.5,0 115.5,0 121.5,-6 121.5,-12 121.5,-12 121.5,-24 121.5,-24 121.5,-30 115.5,-36 109.5,-36\"/>\n",
"<text text-anchor=\"start\" x=\"82.5\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">1,2,4</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;4 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>1&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M118.08,-306.6C133.64,-291.17 154.96,-266.52 164,-240 173.46,-212.24 166.04,-137.37 154,-102 146.37,-79.58 130.99,-57.51 118.28,-41.77\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"113.74,-36.27 120.62,-39.66 115.97,-38.97 118.2,-41.67 118.2,-41.67 118.2,-41.67 115.97,-38.97 115.77,-43.67 113.74,-36.27 113.74,-36.27\"/>\n",
"<text text-anchor=\"start\" x=\"167\" y=\"-174.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; !b</text>\n",
"<text text-anchor=\"start\" x=\"177\" y=\"-159.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;2 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>2&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M36.15,-129.05C45.54,-130.44 54,-127.42 54,-120 54,-114.55 49.44,-111.48 43.3,-110.78\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"36.15,-110.95 43.07,-107.63 39.65,-110.87 43.15,-110.78 43.15,-110.78 43.15,-110.78 39.65,-110.87 43.23,-113.93 36.15,-110.95 36.15,-110.95\"/>\n",
"<text text-anchor=\"start\" x=\"54\" y=\"-123.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b</text>\n",
"<text text-anchor=\"start\" x=\"54\" y=\"-109.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"70\" y=\"-109.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;4 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>2&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M12.78,-101.79C9.62,-87.77 7.76,-68.05 17,-54 28.14,-37.05 49.43,-28.27 67.39,-23.74\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"74.33,-22.16 68.21,-26.79 70.92,-22.94 67.51,-23.72 67.51,-23.72 67.51,-23.72 70.92,-22.94 66.8,-20.64 74.33,-22.16 74.33,-22.16\"/>\n",
"<text text-anchor=\"start\" x=\"17\" y=\"-72.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; !b</text>\n",
"<text text-anchor=\"start\" x=\"27\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;1 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>3&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M100.83,-240.22C100.67,-256.21 100.43,-280.21 100.25,-298.25\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"100.17,-305.58 97.09,-298.55 100.21,-302.08 100.24,-298.58 100.24,-298.58 100.24,-298.58 100.21,-302.08 103.39,-298.61 100.17,-305.58 100.17,-305.58\"/>\n",
"<text text-anchor=\"start\" x=\"105\" y=\"-276.8\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
"<text text-anchor=\"start\" x=\"101\" y=\"-261.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;2 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>3&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M86.54,-203.58C72.74,-186.95 51.86,-161.79 36.77,-143.62\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"32.29,-138.22 39.19,-141.59 34.53,-140.91 36.76,-143.61 36.76,-143.61 36.76,-143.61 34.53,-140.91 34.34,-145.62 32.29,-138.22 32.29,-138.22\"/>\n",
"<text text-anchor=\"start\" x=\"72\" y=\"-174.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b</text>\n",
"<text text-anchor=\"start\" x=\"72\" y=\"-160.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"88\" y=\"-160.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;3 -->\n",
"<g id=\"edge11\" class=\"edge\">\n",
"<title>3&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M124.88,-231.32C134.46,-231.84 142.5,-228.74 142.5,-222 142.5,-217.05 138.16,-214.06 132.07,-213.03\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"124.88,-212.68 132.03,-209.88 128.38,-212.85 131.87,-213.02 131.87,-213.02 131.87,-213.02 128.38,-212.85 131.72,-216.17 124.88,-212.68 124.88,-212.68\"/>\n",
"<text text-anchor=\"start\" x=\"142.5\" y=\"-218.3\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;4 -->\n",
"<g id=\"edge12\" class=\"edge\">\n",
"<title>3&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M105.17,-203.66C106.33,-198.06 107.43,-191.8 108,-186 113.78,-127.62 116.14,-112.1 108,-54 107.5,-50.42 106.72,-46.68 105.81,-43.05\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"103.96,-36.24 108.84,-42.16 104.88,-39.62 105.8,-42.99 105.8,-42.99 105.8,-42.99 104.88,-39.62 102.76,-43.82 103.96,-36.24 103.96,-36.24\"/>\n",
"<text text-anchor=\"start\" x=\"114\" y=\"-123.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; !b</text>\n",
"<text text-anchor=\"start\" x=\"124\" y=\"-108.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"<!-- 4&#45;&gt;2 -->\n",
"<g id=\"edge13\" class=\"edge\">\n",
"<title>4&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M87.33,-36.17C78.67,-49.64 65.84,-68.62 53,-84 49.36,-88.36 45.27,-92.8 41.2,-96.99\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"36.09,-102.14 38.78,-94.95 38.56,-99.66 41.02,-97.17 41.02,-97.17 41.02,-97.17 38.56,-99.66 43.26,-99.39 36.09,-102.14 36.09,-102.14\"/>\n",
"<text text-anchor=\"start\" x=\"76\" y=\"-72.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b</text>\n",
"<text text-anchor=\"start\" x=\"76\" y=\"-58.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"92\" y=\"-58.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"<!-- 4&#45;&gt;4 -->\n",
"<g id=\"edge14\" class=\"edge\">\n",
"<title>4&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M121.88,-27.32C131.46,-27.84 139.5,-24.74 139.5,-18 139.5,-13.05 135.16,-10.06 129.07,-9.03\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"121.88,-8.68 129.03,-5.88 125.38,-8.85 128.87,-9.02 128.87,-9.02 128.87,-9.02 125.38,-8.85 128.72,-12.17 121.88,-8.68 121.88,-8.68\"/>\n",
"<text text-anchor=\"start\" x=\"139.5\" y=\"-21.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; !b</text>\n",
"<text text-anchor=\"start\" x=\"149.5\" y=\"-6.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Pages: 1 -->\n",
"<svg width=\"165pt\" height=\"360pt\"\n",
" viewBox=\"0.00 0.00 164.66 360.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(0.7462686567164178 0.7462686567164178) rotate(0) translate(4 477)\">\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-477 216,-477 216,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"85.5\" y=\"-458.8\" font-family=\"Lato\" font-size=\"14.00\">Inf(</text>\n",
"<text text-anchor=\"start\" x=\"106.5\" y=\"-458.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"122.5\" y=\"-458.8\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"84.5\" y=\"-444.8\" font-family=\"Lato\" font-size=\"14.00\">[Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M106,-399C106,-399 94,-399 94,-399 88,-399 82,-393 82,-387 82,-387 82,-375 82,-375 82,-369 88,-363 94,-363 94,-363 106,-363 106,-363 112,-363 118,-369 118,-375 118,-375 118,-387 118,-387 118,-393 112,-399 106,-399\"/>\n",
"<text text-anchor=\"middle\" x=\"100\" y=\"-377.3\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M100,-435.85C100,-434.21 100,-419.85 100,-406.37\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"100,-399.06 103.15,-406.06 100,-402.56 100,-406.06 100,-406.06 100,-406.06 100,-402.56 96.85,-406.06 100,-399.06 100,-399.06\"/>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>1</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M106,-312C106,-312 94,-312 94,-312 88,-312 82,-306 82,-300 82,-300 82,-288 82,-288 82,-282 88,-276 94,-276 94,-276 106,-276 106,-276 112,-276 118,-282 118,-288 118,-288 118,-300 118,-300 118,-306 112,-312 106,-312\"/>\n",
"<text text-anchor=\"start\" x=\"90\" y=\"-290.3\" font-family=\"Lato\" font-size=\"14.00\">1,3</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M100,-362.8C100,-350.36 100,-333.36 100,-319.5\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"100,-312.18 103.15,-319.18 100,-315.68 100,-319.18 100,-319.18 100,-319.18 100,-315.68 96.85,-319.18 100,-312.18 100,-312.18\"/>\n",
"<text text-anchor=\"middle\" x=\"104.5\" y=\"-333.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M118.15,-301.6C127.54,-302.77 136,-300.23 136,-294 136,-289.42 131.44,-286.84 125.3,-286.25\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"118.15,-286.4 125.09,-283.11 121.65,-286.33 125.15,-286.26 125.15,-286.26 125.15,-286.26 121.65,-286.33 125.22,-289.41 118.15,-286.4 118.15,-286.4\"/>\n",
"<text text-anchor=\"start\" x=\"136\" y=\"-290.3\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>2</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M24,-138C24,-138 12,-138 12,-138 6,-138 0,-132 0,-126 0,-126 0,-114 0,-114 0,-108 6,-102 12,-102 12,-102 24,-102 24,-102 30,-102 36,-108 36,-114 36,-114 36,-126 36,-126 36,-132 30,-138 24,-138\"/>\n",
"<text text-anchor=\"start\" x=\"8\" y=\"-116.3\" font-family=\"Lato\" font-size=\"14.00\">1,4</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>1&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M81.76,-278.87C66.97,-266.36 46.87,-246.76 36,-225 23.4,-199.78 19.45,-167.31 18.29,-145.41\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"17.99,-138.14 21.43,-145 18.14,-141.63 18.28,-145.13 18.28,-145.13 18.28,-145.13 18.14,-141.63 15.13,-145.26 17.99,-138.14 17.99,-138.14\"/>\n",
"<text text-anchor=\"start\" x=\"36\" y=\"-203.3\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>3</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M112.5,-225C112.5,-225 89.5,-225 89.5,-225 83.5,-225 77.5,-219 77.5,-213 77.5,-213 77.5,-201 77.5,-201 77.5,-195 83.5,-189 89.5,-189 89.5,-189 112.5,-189 112.5,-189 118.5,-189 124.5,-195 124.5,-201 124.5,-201 124.5,-213 124.5,-213 124.5,-219 118.5,-225 112.5,-225\"/>\n",
"<text text-anchor=\"start\" x=\"85.5\" y=\"-203.3\" font-family=\"Lato\" font-size=\"14.00\">1,2,3</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;3 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>1&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M89.6,-275.61C85.14,-266.09 81.47,-254.01 84,-243 84.87,-239.21 86.21,-235.36 87.76,-231.67\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"90.72,-225.23 90.66,-232.91 89.26,-228.41 87.79,-231.59 87.79,-231.59 87.79,-231.59 89.26,-228.41 84.93,-230.27 90.72,-225.23 90.72,-225.23\"/>\n",
"<text text-anchor=\"start\" x=\"84\" y=\"-246.8\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
"</g>\n",
"<!-- 4 -->\n",
