ef106e2860
Fixes #382. * spot/twaalgos/alternation.cc: Here. * tests/python/alternation.ipynb: Add test case. * NEWS: Mention it.
4168 lines
323 KiB
Text
4168 lines
323 KiB
Text
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import spot\n",
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"from spot.jupyter import display_inline\n",
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"spot.setup(show_default='.bav')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Support for alternating automata"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The following automata are what we will use as examples."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"aut1, aut2, aut3, aut4, aut5 = spot.automata('''\n",
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"HOA: v1 tool: \"ltl3ba\" \"1.1.3\" name: \"VWAA for FGa && GFb\" States: 6\n",
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"Start: 0 acc-name: co-Buchi Acceptance: 1 Fin(0) AP: 2 \"a\" \"b\" properties:\n",
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"trans-labels explicit-labels state-acc univ-branch very-weak --BODY--\n",
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"State: 0 \"(FG(a) && GF(b))\" [t] 3&1 State: 1 \"GF(b)\" [(1)] 1 [(!1)]\n",
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"2&1 State: 2 \"F(b)\" {0} [(1)] 5 [(!1)] 2 State: 3 \"FG(a)\" {0} [(0)] 4\n",
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"[t] 3 State: 4 \"G(a)\" [(0)] 4 State: 5 \"t\" [t] 5 --END--\n",
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"/* Example from ADL's PSL2TGBA talk. */\n",
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"HOA: v1 States: 3 Start: 0 acc-name: co-Buchi Acceptance: 1 Fin(0) AP:\n",
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"3 \"a\" \"b\" \"p\" --BODY-- State: 0 \"(a;a*;b)*\" {0} [0] 1 [!0] 2 State: 1\n",
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"\"a*;b;(a;a*;b)*\" {0} [0&1&2] 0&1 [!1&2] 1 [!0&!1] 2 [!0&1&2] 0 State:\n",
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"2 [t] 2 --END--\n",
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"HOA: v1 States: 5 Start: 3 acc-name: co-Buchi Acceptance: 1 Fin(0) AP:\n",
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"3 \"a\" \"b\" \"p\" --BODY-- State: 0 \"(a;a*;b)*\" {0} [0] 1 [!0] 2 State: 1\n",
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"\"a*;b;(a;a*;b)*\" {0} [0&1&2] 0&1 [!1&2] 1 [!0&!1] 2 [!0&1&2] 0 State:\n",
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"2 [t] 2 State: 3 [0] 4&0 State: 4 [t] 3 --END--\n",
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"HOA: v1 States: 3 Start: 0 acc-name: co-Buchi Acceptance: 1 Fin(0) AP:\n",
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"3 \"a\" \"b\" \"p\" --BODY-- State: 0 \"(a;a*;b)*\" {0} [0] 1 [!0] 2 State: 1\n",
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"\"a*;b;(a;a*;b)*\" {0} [0&1&2] 0&1 [!1&2] 1 [!0&!1] 2 [!0&1&2] 0 State:\n",
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"2 [t] 2 --END--\n",
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"HOA: v1 tool: \"ltl3dra\" \"0.2.2\" name: \"VWAA for GFa\" States: 3 Start: 0\n",
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"acc-name: co-Buchi Acceptance: 1 Fin(0) AP: 1 \"a\" properties: trans-labels\n",
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"explicit-labels state-acc univ-branch very-weak --BODY-- State: 0 \"GF(a)\"\n",
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"[t] 1&0 State: 1 \"F(a)\" {0} [(0)] 2 [t] 1 State: 2 \"t\" [t] 2 --END--\n",