"<g id=\"node6\" class=\"node\">\n",
"<title>4</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M109.5,-36C109.5,-36 86.5,-36 86.5,-36 80.5,-36 74.5,-30 74.5,-24 74.5,-24 74.5,-12 74.5,-12 74.5,-6 80.5,0 86.5,0 86.5,0 109.5,0 109.5,0 115.5,0 121.5,-6 121.5,-12 121.5,-12 121.5,-24 121.5,-24 121.5,-30 115.5,-36 109.5,-36\"/>\n",
"<text text-anchor=\"start\" x=\"82.5\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">1,2,4</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;4 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>1&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M118,-280.27C133.51,-268.1 154.8,-248.21 164,-225 192.77,-152.45 166.49,-119.47 124,-54 121.4,-49.99 118.5,-45.83 115.6,-41.83\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"111.4,-36.14 118.09,-39.9 113.48,-38.96 115.56,-41.77 115.56,-41.77 115.56,-41.77 113.48,-38.96 113.02,-43.64 111.4,-36.14 111.4,-36.14\"/>\n",
"<text text-anchor=\"start\" x=\"176\" y=\"-159.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; !b</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;2 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>2&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M36.15,-127.6C45.54,-128.77 54,-126.23 54,-120 54,-115.42 49.44,-112.84 43.3,-112.25\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"36.15,-112.4 43.09,-109.11 39.65,-112.33 43.15,-112.26 43.15,-112.26 43.15,-112.26 39.65,-112.33 43.22,-115.41 36.15,-112.4 36.15,-112.4\"/>\n",
"<text text-anchor=\"start\" x=\"54\" y=\"-123.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b</text>\n",
"<text text-anchor=\"start\" x=\"62\" y=\"-108.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;4 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>2&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M12.78,-101.79C9.62,-87.77 7.76,-68.05 17,-54 28.14,-37.05 49.43,-28.27 67.39,-23.74\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"74.33,-22.16 68.21,-26.79 70.92,-22.94 67.51,-23.72 67.51,-23.72 67.51,-23.72 70.92,-22.94 66.8,-20.64 74.33,-22.16 74.33,-22.16\"/>\n",
"<text text-anchor=\"start\" x=\"17\" y=\"-65.3\" font-family=\"Lato\" font-size=\"14.00\">a &amp; !b</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;1 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>3&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M100.8,-225.18C100.65,-237.61 100.45,-254.6 100.29,-268.47\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"100.2,-275.8 97.14,-268.76 100.24,-272.3 100.28,-268.8 100.28,-268.8 100.28,-268.8 100.24,-272.3 103.43,-268.84 100.2,-275.8 100.2,-275.8\"/>\n",
"<text text-anchor=\"start\" x=\"101\" y=\"-246.8\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;2 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>3&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M84.2,-188.8C71.38,-175.66 53.6,-157.46 39.7,-143.22\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"34.77,-138.18 41.92,-140.98 37.22,-140.68 39.66,-143.18 39.66,-143.18 39.66,-143.18 37.22,-140.68 37.41,-145.38 34.77,-138.18 34.77,-138.18\"/>\n",
"<text text-anchor=\"start\" x=\"65\" y=\"-159.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;3 -->\n",
"<g id=\"edge11\" class=\"edge\">\n",
"<title>3&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M124.88,-214.83C134.46,-215.27 142.5,-212.66 142.5,-207 142.5,-202.84 138.16,-200.33 132.07,-199.47\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"124.88,-199.17 132,-196.31 128.38,-199.32 131.88,-199.46 131.88,-199.46 131.88,-199.46 128.38,-199.32 131.75,-202.61 124.88,-199.17 124.88,-199.17\"/>\n",
"<text text-anchor=\"start\" x=\"142.5\" y=\"-203.3\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;4 -->\n",
"<g id=\"edge12\" class=\"edge\">\n",
"<title>3&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M103.88,-188.58C108.1,-160.23 114.78,-102.4 108,-54 107.5,-50.42 106.72,-46.68 105.81,-43.05\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"103.96,-36.24 108.84,-42.16 104.88,-39.62 105.8,-42.99 105.8,-42.99 105.8,-42.99 104.88,-39.62 102.76,-43.82 103.96,-36.24 103.96,-36.24\"/>\n",
"<text text-anchor=\"start\" x=\"111\" y=\"-116.3\" font-family=\"Lato\" font-size=\"14.00\">a &amp; !b</text>\n",
"</g>\n",
"<!-- 4&#45;&gt;2 -->\n",
"<g id=\"edge13\" class=\"edge\">\n",
"<title>4&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M87.33,-36.17C78.67,-49.64 65.84,-68.62 53,-84 49.36,-88.36 45.27,-92.8 41.2,-96.99\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"36.09,-102.14 38.78,-94.95 38.56,-99.66 41.02,-97.17 41.02,-97.17 41.02,-97.17 38.56,-99.66 43.26,-99.39 36.09,-102.14 36.09,-102.14\"/>\n",
"<text text-anchor=\"start\" x=\"76\" y=\"-72.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b</text>\n",
"<text text-anchor=\"start\" x=\"84\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- 4&#45;&gt;4 -->\n",
"<g id=\"edge14\" class=\"edge\">\n",
"<title>4&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M121.88,-27.32C131.46,-27.84 139.5,-24.74 139.5,-18 139.5,-13.05 135.16,-10.06 129.07,-9.03\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"121.88,-8.68 129.03,-5.88 125.38,-8.85 128.87,-9.02 128.87,-9.02 128.87,-9.02 125.38,-8.85 128.72,-12.17 121.88,-8.68 121.88,-8.68\"/>\n",
"<text text-anchor=\"start\" x=\"139.5\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">a &amp; !b</text>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"nba1t = spot.remove_alternation(aut1, True)\n",
"nba1 = spot.scc_filter(nba1t, True)\n",
"display_inline(aut1.show('.bav1u'), nba1t, nba1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's apply this process to the other 4 automata (which are not very-weak, unlike `aut1`). The states marked with `~` are part of a break-point construction."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Pages: 1 -->\n",
"<svg width=\"230pt\" height=\"360pt\"\n",
" viewBox=\"0.00 0.00 229.71 360.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(0.9523809523809523 0.9523809523809523) rotate(0) translate(4 375)\">\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-375 237.83,-375 237.83,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"96.42\" y=\"-356.8\" font-family=\"Lato\" font-size=\"14.00\">Inf(</text>\n",
"<text text-anchor=\"start\" x=\"117.42\" y=\"-356.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"133.42\" y=\"-356.8\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"95.42\" y=\"-342.8\" font-family=\"Lato\" font-size=\"14.00\">[Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M131.83,-297C131.83,-297 119.83,-297 119.83,-297 113.83,-297 107.83,-291 107.83,-285 107.83,-285 107.83,-273 107.83,-273 107.83,-267 113.83,-261 119.83,-261 119.83,-261 131.83,-261 131.83,-261 137.83,-261 143.83,-267 143.83,-273 143.83,-273 143.83,-285 143.83,-285 143.83,-291 137.83,-297 131.83,-297\"/>\n",
"<text text-anchor=\"start\" x=\"117.33\" y=\"-275.3\" font-family=\"Lato\" font-size=\"14.00\">~0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M125.83,-333.85C125.83,-332.21 125.83,-317.85 125.83,-304.37\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"125.83,-297.06 128.98,-304.06 125.83,-300.56 125.83,-304.06 125.83,-304.06 125.83,-304.06 125.83,-300.56 122.68,-304.06 125.83,-297.06 125.83,-297.06\"/>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>1</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M61.83,-210C61.83,-210 49.83,-210 49.83,-210 43.83,-210 37.83,-204 37.83,-198 37.83,-198 37.83,-186 37.83,-186 37.83,-180 43.83,-174 49.83,-174 49.83,-174 61.83,-174 61.83,-174 67.83,-174 73.83,-180 73.83,-186 73.83,-186 73.83,-198 73.83,-198 73.83,-204 67.83,-210 61.83,-210\"/>\n",
"<text text-anchor=\"start\" x=\"47.33\" y=\"-188.3\" font-family=\"Lato\" font-size=\"14.00\">~1</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M107.67,-273.61C92.18,-268.85 70.73,-259.58 59.83,-243 54.9,-235.5 53.29,-225.92 53.13,-217.17\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"53.29,-210.07 56.28,-217.14 53.21,-213.57 53.13,-217.07 53.13,-217.07 53.13,-217.07 53.21,-213.57 49.98,-216.99 53.29,-210.07 53.29,-210.07\"/>\n",
"<text text-anchor=\"start\" x=\"59.83\" y=\"-231.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>2</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M98.83,-36C98.83,-36 86.83,-36 86.83,-36 80.83,-36 74.83,-30 74.83,-24 74.83,-24 74.83,-12 74.83,-12 74.83,-6 80.83,0 86.83,0 86.83,0 98.83,0 98.83,0 104.83,0 110.83,-6 110.83,-12 110.83,-12 110.83,-24 110.83,-24 110.83,-30 104.83,-36 98.83,-36\"/>\n",
"<text text-anchor=\"start\" x=\"87.83\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">{}</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>0&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M144.19,-271.58C167.81,-262.21 207.84,-242.29 224.83,-210 232.28,-195.84 226.72,-189.89 224.83,-174 220.13,-134.5 227.23,-119.16 203.83,-87 182.2,-57.27 143.23,-37.86 117.69,-27.66\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"110.87,-25.03 118.54,-24.61 114.14,-26.29 117.4,-27.55 117.4,-27.55 117.4,-27.55 114.14,-26.29 116.27,-30.49 110.87,-25.03 110.87,-25.03\"/>\n",
"<text text-anchor=\"start\" x=\"222.83\" y=\"-144.8\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M66.35,-210.28C72.69,-220.21 81.19,-232.71 89.83,-243 93.7,-247.61 98.1,-252.27 102.46,-256.63\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"107.53,-261.59 100.32,-258.95 105.02,-259.14 102.52,-256.69 102.52,-256.69 102.52,-256.69 105.02,-259.14 104.72,-254.44 107.53,-261.59 107.53,-261.59\"/>\n",
"<text text-anchor=\"start\" x=\"89.83\" y=\"-231.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M73.98,-199.6C83.37,-200.77 91.83,-198.23 91.83,-192 91.83,-187.42 87.27,-184.84 81.13,-184.25\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"73.98,-184.4 80.92,-181.11 77.48,-184.33 80.98,-184.26 80.98,-184.26 80.98,-184.26 77.48,-184.33 81.05,-187.41 73.98,-184.4 73.98,-184.4\"/>\n",
"<text text-anchor=\"start\" x=\"91.83\" y=\"-188.3\" font-family=\"Lato\" font-size=\"14.00\">!b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>1&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M37.75,-184.65C25.19,-179.18 9.41,-169.94 1.83,-156 -1.35,-150.14 0.87,-147.6 1.83,-141 5.42,-116.23 4.51,-108.19 17.83,-87 30.99,-66.06 52.35,-47.6 68.91,-35.21\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"74.77,-30.93 70.98,-37.6 71.94,-32.99 69.12,-35.06 69.12,-35.06 69.12,-35.06 71.94,-32.99 67.26,-32.51 74.77,-30.93 74.77,-30.93\"/>\n",
"<text text-anchor=\"start\" x=\"17.83\" y=\"-101.3\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>3</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M107.33,-123C107.33,-123 78.33,-123 78.33,-123 72.33,-123 66.33,-117 66.33,-111 66.33,-111 66.33,-99 66.33,-99 66.33,-93 72.33,-87 78.33,-87 78.33,-87 107.33,-87 107.33,-87 113.33,-87 119.33,-93 119.33,-99 119.33,-99 119.33,-111 119.33,-111 119.33,-117 113.33,-123 107.33,-123\"/>\n",
"<text text-anchor=\"start\" x=\"74.33\" y=\"-101.3\" font-family=\"Lato\" font-size=\"14.00\">~1,~0</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;3 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>1&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M63.32,-173.8C68.84,-161.13 76.41,-143.73 82.5,-129.74\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"85.35,-123.18 85.45,-130.85 83.96,-126.38 82.56,-129.59 82.56,-129.59 82.56,-129.59 83.96,-126.38 79.67,-128.34 85.35,-123.18 85.35,-123.18\"/>\n",
"<text text-anchor=\"start\" x=\"76.83\" y=\"-144.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;2 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>2&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M110.98,-25.6C120.37,-26.77 128.83,-24.23 128.83,-18 128.83,-13.42 124.27,-10.84 118.13,-10.25\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"110.98,-10.4 117.92,-7.11 114.48,-10.33 117.98,-10.26 117.98,-10.26 117.98,-10.26 114.48,-10.33 118.05,-13.41 110.98,-10.4 110.98,-10.4\"/>\n",
"<text text-anchor=\"start\" x=\"132.33\" y=\"-21.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"<text text-anchor=\"start\" x=\"128.83\" y=\"-6.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;0 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>3&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M119.39,-121.36C126.44,-126.7 133.34,-133.31 137.83,-141 172.36,-200.06 159.84,-214.88 150.83,-243 149.55,-247.01 147.62,-250.95 145.38,-254.66\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"141.41,-260.65 142.65,-253.07 143.34,-257.73 145.28,-254.82 145.28,-254.82 145.28,-254.82 143.34,-257.73 147.9,-256.56 141.41,-260.65 141.41,-260.65\"/>\n",
"<text text-anchor=\"start\" x=\"159.83\" y=\"-188.3\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;1 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>3&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M66.01,-109.19C46.27,-113.1 20.71,-121.77 7.83,-141 -1.92,-155.56 14.96,-169.74 31.33,-179.26\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"37.76,-182.79 30.11,-182.18 34.69,-181.11 31.63,-179.42 31.63,-179.42 31.63,-179.42 34.69,-181.11 33.14,-176.66 37.76,-182.79 37.76,-182.79\"/>\n",
"<text text-anchor=\"start\" x=\"7.83\" y=\"-144.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; !b &amp; p</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;2 -->\n",
"<g id=\"edge11\" class=\"edge\">\n",
"<title>3&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M92.83,-86.8C92.83,-74.36 92.83,-57.36 92.83,-43.5\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"92.83,-36.18 95.98,-43.18 92.83,-39.68 92.83,-43.18 92.83,-43.18 92.83,-43.18 92.83,-39.68 89.68,-43.18 92.83,-36.18 92.83,-36.18\"/>\n",
"<text text-anchor=\"start\" x=\"92.83\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;3 -->\n",
"<g id=\"edge12\" class=\"edge\">\n",
"<title>3&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M119.77,-112.87C129.44,-113.04 137.33,-110.41 137.33,-105 137.33,-101.02 133.08,-98.55 126.99,-97.59\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"119.77,-97.13 126.95,-94.43 123.26,-97.35 126.76,-97.57 126.76,-97.57 126.76,-97.57 123.26,-97.35 126.56,-100.72 119.77,-97.13 119.77,-97.13\"/>\n",
"<text text-anchor=\"start\" x=\"137.33\" y=\"-101.3\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; p</text>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Pages: 1 -->\n",
"<svg width=\"229pt\" height=\"360pt\"\n",
" viewBox=\"0.00 0.00 228.81 360.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(0.5263157894736842 0.5263157894736842) rotate(0) translate(4 681)\">\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-681 431.38,-681 431.38,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"193.19\" y=\"-662.8\" font-family=\"Lato\" font-size=\"14.00\">Inf(</text>\n",
"<text text-anchor=\"start\" x=\"214.19\" y=\"-662.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"230.19\" y=\"-662.8\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"192.19\" y=\"-648.8\" font-family=\"Lato\" font-size=\"14.00\">[Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M196.38,-603C196.38,-603 184.38,-603 184.38,-603 178.38,-603 172.38,-597 172.38,-591 172.38,-591 172.38,-579 172.38,-579 172.38,-573 178.38,-567 184.38,-567 184.38,-567 196.38,-567 196.38,-567 202.38,-567 208.38,-573 208.38,-579 208.38,-579 208.38,-591 208.38,-591 208.38,-597 202.38,-603 196.38,-603\"/>\n",
"<text text-anchor=\"start\" x=\"185.88\" y=\"-581.3\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M190.38,-639.85C190.38,-638.21 190.38,-623.85 190.38,-610.37\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"190.38,-603.06 193.53,-610.06 190.38,-606.56 190.38,-610.06 190.38,-610.06 190.38,-610.06 190.38,-606.56 187.23,-610.06 190.38,-603.06 190.38,-603.06\"/>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>1</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M201.38,-501C201.38,-501 181.38,-501 181.38,-501 175.38,-501 169.38,-495 169.38,-489 169.38,-489 169.38,-477 169.38,-477 169.38,-471 175.38,-465 181.38,-465 181.38,-465 201.38,-465 201.38,-465 207.38,-465 213.38,-471 213.38,-477 213.38,-477 213.38,-489 213.38,-489 213.38,-495 207.38,-501 201.38,-501\"/>\n",
"<text text-anchor=\"start\" x=\"177.38\" y=\"-479.3\" font-family=\"Lato\" font-size=\"14.00\">~0,4</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M179.5,-566.83C176.6,-561.35 173.86,-555.11 172.38,-549 169.24,-536.04 169.09,-531.92 172.38,-519 173.35,-515.15 174.85,-511.26 176.59,-507.55\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"179.9,-501.1 179.5,-508.76 178.3,-504.21 176.7,-507.32 176.7,-507.32 176.7,-507.32 178.3,-504.21 173.9,-505.88 179.9,-501.1 179.9,-501.1\"/>\n",
"<text text-anchor=\"start\" x=\"176.88\" y=\"-537.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"<text text-anchor=\"start\" x=\"172.38\" y=\"-522.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M191.2,-501.22C191.04,-517.21 190.8,-541.21 190.62,-559.25\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"190.55,-566.58 187.47,-559.55 190.59,-563.08 190.62,-559.58 190.62,-559.58 190.62,-559.58 190.59,-563.08 193.77,-559.61 190.55,-566.58 190.55,-566.58\"/>\n",
"<text text-anchor=\"start\" x=\"192.88\" y=\"-537.8\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"<text text-anchor=\"start\" x=\"190.38\" y=\"-522.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>2</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M201.38,-399C201.38,-399 181.38,-399 181.38,-399 175.38,-399 169.38,-393 169.38,-387 169.38,-387 169.38,-375 169.38,-375 169.38,-369 175.38,-363 181.38,-363 181.38,-363 201.38,-363 201.38,-363 207.38,-363 213.38,-369 213.38,-375 213.38,-375 213.38,-387 213.38,-387 213.38,-393 207.38,-399 201.38,-399\"/>\n",
"<text text-anchor=\"start\" x=\"177.38\" y=\"-377.3\" font-family=\"Lato\" font-size=\"14.00\">3,~1</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>1&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M191.38,-464.58C191.38,-448.52 191.38,-424.52 191.38,-406.52\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"191.38,-399.22 194.53,-406.22 191.38,-402.72 191.38,-406.22 191.38,-406.22 191.38,-406.22 191.38,-402.72 188.23,-406.22 191.38,-399.22 191.38,-399.22\"/>\n",
"<text text-anchor=\"start\" x=\"191.38\" y=\"-428.3\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>3</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M72.38,-297C72.38,-297 32.38,-297 32.38,-297 26.38,-297 20.38,-291 20.38,-285 20.38,-285 20.38,-273 20.38,-273 20.38,-267 26.38,-261 32.38,-261 32.38,-261 72.38,-261 72.38,-261 78.38,-261 84.38,-267 84.38,-273 84.38,-273 84.38,-285 84.38,-285 84.38,-291 78.38,-297 72.38,-297\"/>\n",
"<text text-anchor=\"start\" x=\"28.38\" y=\"-275.3\" font-family=\"Lato\" font-size=\"14.00\">4,~1,~0</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;3 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>2&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M173.46,-362.99C167.83,-357.41 161.7,-351.07 156.38,-345 145.3,-332.37 146.63,-325.33 133.38,-315 120.92,-305.29 105.35,-297.72 91.21,-292.14\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"84.39,-289.57 92.06,-289.1 87.67,-290.81 90.94,-292.04 90.94,-292.04 90.94,-292.04 87.67,-290.81 89.83,-294.99 84.39,-289.57 84.39,-289.57\"/>\n",
"<text text-anchor=\"start\" x=\"156.38\" y=\"-326.3\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 4 -->\n",
"<g id=\"node6\" class=\"node\">\n",
"<title>4</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M205.38,-123C205.38,-123 173.38,-123 173.38,-123 167.38,-123 161.38,-117 161.38,-111 161.38,-111 161.38,-99 161.38,-99 161.38,-93 167.38,-87 173.38,-87 173.38,-87 205.38,-87 205.38,-87 211.38,-87 217.38,-93 217.38,-99 217.38,-99 217.38,-111 217.38,-111 217.38,-117 211.38,-123 205.38,-123\"/>\n",
"<text text-anchor=\"start\" x=\"169.38\" y=\"-101.3\" font-family=\"Lato\" font-size=\"14.00\">0,4,~1</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;4 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>2&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M204.87,-362.77C208.34,-357.38 211.59,-351.21 213.38,-345 217.07,-332.19 213.53,-328.33 213.38,-315 212.49,-237.65 230.09,-215.53 209.38,-141 208.27,-137.03 206.62,-133.03 204.72,-129.22\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"201.36,-123.05 207.47,-127.69 203.03,-126.12 204.71,-129.2 204.71,-129.2 204.71,-129.2 203.03,-126.12 201.94,-130.7 201.36,-123.05 201.36,-123.05\"/>\n",