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"''')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Various display options"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Here is the default output, using the `bav` options as set by default in the first cell. "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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"</g>\n",
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],
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"text/plain": [
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]
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"display_inline(aut1, aut2, aut3, aut4, aut5)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
|
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"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."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"<g class=\"graph\" id=\"graph0\" transform=\"scale(.6817 .6817) rotate(0) translate(4 524.0802)\">\n",
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"<g class=\"edge\" id=\"edge9\">\n",
|
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"<title>2->5</title>\n",
|
|
"<path d=\"M26.8701,-86.9098C26.8701,-73.2648 26.8701,-56.7955 26.8701,-43.3794\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"26.8701,-36.2775 30.0202,-43.2775 26.8701,-39.7775 26.8702,-43.2775 26.8702,-43.2775 26.8702,-43.2775 26.8701,-39.7775 23.7202,-43.2776 26.8701,-36.2775 26.8701,-36.2775\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"26.8701\" y=\"-57.8\">b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->5 -->\n",
|
|
"<g class=\"edge\" id=\"edge14\">\n",
|
|
"<title>5->5</title>\n",
|
|
"<path d=\"M43.5341,-25.3828C53.4951,-27.0234 62.8701,-24.5625 62.8701,-18 62.8701,-13.0781 57.5966,-10.4634 50.7576,-10.1558\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"43.5341,-10.6172 50.319,-7.0273 47.027,-10.394 50.5199,-10.1709 50.5199,-10.1709 50.5199,-10.1709 47.027,-10.394 50.7207,-13.3145 43.5341,-10.6172 43.5341,-10.6172\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"62.8701\" y=\"-14.3\">1</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4->4 -->\n",
|
|
"<g class=\"edge\" id=\"edge13\">\n",
|
|
"<title>4->4</title>\n",
|
|
"<path d=\"M133.9074,-202.1193C143.728,-203.4212 152.8701,-201.2948 152.8701,-195.7401 152.8701,-191.5741 147.7276,-189.3365 141.0134,-189.0273\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"133.9074,-189.3609 140.7519,-185.886 137.4035,-189.1967 140.8997,-189.0325 140.8997,-189.0325 140.8997,-189.0325 137.4035,-189.1967 141.0474,-192.1791 133.9074,-189.3609 133.9074,-189.3609\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"152.8701\" y=\"-192.0401\">a</text>\n",
|
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"</g>\n",
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|
"</g>\n",
|
|
"</svg></div><div style='vertical-align:text-top;display:inline-block;'><svg height=\"327pt\" viewBox=\"0.00 0.00 193.79 327.48\" width=\"194pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
|
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"<g class=\"graph\" id=\"graph0\" transform=\"scale(1 1) rotate(0) translate(4 323.4802)\">\n",
|
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"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-323.4802 189.7888,-323.4802 189.7888,4 -4,4\" stroke=\"transparent\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"70.3944\" y=\"-305.2802\">Fin(</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"95.3944\" y=\"-305.2802\">⓿</text>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"111.3944\" y=\"-305.2802\">)</text>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"60.3944\" y=\"-291.2802\">[co-Büchi]</text>\n",
|
|
"<!-- I -->\n",
|
|
"<!-- 0 -->\n",
|
|
"<g class=\"node\" id=\"node2\">\n",
|
|
"<title>0</title>\n",
|
|