"<text text-anchor=\"start\" x=\"218.38\" y=\"-231.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; !b &amp; p</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;0 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>3&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M50.07,-297.13C48.83,-310.41 48.28,-329.16 52.38,-345 75,-432.54 139.26,-520.9 171.48,-561.29\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"175.99,-566.9 169.15,-563.42 173.8,-564.17 171.6,-561.45 171.6,-561.45 171.6,-561.45 173.8,-564.17 174.06,-559.47 175.99,-566.9 175.99,-566.9\"/>\n",
"<text text-anchor=\"start\" x=\"94.38\" y=\"-435.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"<text text-anchor=\"start\" x=\"106.38\" y=\"-420.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;2 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>3&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M52.08,-297.17C52.77,-311.76 56.11,-332.29 68.38,-345 92.72,-370.23 133.82,-377.65 161.75,-379.63\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"168.9,-380.04 161.73,-382.79 165.41,-379.84 161.91,-379.64 161.91,-379.64 161.91,-379.64 165.41,-379.84 162.09,-376.5 168.9,-380.04 168.9,-380.04\"/>\n",
"<text text-anchor=\"start\" x=\"68.38\" y=\"-326.3\" font-family=\"Lato\" font-size=\"14.00\">a &amp; !b &amp; p</text>\n",
"</g>\n",
"<!-- 5 -->\n",
"<g id=\"node7\" class=\"node\">\n",
"<title>5</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M115.38,-36C115.38,-36 95.38,-36 95.38,-36 89.38,-36 83.38,-30 83.38,-24 83.38,-24 83.38,-12 83.38,-12 83.38,-6 89.38,0 95.38,0 95.38,0 115.38,0 115.38,0 121.38,0 127.38,-6 127.38,-12 127.38,-12 127.38,-24 127.38,-24 127.38,-30 121.38,-36 115.38,-36\"/>\n",
"<text text-anchor=\"start\" x=\"91.38\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">3,~0</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;5 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>3&#45;&gt;5</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M38.45,-260.66C19.31,-234.63 -11.08,-183.92 4.38,-141 19.1,-100.11 54.14,-63.21 78.8,-40.96\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"84.2,-36.16 81.06,-43.17 81.59,-38.49 78.97,-40.81 78.97,-40.81 78.97,-40.81 81.59,-38.49 76.88,-38.45 84.2,-36.16 84.2,-36.16\"/>\n",
"<text text-anchor=\"start\" x=\"4.38\" y=\"-144.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 6 -->\n",
"<g id=\"node8\" class=\"node\">\n",
"<title>6</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M107.38,-210C107.38,-210 67.38,-210 67.38,-210 61.38,-210 55.38,-204 55.38,-198 55.38,-198 55.38,-186 55.38,-186 55.38,-180 61.38,-174 67.38,-174 67.38,-174 107.38,-174 107.38,-174 113.38,-174 119.38,-180 119.38,-186 119.38,-186 119.38,-198 119.38,-198 119.38,-204 113.38,-210 107.38,-210\"/>\n",
"<text text-anchor=\"start\" x=\"63.38\" y=\"-188.3\" font-family=\"Lato\" font-size=\"14.00\">3,~1,~0</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;6 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>3&#45;&gt;6</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M80.71,-260.98C86.63,-255.98 92.07,-249.95 95.38,-243 99.15,-235.06 98.76,-225.69 96.87,-217.23\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"95,-210.38 99.88,-216.3 95.92,-213.75 96.85,-217.13 96.85,-217.13 96.85,-217.13 95.92,-213.75 93.81,-217.96 95,-210.38 95,-210.38\"/>\n",
"<text text-anchor=\"start\" x=\"98.38\" y=\"-231.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 4&#45;&gt;0 -->\n",
"<g id=\"edge11\" class=\"edge\">\n",
"<title>4&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M217.75,-105.75C272.49,-106.92 387.38,-118.05 387.38,-191 387.38,-484 387.38,-484 387.38,-484 387.38,-560.2 268.75,-578.35 215.6,-582.66\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"208.56,-583.19 215.31,-579.53 212.05,-582.93 215.54,-582.67 215.54,-582.67 215.54,-582.67 212.05,-582.93 215.77,-585.81 208.56,-583.19 208.56,-583.19\"/>\n",
"<text text-anchor=\"start\" x=\"387.38\" y=\"-333.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"<text text-anchor=\"start\" x=\"399.38\" y=\"-318.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- 4&#45;&gt;2 -->\n",
"<g id=\"edge12\" class=\"edge\">\n",
"<title>4&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M209.56,-123.34C232.96,-145.01 270.03,-184.55 283.38,-228 299.04,-279.01 251.52,-330.49 219.06,-358.51\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"213.6,-363.13 216.91,-356.21 216.27,-360.87 218.94,-358.61 218.94,-358.61 218.94,-358.61 216.27,-360.87 220.97,-361.02 213.6,-363.13 213.6,-363.13\"/>\n",
"<text text-anchor=\"start\" x=\"285.38\" y=\"-231.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; !b &amp; p</text>\n",
"</g>\n",
"<!-- 4&#45;&gt;5 -->\n",
"<g id=\"edge13\" class=\"edge\">\n",
"<title>4&#45;&gt;5</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M161.26,-100.12C142.33,-95.89 118.66,-87.12 106.38,-69 101.35,-61.59 100.21,-52.04 100.64,-43.27\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"101.33,-36.15 103.79,-43.42 100.99,-39.64 100.66,-43.12 100.66,-43.12 100.66,-43.12 100.99,-39.64 97.52,-42.82 101.33,-36.15 101.33,-36.15\"/>\n",
"<text text-anchor=\"start\" x=\"106.38\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 4&#45;&gt;6 -->\n",
"<g id=\"edge14\" class=\"edge\">\n",
"<title>4&#45;&gt;6</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M161.16,-105.58C133.53,-106.88 92.7,-113.71 72.38,-141 66.63,-148.72 68.23,-158.64 72.08,-167.61\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"75.2,-173.92 69.27,-169.05 73.65,-170.79 72.1,-167.65 72.1,-167.65 72.1,-167.65 73.65,-170.79 74.92,-166.25 75.2,-173.92 75.2,-173.92\"/>\n",
"<text text-anchor=\"start\" x=\"72.38\" y=\"-144.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 5&#45;&gt;4 -->\n",
"<g id=\"edge15\" class=\"edge\">\n",
"<title>5&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M127.51,-27.3C140.53,-33.11 156.51,-42 167.38,-54 174.07,-61.4 178.98,-71.16 182.44,-80.09\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"184.81,-86.7 179.48,-81.17 183.63,-83.41 182.45,-80.11 182.45,-80.11 182.45,-80.11 183.63,-83.41 185.41,-79.05 184.81,-86.7 184.81,-86.7\"/>\n",
"<text text-anchor=\"start\" x=\"176.38\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- 6&#45;&gt;3 -->\n",
"<g id=\"edge16\" class=\"edge\">\n",
"<title>6&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M55.35,-207.04C47.02,-212.34 39.08,-219.26 34.38,-228 29.92,-236.29 31.87,-245.91 35.83,-254.48\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"39.18,-260.8 33.12,-256.09 37.54,-257.71 35.9,-254.62 35.9,-254.62 35.9,-254.62 37.54,-257.71 38.68,-253.14 39.18,-260.8 39.18,-260.8\"/>\n",
"<text text-anchor=\"start\" x=\"34.38\" y=\"-231.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 6&#45;&gt;4 -->\n",
"<g id=\"edge17\" class=\"edge\">\n",
"<title>6&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M108.02,-173.8C123.92,-160.55 146.01,-142.14 163.16,-127.85\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"168.77,-123.18 165.4,-130.08 166.08,-125.42 163.39,-127.66 163.39,-127.66 163.39,-127.66 166.08,-125.42 161.37,-125.24 168.77,-123.18 168.77,-123.18\"/>\n",
"<text text-anchor=\"start\" x=\"144.38\" y=\"-144.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; !b &amp; p</text>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Pages: 1 -->\n",
"<svg width=\"230pt\" height=\"360pt\"\n",
" viewBox=\"0.00 0.00 229.71 360.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(0.9523809523809523 0.9523809523809523) rotate(0) translate(4 375)\">\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-375 237.83,-375 237.83,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"96.42\" y=\"-356.8\" font-family=\"Lato\" font-size=\"14.00\">Inf(</text>\n",
"<text text-anchor=\"start\" x=\"117.42\" y=\"-356.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"133.42\" y=\"-356.8\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"95.42\" y=\"-342.8\" font-family=\"Lato\" font-size=\"14.00\">[Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M131.83,-297C131.83,-297 119.83,-297 119.83,-297 113.83,-297 107.83,-291 107.83,-285 107.83,-285 107.83,-273 107.83,-273 107.83,-267 113.83,-261 119.83,-261 119.83,-261 131.83,-261 131.83,-261 137.83,-261 143.83,-267 143.83,-273 143.83,-273 143.83,-285 143.83,-285 143.83,-291 137.83,-297 131.83,-297\"/>\n",
"<text text-anchor=\"start\" x=\"117.33\" y=\"-275.3\" font-family=\"Lato\" font-size=\"14.00\">~0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M125.83,-333.85C125.83,-332.21 125.83,-317.85 125.83,-304.37\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"125.83,-297.06 128.98,-304.06 125.83,-300.56 125.83,-304.06 125.83,-304.06 125.83,-304.06 125.83,-300.56 122.68,-304.06 125.83,-297.06 125.83,-297.06\"/>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>1</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M61.83,-210C61.83,-210 49.83,-210 49.83,-210 43.83,-210 37.83,-204 37.83,-198 37.83,-198 37.83,-186 37.83,-186 37.83,-180 43.83,-174 49.83,-174 49.83,-174 61.83,-174 61.83,-174 67.83,-174 73.83,-180 73.83,-186 73.83,-186 73.83,-198 73.83,-198 73.83,-204 67.83,-210 61.83,-210\"/>\n",
"<text text-anchor=\"start\" x=\"47.33\" y=\"-188.3\" font-family=\"Lato\" font-size=\"14.00\">~1</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M107.67,-273.61C92.18,-268.85 70.73,-259.58 59.83,-243 54.9,-235.5 53.29,-225.92 53.13,-217.17\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"53.29,-210.07 56.28,-217.14 53.21,-213.57 53.13,-217.07 53.13,-217.07 53.13,-217.07 53.21,-213.57 49.98,-216.99 53.29,-210.07 53.29,-210.07\"/>\n",
"<text text-anchor=\"start\" x=\"59.83\" y=\"-231.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>2</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M98.83,-36C98.83,-36 86.83,-36 86.83,-36 80.83,-36 74.83,-30 74.83,-24 74.83,-24 74.83,-12 74.83,-12 74.83,-6 80.83,0 86.83,0 86.83,0 98.83,0 98.83,0 104.83,0 110.83,-6 110.83,-12 110.83,-12 110.83,-24 110.83,-24 110.83,-30 104.83,-36 98.83,-36\"/>\n",
"<text text-anchor=\"start\" x=\"87.83\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">{}</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>0&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M144.19,-271.58C167.81,-262.21 207.84,-242.29 224.83,-210 232.28,-195.84 226.72,-189.89 224.83,-174 220.13,-134.5 227.23,-119.16 203.83,-87 182.2,-57.27 143.23,-37.86 117.69,-27.66\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"110.87,-25.03 118.54,-24.61 114.14,-26.29 117.4,-27.55 117.4,-27.55 117.4,-27.55 114.14,-26.29 116.27,-30.49 110.87,-25.03 110.87,-25.03\"/>\n",
"<text text-anchor=\"start\" x=\"222.83\" y=\"-144.8\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>1&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M66.35,-210.28C72.69,-220.21 81.19,-232.71 89.83,-243 93.7,-247.61 98.1,-252.27 102.46,-256.63\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"107.53,-261.59 100.32,-258.95 105.02,-259.14 102.52,-256.69 102.52,-256.69 102.52,-256.69 105.02,-259.14 104.72,-254.44 107.53,-261.59 107.53,-261.59\"/>\n",
"<text text-anchor=\"start\" x=\"89.83\" y=\"-231.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M73.98,-199.6C83.37,-200.77 91.83,-198.23 91.83,-192 91.83,-187.42 87.27,-184.84 81.13,-184.25\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"73.98,-184.4 80.92,-181.11 77.48,-184.33 80.98,-184.26 80.98,-184.26 80.98,-184.26 77.48,-184.33 81.05,-187.41 73.98,-184.4 73.98,-184.4\"/>\n",
"<text text-anchor=\"start\" x=\"91.83\" y=\"-188.3\" font-family=\"Lato\" font-size=\"14.00\">!b &amp; p</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>1&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M37.75,-184.65C25.19,-179.18 9.41,-169.94 1.83,-156 -1.35,-150.14 0.87,-147.6 1.83,-141 5.42,-116.23 4.51,-108.19 17.83,-87 30.99,-66.06 52.35,-47.6 68.91,-35.21\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"74.77,-30.93 70.98,-37.6 71.94,-32.99 69.12,-35.06 69.12,-35.06 69.12,-35.06 71.94,-32.99 67.26,-32.51 74.77,-30.93 74.77,-30.93\"/>\n",
"<text text-anchor=\"start\" x=\"17.83\" y=\"-101.3\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>3</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M107.33,-123C107.33,-123 78.33,-123 78.33,-123 72.33,-123 66.33,-117 66.33,-111 66.33,-111 66.33,-99 66.33,-99 66.33,-93 72.33,-87 78.33,-87 78.33,-87 107.33,-87 107.33,-87 113.33,-87 119.33,-93 119.33,-99 119.33,-99 119.33,-111 119.33,-111 119.33,-117 113.33,-123 107.33,-123\"/>\n",
"<text text-anchor=\"start\" x=\"74.33\" y=\"-101.3\" font-family=\"Lato\" font-size=\"14.00\">~1,~0</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;3 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>1&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M63.32,-173.8C68.84,-161.13 76.41,-143.73 82.5,-129.74\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"85.35,-123.18 85.45,-130.85 83.96,-126.38 82.56,-129.59 82.56,-129.59 82.56,-129.59 83.96,-126.38 79.67,-128.34 85.35,-123.18 85.35,-123.18\"/>\n",
"<text text-anchor=\"start\" x=\"76.83\" y=\"-144.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;2 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>2&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M110.98,-25.6C120.37,-26.77 128.83,-24.23 128.83,-18 128.83,-13.42 124.27,-10.84 118.13,-10.25\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"110.98,-10.4 117.92,-7.11 114.48,-10.33 117.98,-10.26 117.98,-10.26 117.98,-10.26 114.48,-10.33 118.05,-13.41 110.98,-10.4 110.98,-10.4\"/>\n",
"<text text-anchor=\"start\" x=\"132.33\" y=\"-21.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"<text text-anchor=\"start\" x=\"128.83\" y=\"-6.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;0 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>3&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M119.39,-121.36C126.44,-126.7 133.34,-133.31 137.83,-141 172.36,-200.06 159.84,-214.88 150.83,-243 149.55,-247.01 147.62,-250.95 145.38,-254.66\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"141.41,-260.65 142.65,-253.07 143.34,-257.73 145.28,-254.82 145.28,-254.82 145.28,-254.82 143.34,-257.73 147.9,-256.56 141.41,-260.65 141.41,-260.65\"/>\n",
"<text text-anchor=\"start\" x=\"159.83\" y=\"-188.3\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b &amp; p</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;1 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>3&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M66.01,-109.19C46.27,-113.1 20.71,-121.77 7.83,-141 -1.92,-155.56 14.96,-169.74 31.33,-179.26\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"37.76,-182.79 30.11,-182.18 34.69,-181.11 31.63,-179.42 31.63,-179.42 31.63,-179.42 34.69,-181.11 33.14,-176.66 37.76,-182.79 37.76,-182.79\"/>\n",
"<text text-anchor=\"start\" x=\"7.83\" y=\"-144.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; !b &amp; p</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;2 -->\n",
"<g id=\"edge11\" class=\"edge\">\n",
"<title>3&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M92.83,-86.8C92.83,-74.36 92.83,-57.36 92.83,-43.5\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"92.83,-36.18 95.98,-43.18 92.83,-39.68 92.83,-43.18 92.83,-43.18 92.83,-43.18 92.83,-39.68 89.68,-43.18 92.83,-36.18 92.83,-36.18\"/>\n",
"<text text-anchor=\"start\" x=\"92.83\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;3 -->\n",
"<g id=\"edge12\" class=\"edge\">\n",
"<title>3&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M119.77,-112.87C129.44,-113.04 137.33,-110.41 137.33,-105 137.33,-101.02 133.08,-98.55 126.99,-97.59\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"119.77,-97.13 126.95,-94.43 123.26,-97.35 126.76,-97.57 126.76,-97.57 126.76,-97.57 123.26,-97.35 126.56,-100.72 119.77,-97.13 119.77,-97.13\"/>\n",
"<text text-anchor=\"start\" x=\"137.33\" y=\"-101.3\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; p</text>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Pages: 1 -->\n",
"<svg width=\"118pt\" height=\"205pt\"\n",
" viewBox=\"0.00 0.00 117.80 205.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1.0 1.0) rotate(0) translate(4 201)\">\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-201 113.8,-201 113.8,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"34.4\" y=\"-182.8\" font-family=\"Lato\" font-size=\"14.00\">Inf(</text>\n",
"<text text-anchor=\"start\" x=\"55.4\" y=\"-182.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"71.4\" y=\"-182.8\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"33.4\" y=\"-168.8\" font-family=\"Lato\" font-size=\"14.00\">[Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"23.4\" cy=\"-105\" rx=\"18\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"23.4\" y=\"-101.3\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M23.4,-159.85C23.4,-158.21 23.4,-143.85 23.4,-130.37\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"23.4,-123.06 26.55,-130.06 23.4,-126.56 23.4,-130.06 23.4,-130.06 23.4,-130.06 23.4,-126.56 20.25,-130.06 23.4,-123.06 23.4,-123.06\"/>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"23.4\" cy=\"-18\" rx=\"23.3\" ry=\"18\"/>\n",
"<text text-anchor=\"start\" x=\"13.4\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">0,1</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M23.4,-86.8C23.4,-74.36 23.4,-57.36 23.4,-43.5\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"23.4,-36.18 26.55,-43.18 23.4,-39.68 23.4,-43.18 23.4,-43.18 23.4,-43.18 23.4,-39.68 20.25,-43.18 23.4,-36.18 23.4,-36.18\"/>\n",
"<text text-anchor=\"middle\" x=\"27.9\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M46.39,-21.89C56.3,-22.21 64.8,-20.91 64.8,-18 64.8,-15.82 60.02,-14.54 53.45,-14.17\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"46.39,-14.11 53.41,-11.02 49.89,-14.14 53.39,-14.17 53.39,-14.17 53.39,-14.17 49.89,-14.14 53.36,-17.32 46.39,-14.11 46.39,-14.11\"/>\n",
"<text text-anchor=\"start\" x=\"64.8\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M45.33,-24.67C63.65,-27.53 82.8,-25.3 82.8,-18 82.8,-11.67 68.4,-9.16 52.63,-10.46\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"45.33,-11.33 51.91,-7.37 48.81,-10.91 52.28,-10.5 52.28,-10.5 52.28,-10.5 48.81,-10.91 52.65,-13.63 45.33,-11.33 45.33,-11.33\"/>\n",
"<text text-anchor=\"start\" x=\"87.3\" y=\"-21.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"<text text-anchor=\"start\" x=\"82.8\" y=\"-6.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"nba2, nba3, nba4, nba5 = [spot.scc_filter(spot.remove_alternation(a, True), True) for a in (aut2, aut3, aut4, aut5)]\n",
"display_inline(nba2, nba3, nba4, nba5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The following demonstrate that very weak (non-alternating) Büchi automata can be complemented via alternation removal."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Title: (a &amp; (Fa R XFb)) | (!a &amp; (G!a U\\nXG!b)) Pages: 1 -->\n",
"<svg width=\"270pt\" height=\"296pt\"\n",
" viewBox=\"0.00 0.00 270.00 296.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1.0 1.0) rotate(0) translate(4 292)\">\n",
"<title>(a &amp; (Fa R XFb)) | (!a &amp; (G!a U\\nXG!b))</title>\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-292 266,-292 266,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"110.5\" y=\"-273.8\" font-family=\"Lato\" font-size=\"14.00\">Inf(</text>\n",
"<text text-anchor=\"start\" x=\"131.5\" y=\"-273.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"147.5\" y=\"-273.8\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"109.5\" y=\"-259.8\" font-family=\"Lato\" font-size=\"14.00\">[Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M108,-214C108,-214 96,-214 96,-214 90,-214 84,-208 84,-202 84,-202 84,-190 84,-190 84,-184 90,-178 96,-178 96,-178 108,-178 108,-178 114,-178 120,-184 120,-190 120,-190 120,-202 120,-202 120,-208 114,-214 108,-214\"/>\n",
"<text text-anchor=\"middle\" x=\"102\" y=\"-192.3\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M102,-250.85C102,-249.21 102,-234.85 102,-221.37\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"102,-214.06 105.15,-221.06 102,-217.56 102,-221.06 102,-221.06 102,-221.06 102,-217.56 98.85,-221.06 102,-214.06 102,-214.06\"/>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>1</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M24,-126C24,-126 12,-126 12,-126 6,-126 0,-120 0,-114 0,-114 0,-102 0,-102 0,-96 6,-90 12,-90 12,-90 24,-90 24,-90 30,-90 36,-96 36,-102 36,-102 36,-114 36,-114 36,-120 30,-126 24,-126\"/>\n",
"<text text-anchor=\"middle\" x=\"18\" y=\"-104.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M85,-177.6C71.94,-164.22 53.8,-145.65 39.69,-131.2\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"34.69,-126.08 41.83,-128.89 37.13,-128.59 39.58,-131.09 39.58,-131.09 39.58,-131.09 37.13,-128.59 37.32,-133.29 34.69,-126.08 34.69,-126.08\"/>\n",