"<g id=\"a_node2\"><a xlink:title=\"(a;a*;b)*\">\n",
|
|
"<ellipse cx=\"86\" cy=\"-218.6102\" fill=\"#ffffaa\" rx=\"26.7407\" ry=\"26.7407\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"81.5\" y=\"-222.4102\">0</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"78\" y=\"-207.4102\">⓿</text>\n",
|
|
"</a>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"<!-- I->0 -->\n",
|
|
"<g class=\"edge\" id=\"edge1\">\n",
|
|
"<title>I->0</title>\n",
|
|
"<path d=\"M86,-282.2573C86,-279.1051 86,-266.1173 86,-252.6885\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"86,-245.6757 89.1501,-252.6756 86,-249.1757 86.0001,-252.6757 86.0001,-252.6757 86.0001,-252.6757 86,-249.1757 82.8501,-252.6757 86,-245.6757 86,-245.6757\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 1 -->\n",
|
|
"<g class=\"node\" id=\"node3\">\n",
|
|
"<title>1</title>\n",
|
|
"<g id=\"a_node3\"><a xlink:title=\"a*;b;(a;a*;b)*\">\n",
|
|
"<ellipse cx=\"86\" cy=\"-113.8701\" fill=\"#ffffaa\" rx=\"26.7407\" ry=\"26.7407\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"81.5\" y=\"-117.6701\">1</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"78\" y=\"-102.6701\">⓿</text>\n",
|
|
"</a>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"<!-- 0->1 -->\n",
|
|
"<g class=\"edge\" id=\"edge2\">\n",
|
|
"<title>0->1</title>\n",
|
|
"<path d=\"M77.1095,-193.098C74.411,-182.5207 72.5083,-170.0914 74,-158.7401 74.5122,-154.8426 75.2645,-150.8023 76.1468,-146.815\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"77.8518,-139.7373 79.2747,-147.2804 77.032,-143.14 76.2123,-146.5427 76.2123,-146.5427 76.2123,-146.5427 77.032,-143.14 73.1499,-145.8049 77.8518,-139.7373 77.8518,-139.7373\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"74\" y=\"-162.5401\">a</text>\n",
|
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"</g>\n",
|
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"<!-- 2 -->\n",
|
|
"<g class=\"node\" id=\"node4\">\n",
|
|
"<title>2</title>\n",
|
|
"<ellipse cx=\"18\" cy=\"-18\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"18\" y=\"-14.3\">2</text>\n",
|
|
"</g>\n",
|
|
"<!-- 0->2 -->\n",
|
|
"<g class=\"edge\" id=\"edge3\">\n",
|
|
"<title>0->2</title>\n",
|
|
"<path d=\"M70.1054,-196.826C59.8191,-181.7592 46.9152,-160.8734 39,-140.7401 27.0818,-110.4247 29.2415,-101.1495 24,-69 22.6242,-60.5612 21.4371,-51.2874 20.4905,-42.9887\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"19.7218,-35.9924 23.6175,-42.6064 20.1041,-39.4714 20.4864,-42.9505 20.4864,-42.9505 20.4864,-42.9505 20.1041,-39.4714 17.3552,-43.2946 19.7218,-35.9924 19.7218,-35.9924\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"39\" y=\"-110.1701\">!a</text>\n",
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"</g>\n",
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"<!-- 1->0 -->\n",
|
|
"<g class=\"edge\" id=\"edge9\">\n",
|
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"<title>1->0</title>\n",
|
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"<path d=\"M86,-140.7518C86,-154.0554 86,-170.261 86,-184.4358\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"86,-191.637 82.8501,-184.6369 86,-188.137 86.0001,-184.637 86.0001,-184.637 86.0001,-184.637 86,-188.137 89.1501,-184.637 86,-191.637 86,-191.637\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"86\" y=\"-162.5401\">!a & b & p</text>\n",
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"</g>\n",
|
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"<!-- 1->1 -->\n",
|
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"<g class=\"edge\" id=\"edge7\">\n",
|
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"<title>1->1</title>\n",
|
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"<path d=\"M111.37,-123.5344C121.9238,-124.2009 130.8701,-120.9794 130.8701,-113.8701 130.8701,-108.4269 125.6259,-105.2629 118.4312,-104.3778\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"111.37,-104.2058 118.4447,-101.2273 114.869,-104.2911 118.3679,-104.3764 118.3679,-104.3764 118.3679,-104.3764 114.869,-104.2911 118.2911,-107.5254 111.37,-104.2058 111.37,-104.2058\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"130.8701\" y=\"-110.1701\">!b & p</text>\n",
|
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"</g>\n",
|
|
"<!-- 1->2 -->\n",
|
|
"<g class=\"edge\" id=\"edge8\">\n",
|
|
"<title>1->2</title>\n",
|
|
"<path d=\"M63.7074,-98.5189C53.74,-90.6832 42.5599,-80.4015 35,-69 29.7908,-61.1437 26.0458,-51.5481 23.4206,-42.8085\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"21.5487,-36.0326 26.449,-41.941 22.4807,-39.4062 23.4128,-42.7799 23.4128,-42.7799 23.4128,-42.7799 22.4807,-39.4062 20.3765,-43.6187 21.5487,-36.0326 21.5487,-36.0326\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"35\" y=\"-57.8\">!a & !b</text>\n",
|
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"</g>\n",
|
|
"<!-- -1 -->\n",
|
|
"<g class=\"node\" id=\"node5\">\n",
|
|
"<title>-1</title>\n",
|
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"<ellipse cx=\"173\" cy=\"-18\" fill=\"#ffffaa\" rx=\"1.8\" ry=\"1.8\" stroke=\"#000000\"/>\n",
|
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"</g>\n",
|
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"<!-- 1->-1 -->\n",
|
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"<g class=\"edge\" id=\"edge4\">\n",
|
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"<title>1->-1</title>\n",
|
|
"<path d=\"M86.7675,-86.9417C88.2935,-75.7727 91.7063,-63.2839 99,-54 115.6814,-32.7669 148.066,-23.2637 163.8748,-19.7437\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"none\" points=\"164.3646,-22.1444 170.7471,-18.3673 163.4022,-17.3398 164.3646,-22.1444\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"99\" y=\"-57.8\">a & b & p</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2->2 -->\n",
|
|
"<g class=\"edge\" id=\"edge10\">\n",
|
|
"<title>2->2</title>\n",
|
|
"<path d=\"M34.6641,-25.3828C44.625,-27.0234 54,-24.5625 54,-18 54,-13.0781 48.7266,-10.4634 41.8876,-10.1558\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"34.6641,-10.6172 41.449,-7.0273 38.1569,-10.394 41.6498,-10.1709 41.6498,-10.1709 41.6498,-10.1709 38.1569,-10.394 41.8507,-13.3145 34.6641,-10.6172 34.6641,-10.6172\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"58.5\" y=\"-14.3\">1</text>\n",
|
|
"</g>\n",
|
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"<!-- -1->0 -->\n",
|
|
"<g class=\"edge\" id=\"edge5\">\n",
|
|
"<title>-1->0</title>\n",
|
|
"<path d=\"M173.564,-19.7969C177.0283,-31.1379 194.7654,-93.822 179,-140.7401 169.1903,-169.9339 140.2364,-191.1861 117.2137,-204.0425\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"110.8982,-207.4457 115.5662,-201.352 113.9794,-205.7853 117.0605,-204.125 117.0605,-204.125 117.0605,-204.125 113.9794,-205.7853 118.5548,-206.898 110.8982,-207.4457 110.8982,-207.4457\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- -1->1 -->\n",
|
|
"<g class=\"edge\" id=\"edge6\">\n",
|
|
"<title>-1->1</title>\n",
|
|
"<path d=\"M172.9533,-20.1844C172.6868,-27.7353 170.9041,-53.1374 159,-69 148.4691,-83.0327 132.1479,-93.659 117.6064,-101.0393\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"111.0777,-104.2023 116.0039,-98.3154 114.2275,-102.6763 117.3773,-101.1502 117.3773,-101.1502 117.3773,-101.1502 114.2275,-102.6763 118.7508,-103.9851 111.0777,-104.2023 111.0777,-104.2023\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"</svg></div><div style='vertical-align:text-top;display:inline-block;'><svg height=\"360pt\" viewBox=\"0.00 0.00 149.55 360.00\" width=\"150pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