"<text text-anchor=\"start\" x=\"68\" y=\"-148.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>2</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M108,-127C108,-127 96,-127 96,-127 90,-127 84,-121 84,-115 84,-115 84,-101 84,-101 84,-95 90,-89 96,-89 96,-89 108,-89 108,-89 114,-89 120,-95 120,-101 120,-101 120,-115 120,-115 120,-121 114,-127 108,-127\"/>\n",
"<text text-anchor=\"start\" x=\"97.5\" y=\"-111.8\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
"<text text-anchor=\"start\" x=\"94\" y=\"-96.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>0&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M102,-177.6C102,-165.26 102,-148.49 102,-134.63\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"102,-127.27 105.15,-134.27 102,-130.77 102,-134.27 102,-134.27 102,-134.27 102,-130.77 98.85,-134.27 102,-127.27 102,-127.27\"/>\n",
"<text text-anchor=\"start\" x=\"102\" y=\"-148.8\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>3</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M192,-126C192,-126 180,-126 180,-126 174,-126 168,-120 168,-114 168,-114 168,-102 168,-102 168,-96 174,-90 180,-90 180,-90 192,-90 192,-90 198,-90 204,-96 204,-102 204,-102 204,-114 204,-114 204,-120 198,-126 192,-126\"/>\n",
"<text text-anchor=\"middle\" x=\"186\" y=\"-104.3\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;3 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>0&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M119,-177.6C132.06,-164.22 150.2,-145.65 164.31,-131.2\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"169.31,-126.08 166.68,-133.29 166.87,-128.59 164.42,-131.09 164.42,-131.09 164.42,-131.09 166.87,-128.59 162.17,-128.89 169.31,-126.08 169.31,-126.08\"/>\n",
"<text text-anchor=\"start\" x=\"150\" y=\"-148.8\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M36.15,-115.96C45.54,-117.18 54,-114.53 54,-108 54,-103.2 49.44,-100.5 43.3,-99.89\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"36.15,-100.04 43.08,-96.74 39.65,-99.96 43.15,-99.89 43.15,-99.89 43.15,-99.89 39.65,-99.96 43.22,-103.04 36.15,-100.04 36.15,-100.04\"/>\n",
"<text text-anchor=\"start\" x=\"54\" y=\"-104.3\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
"</g>\n",
"<!-- 4 -->\n",
"<g id=\"node6\" class=\"node\">\n",
"<title>4</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M24,-38C24,-38 12,-38 12,-38 6,-38 0,-32 0,-26 0,-26 0,-12 0,-12 0,-6 6,0 12,0 12,0 24,0 24,0 30,0 36,-6 36,-12 36,-12 36,-26 36,-26 36,-32 30,-38 24,-38\"/>\n",
"<text text-anchor=\"start\" x=\"13.5\" y=\"-22.8\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
"<text text-anchor=\"start\" x=\"10\" y=\"-7.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;4 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>1&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M18,-89.81C18,-77.08 18,-59.52 18,-45.2\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"18,-38.05 21.15,-45.05 18,-41.55 18,-45.05 18,-45.05 18,-45.05 18,-41.55 14.85,-45.05 18,-38.05 18,-38.05\"/>\n",
"<text text-anchor=\"start\" x=\"18\" y=\"-59.8\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;2 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>2&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M120.15,-115.96C129.54,-117.18 138,-114.53 138,-108 138,-103.2 133.44,-100.5 127.3,-99.89\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"120.15,-100.04 127.08,-96.74 123.65,-99.96 127.15,-99.89 127.15,-99.89 127.15,-99.89 123.65,-99.96 127.22,-103.04 120.15,-100.04 120.15,-100.04\"/>\n",
"<text text-anchor=\"start\" x=\"138\" y=\"-104.3\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;3 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>3&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M204.15,-115.96C213.54,-117.18 222,-114.53 222,-108 222,-103.2 217.44,-100.5 211.3,-99.89\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"204.15,-100.04 211.08,-96.74 207.65,-99.96 211.15,-99.89 211.15,-99.89 211.15,-99.89 207.65,-99.96 211.22,-103.04 204.15,-100.04 204.15,-100.04\"/>\n",
"<text text-anchor=\"start\" x=\"222\" y=\"-104.3\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- 5 -->\n",
"<g id=\"node7\" class=\"node\">\n",
"<title>5</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M192,-38C192,-38 180,-38 180,-38 174,-38 168,-32 168,-26 168,-26 168,-12 168,-12 168,-6 174,0 180,0 180,0 192,0 192,0 198,0 204,-6 204,-12 204,-12 204,-26 204,-26 204,-32 198,-38 192,-38\"/>\n",
"<text text-anchor=\"start\" x=\"181.5\" y=\"-22.8\" font-family=\"Lato\" font-size=\"14.00\">5</text>\n",
"<text text-anchor=\"start\" x=\"178\" y=\"-7.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;5 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>3&#45;&gt;5</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M186,-89.81C186,-77.08 186,-59.52 186,-45.2\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"186,-38.05 189.15,-45.05 186,-41.55 186,-45.05 186,-45.05 186,-45.05 186,-41.55 182.85,-45.05 186,-38.05 186,-38.05\"/>\n",
"<text text-anchor=\"start\" x=\"186\" y=\"-59.8\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- 4&#45;&gt;4 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>4&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M36.15,-26.96C45.54,-28.18 54,-25.53 54,-19 54,-14.2 49.44,-11.5 43.3,-10.89\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"36.15,-11.04 43.08,-7.74 39.65,-10.96 43.15,-10.89 43.15,-10.89 43.15,-10.89 39.65,-10.96 43.22,-14.04 36.15,-11.04 36.15,-11.04\"/>\n",
"<text text-anchor=\"middle\" x=\"58.5\" y=\"-15.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 5&#45;&gt;5 -->\n",
"<g id=\"edge11\" class=\"edge\">\n",
"<title>5&#45;&gt;5</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M204.15,-26.96C213.54,-28.18 222,-25.53 222,-19 222,-14.2 217.44,-11.5 211.3,-10.89\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"204.15,-11.04 211.08,-7.74 207.65,-10.96 211.15,-10.89 211.15,-10.89 211.15,-10.89 207.65,-10.96 211.22,-14.04 204.15,-11.04 204.15,-11.04\"/>\n",
"<text text-anchor=\"start\" x=\"222\" y=\"-15.3\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Pages: 1 -->\n",
"<svg width=\"173pt\" height=\"360pt\"\n",
" viewBox=\"0.00 0.00 173.14 360.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(0.78125 0.78125) rotate(0) translate(4 457.6)\">\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-457.6 218,-457.6 218,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"85.5\" y=\"-439.4\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
"<text text-anchor=\"start\" x=\"108.5\" y=\"-439.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"124.5\" y=\"-439.4\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"75.5\" y=\"-425.4\" font-family=\"Lato\" font-size=\"14.00\">[co&#45;Büchi]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M58,-379.6C58,-379.6 46,-379.6 46,-379.6 40,-379.6 34,-373.6 34,-367.6 34,-367.6 34,-355.6 34,-355.6 34,-349.6 40,-343.6 46,-343.6 46,-343.6 58,-343.6 58,-343.6 64,-343.6 70,-349.6 70,-355.6 70,-355.6 70,-367.6 70,-367.6 70,-373.6 64,-379.6 58,-379.6\"/>\n",
"<text text-anchor=\"middle\" x=\"52\" y=\"-357.9\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M52,-416.45C52,-414.81 52,-400.45 52,-386.97\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"52,-379.66 55.15,-386.66 52,-383.16 52,-386.66 52,-386.66 52,-386.66 52,-383.16 48.85,-386.66 52,-379.66 52,-379.66\"/>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>1</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M24,-292.6C24,-292.6 12,-292.6 12,-292.6 6,-292.6 0,-286.6 0,-280.6 0,-280.6 0,-268.6 0,-268.6 0,-262.6 6,-256.6 12,-256.6 12,-256.6 24,-256.6 24,-256.6 30,-256.6 36,-262.6 36,-268.6 36,-268.6 36,-280.6 36,-280.6 36,-286.6 30,-292.6 24,-292.6\"/>\n",
"<text text-anchor=\"middle\" x=\"18\" y=\"-270.9\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M45.12,-343.4C40.05,-330.73 33.09,-313.33 27.5,-299.34\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"24.87,-292.78 30.39,-298.1 26.17,-296.03 27.47,-299.27 27.47,-299.27 27.47,-299.27 26.17,-296.03 24.55,-300.44 24.87,-292.78 24.87,-292.78\"/>\n",
"<text text-anchor=\"start\" x=\"38\" y=\"-314.4\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- &#45;1 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>&#45;1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"86\" cy=\"-274.6\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 0&#45;&gt;&#45;1 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>0&#45;&gt;&#45;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M58.88,-343.4C66.2,-325.11 77.44,-297 82.86,-283.44\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"85.24,-284.09 85.57,-276.68 80.69,-282.27 85.24,-284.09\"/>\n",
"<text text-anchor=\"start\" x=\"72\" y=\"-314.4\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M36.15,-281.11C45.54,-282.11 54,-279.94 54,-274.6 54,-270.68 49.44,-268.46 43.3,-267.96\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"36.15,-268.09 43.1,-264.81 39.65,-268.03 43.15,-267.96 43.15,-267.96 43.15,-267.96 39.65,-268.03 43.21,-271.11 36.15,-268.09 36.15,-268.09\"/>\n",
"<text text-anchor=\"start\" x=\"54\" y=\"-270.9\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>2</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M43,-219.6C43,-219.6 31,-219.6 31,-219.6 25,-219.6 19,-213.6 19,-207.6 19,-207.6 19,-193.6 19,-193.6 19,-187.6 25,-181.6 31,-181.6 31,-181.6 43,-181.6 43,-181.6 49,-181.6 55,-187.6 55,-193.6 55,-193.6 55,-207.6 55,-207.6 55,-213.6 49,-219.6 43,-219.6\"/>\n",
"<text text-anchor=\"start\" x=\"32.5\" y=\"-204.4\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
"<text text-anchor=\"start\" x=\"29\" y=\"-189.4\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;2 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M85.41,-272.67C83.79,-270.1 79.06,-262.68 75,-256.6 68.16,-246.37 60.47,-235.19 53.81,-225.59\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"49.81,-219.84 56.39,-223.79 51.81,-222.71 53.8,-225.58 53.8,-225.58 53.8,-225.58 51.81,-222.71 51.22,-227.38 49.81,-219.84 49.81,-219.84\"/>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g id=\"node6\" class=\"node\">\n",
"<title>3</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M127,-218.6C127,-218.6 115,-218.6 115,-218.6 109,-218.6 103,-212.6 103,-206.6 103,-206.6 103,-194.6 103,-194.6 103,-188.6 109,-182.6 115,-182.6 115,-182.6 127,-182.6 127,-182.6 133,-182.6 139,-188.6 139,-194.6 139,-194.6 139,-206.6 139,-206.6 139,-212.6 133,-218.6 127,-218.6\"/>\n",
"<text text-anchor=\"middle\" x=\"121\" y=\"-196.9\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
"</g>\n",
"<!-- &#45;1&#45;&gt;3 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>&#45;1&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M86.39,-272.79C88.65,-268.14 100.22,-244.35 109.37,-225.53\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"112.61,-218.87 112.38,-226.54 111.08,-222.02 109.55,-225.16 109.55,-225.16 109.55,-225.16 111.08,-222.02 106.71,-223.79 112.61,-218.87 112.61,-218.87\"/>\n",
"</g>\n",
"<!-- 2&#45;&gt;2 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>2&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M55.15,-207.11C64.54,-208.11 73,-205.94 73,-200.6 73,-196.68 68.44,-194.46 62.3,-193.96\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"55.15,-194.09 62.1,-190.81 58.65,-194.03 62.15,-193.96 62.15,-193.96 62.15,-193.96 58.65,-194.03 62.21,-197.11 55.15,-194.09 55.15,-194.09\"/>\n",
"<text text-anchor=\"start\" x=\"73\" y=\"-196.9\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
"</g>\n",
"<!-- T5T2 -->\n",
"<!-- 2&#45;&gt;T5T2 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>2&#45;&gt;T5T2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M37,-181.26C37,-166.86 37,-147.57 37,-137.17\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"37,-129.89 40.15,-136.89 37,-133.39 37,-136.89 37,-136.89 37,-136.89 37,-133.39 33.85,-136.89 37,-129.89 37,-129.89\"/>\n",
"<text text-anchor=\"start\" x=\"37\" y=\"-152.4\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
"</g>\n",
"<!-- T5T3 -->\n",
"<!-- 3&#45;&gt;T5T3 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>3&#45;&gt;T5T3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M113.58,-182.35C107.2,-167.48 98.32,-146.83 93.83,-136.4\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"91.04,-129.89 96.7,-135.08 92.42,-133.11 93.8,-136.32 93.8,-136.32 93.8,-136.32 92.42,-133.11 90.91,-137.57 91.04,-129.89 91.04,-129.89\"/>\n",
"<text text-anchor=\"start\" x=\"106\" y=\"-152.4\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"</g>\n",
"<!-- &#45;4 -->\n",
"<g id=\"node9\" class=\"node\">\n",
"<title>&#45;4</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"138\" cy=\"-128.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
"</g>\n",
"<!-- 3&#45;&gt;&#45;4 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>3&#45;&gt;&#45;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M118.52,-182.52C117.72,-172.35 117.92,-159.37 122,-148.6 123.93,-143.52 127.87,-138.86 131.36,-135.45\"/>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"133.19,-137.1 136.86,-130.66 129.97,-133.41 133.19,-137.1\"/>\n",
"<text text-anchor=\"start\" x=\"122\" y=\"-152.4\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"</g>\n",
"<!-- &#45;4&#45;&gt;3 -->\n",
"<g id=\"edge11\" class=\"edge\">\n",
"<title>&#45;4&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M137.93,-130.65C137.6,-134.49 136.08,-150.68 133,-163.6 132.04,-167.62 130.83,-171.84 129.55,-175.91\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"127.36,-182.56 126.55,-174.93 128.45,-179.24 129.55,-175.91 129.55,-175.91 129.55,-175.91 128.45,-179.24 132.54,-176.9 127.36,-182.56 127.36,-182.56\"/>\n",
"</g>\n",
"<!-- 4 -->\n",
"<g id=\"node10\" class=\"node\">\n",
"<title>4</title>\n",
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M144,-90C144,-90 132,-90 132,-90 126,-90 120,-84 120,-78 120,-78 120,-64 120,-64 120,-58 126,-52 132,-52 132,-52 144,-52 144,-52 150,-52 156,-58 156,-64 156,-64 156,-78 156,-78 156,-84 150,-90 144,-90\"/>\n",
"<text text-anchor=\"start\" x=\"133.5\" y=\"-74.8\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
"<text text-anchor=\"start\" x=\"130\" y=\"-59.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- &#45;4&#45;&gt;4 -->\n",
"<g id=\"edge12\" class=\"edge\">\n",
"<title>&#45;4&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M138,-126.83C138,-123.2 138,-109.97 138,-97.42\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"138,-90.18 141.15,-97.18 138,-93.68 138,-97.18 138,-97.18 138,-97.18 138,-93.68 134.85,-97.18 138,-90.18 138,-90.18\"/>\n",
"</g>\n",
"<!-- 4&#45;&gt;4 -->\n",
"<g id=\"edge13\" class=\"edge\">\n",
"<title>4&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M156.15,-77.51C165.54,-78.51 174,-76.34 174,-71 174,-67.08 169.44,-64.86 163.3,-64.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"156.15,-64.49 163.1,-61.21 159.65,-64.43 163.15,-64.36 163.15,-64.36 163.15,-64.36 159.65,-64.43 163.21,-67.51 156.15,-64.49 156.15,-64.49\"/>\n",
"<text text-anchor=\"start\" x=\"174\" y=\"-67.3\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"</g>\n",
"<!-- T5T4 -->\n",
"<!-- 4&#45;&gt;T5T4 -->\n",
"<g id=\"edge14\" class=\"edge\">\n",
"<title>4&#45;&gt;T5T4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M138,-51.87C138,-37.64 138,-18.56 138,-8.29\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"138,-1.09 141.15,-8.09 138,-4.59 138,-8.09 138,-8.09 138,-8.09 138,-4.59 134.85,-8.09 138,-1.09 138,-1.09\"/>\n",
"<text text-anchor=\"start\" x=\"138\" y=\"-22.8\" font-family=\"Lato\" font-size=\"14.00\">a | b</text>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.43.0 (0)\n",
" -->\n",
"<!-- Pages: 1 -->\n",
"<svg width=\"278pt\" height=\"360pt\"\n",
" viewBox=\"0.00 0.00 277.96 360.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(0.7092198581560284 0.7092198581560284) rotate(0) translate(4 505)\">\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-505 389,-505 389,4 -4,4\"/>\n",
"<text text-anchor=\"start\" x=\"147\" y=\"-486.8\" font-family=\"Lato\" font-size=\"14.00\">Inf(</text>\n",
"<text text-anchor=\"start\" x=\"168\" y=\"-486.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"184\" y=\"-486.8\" font-family=\"Lato\" font-size=\"14.00\">)&amp;Inf(</text>\n",
"<text text-anchor=\"start\" x=\"218\" y=\"-486.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"<text text-anchor=\"start\" x=\"234\" y=\"-486.8\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
"<text text-anchor=\"start\" x=\"150\" y=\"-472.8\" font-family=\"Lato\" font-size=\"14.00\">[gen. Büchi 2]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>0</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"69\" cy=\"-409\" rx=\"18\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"69\" y=\"-405.3\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>I&#45;&gt;0</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M69,-463.85C69,-462.21 69,-447.85 69,-434.37\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"69,-427.06 72.15,-434.06 69,-430.56 69,-434.06 69,-434.06 69,-434.06 69,-430.56 65.85,-434.06 69,-427.06 69,-427.06\"/>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>1</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"18\" cy=\"-307\" rx=\"18\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"18\" y=\"-303.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;1 -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>0&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M61.03,-392.38C52.5,-375.64 38.89,-348.96 29.26,-330.08\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"25.91,-323.52 31.9,-328.32 27.5,-326.63 29.09,-329.75 29.09,-329.75 29.09,-329.75 27.5,-326.63 26.29,-331.18 25.91,-323.52 25.91,-323.52\"/>\n",
"<text text-anchor=\"start\" x=\"64.5\" y=\"-361.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"<text text-anchor=\"start\" x=\"52\" y=\"-347.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"68\" y=\"-347.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>2</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"122\" cy=\"-307\" rx=\"18\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"122\" y=\"-303.3\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>0&#45;&gt;2</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M77.05,-392.81C85.92,-376.07 100.27,-349 110.37,-329.95\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"113.87,-323.33 113.38,-330.99 112.24,-326.42 110.6,-329.52 110.6,-329.52 110.6,-329.52 112.24,-326.42 107.81,-328.04 113.87,-323.33 113.87,-323.33\"/>\n",
"<text text-anchor=\"start\" x=\"105.5\" y=\"-361.8\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
"<text text-anchor=\"start\" x=\"103\" y=\"-346.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>1&#45;&gt;1</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M34.66,-314.38C44.62,-316.02 54,-313.56 54,-307 54,-302.08 48.73,-299.46 41.89,-299.16\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"34.66,-299.62 41.45,-296.03 38.16,-299.39 41.65,-299.17 41.65,-299.17 41.65,-299.17 38.16,-299.39 41.85,-302.31 34.66,-299.62 34.66,-299.62\"/>\n",
"<text text-anchor=\"start\" x=\"64\" y=\"-310.8\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
"<text text-anchor=\"start\" x=\"54\" y=\"-296.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"70\" y=\"-296.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>3</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"115\" cy=\"-18\" rx=\"18\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"115\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;3 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>2&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M111.51,-292.29C107.14,-286.06 102.32,-278.44 99,-271 82.69,-234.48 81.15,-223.66 76,-184 68.45,-125.89 78.77,-109.35 98,-54 99.54,-49.56 101.5,-44.95 103.54,-40.59\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"106.75,-34 106.51,-41.67 105.22,-37.15 103.68,-40.29 103.68,-40.29 103.68,-40.29 105.22,-37.15 100.85,-38.91 106.75,-34 106.75,-34\"/>\n",
"<text text-anchor=\"start\" x=\"76\" y=\"-172.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b</text>\n",
"<text text-anchor=\"start\" x=\"76\" y=\"-158.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"92\" y=\"-158.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"<!-- 4 -->\n",
"<g id=\"node6\" class=\"node\">\n",
"<title>4</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"167\" cy=\"-118\" rx=\"18\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"167\" y=\"-114.3\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;4 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>2&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M114.66,-290.48C105.94,-269.83 93.77,-232.39 104,-202 112.79,-175.89 133.42,-151.47 148.69,-135.97\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"154.04,-130.68 151.28,-137.84 151.55,-133.14 149.06,-135.6 149.06,-135.6 149.06,-135.6 151.55,-133.14 146.85,-133.36 154.04,-130.68 154.04,-130.68\"/>\n",
"<text text-anchor=\"start\" x=\"104\" y=\"-223.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b</text>\n",
"<text text-anchor=\"start\" x=\"114\" y=\"-208.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- 5 -->\n",
"<g id=\"node7\" class=\"node\">\n",
"<title>5</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"333\" cy=\"-118\" rx=\"18\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"333\" y=\"-114.3\" font-family=\"Lato\" font-size=\"14.00\">5</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;5 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>2&#45;&gt;5</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M138.66,-300.18C164.93,-290.4 216.6,-268.71 252,-238 283.89,-210.34 308.96,-167.38 322.33,-141.34\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"325.63,-134.79 325.29,-142.46 324.05,-137.92 322.48,-141.05 322.48,-141.05 322.48,-141.05 324.05,-137.92 319.66,-139.63 325.63,-134.79 325.63,-134.79\"/>\n",
"<text text-anchor=\"start\" x=\"284\" y=\"-223.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; !b</text>\n",
"<text text-anchor=\"start\" x=\"294\" y=\"-208.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"<!-- 6 -->\n",
"<g id=\"node8\" class=\"node\">\n",
"<title>6</title>\n",
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"167\" cy=\"-220\" rx=\"18\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"167\" y=\"-216.3\" font-family=\"Lato\" font-size=\"14.00\">6</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;6 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>2&#45;&gt;6</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M130.05,-290.8C137.1,-277.47 147.46,-257.92 155.41,-242.9\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"158.87,-236.35 158.38,-244.01 157.24,-239.44 155.6,-242.54 155.6,-242.54 155.6,-242.54 157.24,-239.44 152.81,-241.06 158.87,-236.35 158.87,-236.35\"/>\n",
"<text text-anchor=\"start\" x=\"147\" y=\"-259.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;3 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>3&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M130.92,-26.63C141.15,-28.89 151,-26.01 151,-18 151,-11.87 145.23,-8.75 137.93,-8.63\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"130.92,-9.37 137.55,-5.5 134.4,-9 137.88,-8.63 137.88,-8.63 137.88,-8.63 134.4,-9 138.21,-11.77 130.92,-9.37 130.92,-9.37\"/>\n",
"<text text-anchor=\"start\" x=\"162.5\" y=\"-21.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
"<text text-anchor=\"start\" x=\"151\" y=\"-7.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"167\" y=\"-7.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"<!-- 4&#45;&gt;3 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>4&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M158.88,-101.69C150.17,-85.29 136.3,-59.14 126.48,-40.64\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"123.07,-34.2 129.13,-38.91 124.71,-37.3 126.35,-40.39 126.35,-40.39 126.35,-40.39 124.71,-37.3 123.57,-41.86 123.07,-34.2 123.07,-34.2\"/>\n",
"<text text-anchor=\"start\" x=\"159.5\" y=\"-71.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
"<text text-anchor=\"start\" x=\"147\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"163\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"<!-- 4&#45;&gt;4 -->\n",
"<g id=\"edge11\" class=\"edge\">\n",
"<title>4&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M184.78,-122.49C194.31,-123.26 203,-121.76 203,-118 203,-115.24 198.32,-113.7 192.05,-113.38\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"184.78,-113.51 191.72,-110.23 188.28,-113.44 191.78,-113.38 191.78,-113.38 191.78,-113.38 188.28,-113.44 191.84,-116.53 184.78,-113.51 184.78,-113.51\"/>\n",
"<text text-anchor=\"start\" x=\"203\" y=\"-121.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"<text text-anchor=\"start\" x=\"215\" y=\"-106.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"</g>\n",
"<!-- 4&#45;&gt;4 -->\n",
"<g id=\"edge12\" class=\"edge\">\n",
"<title>4&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M183.89,-124.49C207.95,-129.88 243,-127.72 243,-118 243,-109.19 214.22,-106.59 190.91,-110.19\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"183.89,-111.51 190.19,-107.12 187.33,-110.86 190.77,-110.22 190.77,-110.22 190.77,-110.22 187.33,-110.86 191.35,-113.31 183.89,-111.51 183.89,-111.51\"/>\n",
"<text text-anchor=\"start\" x=\"243\" y=\"-121.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b</text>\n",
"<text text-anchor=\"start\" x=\"245\" y=\"-107.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"261\" y=\"-107.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"<!-- 5&#45;&gt;3 -->\n",
"<g id=\"edge13\" class=\"edge\">\n",
"<title>5&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M318.4,-107.21C314.45,-104.73 310.12,-102.15 306,-100 247.64,-69.51 175.23,-41.26 138.6,-27.6\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"131.76,-25.06 139.42,-24.54 135.04,-26.28 138.33,-27.5 138.33,-27.5 138.33,-27.5 135.04,-26.28 137.23,-30.45 131.76,-25.06 131.76,-25.06\"/>\n",
"<text text-anchor=\"start\" x=\"277\" y=\"-71.8\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
"<text text-anchor=\"start\" x=\"265\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"281\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"<!-- 5&#45;&gt;5 -->\n",
"<g id=\"edge14\" class=\"edge\">\n",
"<title>5&#45;&gt;5</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M348.92,-126.63C359.15,-128.89 369,-126.01 369,-118 369,-111.87 363.23,-108.75 355.93,-108.63\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"348.92,-109.37 355.55,-105.5 352.4,-109 355.88,-108.63 355.88,-108.63 355.88,-108.63 352.4,-109 356.21,-111.77 348.92,-109.37 348.92,-109.37\"/>\n",
"<text text-anchor=\"start\" x=\"371\" y=\"-121.8\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
"<text text-anchor=\"start\" x=\"369\" y=\"-106.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"<!-- 6&#45;&gt;3 -->\n",
"<g id=\"edge15\" class=\"edge\">\n",
"<title>6&#45;&gt;3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M154.59,-206.89C140.16,-191.84 117.14,-164.63 108,-136 98.07,-104.9 103.34,-66.84 108.65,-42.75\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"110.28,-35.75 111.76,-43.28 109.49,-39.16 108.69,-42.56 108.69,-42.56 108.69,-42.56 109.49,-39.16 105.62,-41.85 110.28,-35.75 110.28,-35.75\"/>\n",
"<text text-anchor=\"start\" x=\"108\" y=\"-121.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b</text>\n",
"<text text-anchor=\"start\" x=\"108\" y=\"-107.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"124\" y=\"-107.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"<!-- 6&#45;&gt;4 -->\n",
"<g id=\"edge16\" class=\"edge\">\n",
"<title>6&#45;&gt;4</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M167,-201.58C167,-185.52 167,-161.52 167,-143.52\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"167,-136.22 170.15,-143.22 167,-139.72 167,-143.22 167,-143.22 167,-143.22 167,-139.72 163.85,-143.22 167,-136.22 167,-136.22\"/>\n",
"<text text-anchor=\"start\" x=\"167\" y=\"-172.8\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b</text>\n",
"<text text-anchor=\"start\" x=\"169\" y=\"-158.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
"<text text-anchor=\"start\" x=\"185\" y=\"-158.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"<!-- 6&#45;&gt;5 -->\n",
"<g id=\"edge17\" class=\"edge\">\n",
"<title>6&#45;&gt;5</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M180.07,-207.58C196.75,-193.47 226.93,-169.44 256,-154 276.86,-142.92 284.77,-146.35 306,-136 308.09,-134.98 310.22,-133.84 312.33,-132.64\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"318.48,-128.95 314.1,-135.25 315.48,-130.75 312.47,-132.55 312.47,-132.55 312.47,-132.55 315.48,-130.75 310.85,-129.85 318.48,-128.95 318.48,-128.95\"/>\n",
"<text text-anchor=\"start\" x=\"256\" y=\"-172.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; !b</text>\n",
"<text text-anchor=\"start\" x=\"266\" y=\"-157.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
"</g>\n",
"<!-- 6&#45;&gt;6 -->\n",
"<g id=\"edge18\" class=\"edge\">\n",
"<title>6&#45;&gt;6</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M183.66,-227.38C193.62,-229.02 203,-226.56 203,-220 203,-215.08 197.73,-212.46 190.89,-212.16\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"183.66,-212.62 190.45,-209.03 187.16,-212.39 190.65,-212.17 190.65,-212.17 190.65,-212.17 187.16,-212.39 190.85,-215.31 183.66,-212.62 183.66,-212.62\"/>\n",
"<text text-anchor=\"start\" x=\"203\" y=\"-216.3\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; !b</text>\n",
"</g>\n",
"</g>\n",
"</svg>\n",
"</div>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pos = spot.automaton(\"\"\"HOA: v1 name: \"(a & (Fa R XFb)) | (!a & (G!a U\n",
"XG!b))\" States: 6 Start: 0 AP: 2 \"a\" \"b\" acc-name: Buchi Acceptance: 1\n",
"Inf(0) properties: trans-labels explicit-labels state-acc\n",
"semi-deterministic --BODY-- State: 0 [0] 1 [!0] 2 [!0] 3 State: 1 [!1]\n",
"1 [1] 4 State: 2 {0} [!1] 2 State: 3 [!0] 3 [!0] 5 State: 4 {0} [t] 4\n",
"State: 5 {0} [!0&!1] 5 --END--\"\"\")\n",
"altneg = spot.dualize(pos)\n",
"neg = spot.remove_alternation(altneg)\n",
"display_inline(pos, altneg.show('.bvu'), neg)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"# Issue #382.\n",
"w = spot.parse_word('cycle{!a&b}').as_automaton()\n",
"assert pos.intersects(w) != neg.intersects(w)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.1+"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
Reference in a new issue View git blame Copy permalink