|
|
"<g class=\"graph\" id=\"graph0\" transform=\"scale(.7717 .7717) rotate(0) translate(4 462.4802)\">\n",
|
|
"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-462.4802 189.7888,-462.4802 189.7888,4 -4,4\" stroke=\"transparent\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"70.3944\" y=\"-444.2802\">Fin(</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"95.3944\" y=\"-444.2802\">⓿</text>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"111.3944\" y=\"-444.2802\">)</text>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"60.3944\" y=\"-430.2802\">[co-Büchi]</text>\n",
|
|
"<!-- I -->\n",
|
|
"<!-- 3 -->\n",
|
|
"<g class=\"node\" id=\"node2\">\n",
|
|
"<title>3</title>\n",
|
|
"<ellipse cx=\"130\" cy=\"-366.4802\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"130\" y=\"-362.7802\">3</text>\n",
|
|
"</g>\n",
|
|
"<!-- I->3 -->\n",
|
|
"<g class=\"edge\" id=\"edge1\">\n",
|
|
"<title>I->3</title>\n",
|
|
"<path d=\"M130,-421.3569C130,-418.3023 130,-404.5354 130,-391.5561\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"130,-384.4995 133.1501,-391.4994 130,-387.9995 130.0001,-391.4995 130.0001,-391.4995 130.0001,-391.4995 130,-387.9995 126.8501,-391.4995 130,-384.4995 130,-384.4995\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- -4 -->\n",
|
|
"<g class=\"node\" id=\"node7\">\n",
|
|
"<title>-4</title>\n",
|
|
"<ellipse cx=\"111\" cy=\"-289.9802\" fill=\"#ffffaa\" rx=\"1.8\" ry=\"1.8\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 3->-4 -->\n",
|
|
"<g class=\"edge\" id=\"edge11\">\n",
|
|
"<title>3->-4</title>\n",
|
|
"<path d=\"M125.5933,-348.7373C121.7119,-333.1095 116.22,-310.9976 113.2012,-298.8428\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"none\" points=\"115.5636,-298.1901 111.4984,-291.9871 110.8081,-299.3713 115.5636,-298.1901\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"121\" y=\"-319.2802\">a</text>\n",
|
|
"</g>\n",
|
|
"<!-- 0 -->\n",
|
|
"<g class=\"node\" id=\"node3\">\n",
|
|
"<title>0</title>\n",
|
|
"<g id=\"a_node3\"><a xlink:title=\"(a;a*;b)*\">\n",
|
|
"<ellipse cx=\"86\" cy=\"-218.6102\" fill=\"#ffffaa\" rx=\"26.7407\" ry=\"26.7407\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"81.5\" y=\"-222.4102\">0</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"78\" y=\"-207.4102\">⓿</text>\n",
|
|
"</a>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"<!-- 1 -->\n",
|
|
"<g class=\"node\" id=\"node4\">\n",
|
|
"<title>1</title>\n",
|
|
"<g id=\"a_node4\"><a xlink:title=\"a*;b;(a;a*;b)*\">\n",
|
|
"<ellipse cx=\"86\" cy=\"-113.8701\" fill=\"#ffffaa\" rx=\"26.7407\" ry=\"26.7407\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"81.5\" y=\"-117.6701\">1</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"78\" y=\"-102.6701\">⓿</text>\n",
|
|
"</a>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"<!-- 0->1 -->\n",
|
|
"<g class=\"edge\" id=\"edge2\">\n",
|
|
"<title>0->1</title>\n",
|
|
"<path d=\"M77.8518,-192.7429C76.2536,-186.5777 74.8195,-179.9762 74,-173.7401 72.823,-164.7832 73.7593,-155.1552 75.5325,-146.2954\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"77.1095,-139.3822 78.6237,-146.9075 76.331,-142.7946 75.5526,-146.2069 75.5526,-146.2069 75.5526,-146.2069 76.331,-142.7946 72.4815,-145.5063 77.1095,-139.3822 77.1095,-139.3822\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"74\" y=\"-162.5401\">a</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2 -->\n",
|
|
"<g class=\"node\" id=\"node5\">\n",
|
|
"<title>2</title>\n",
|
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"<ellipse cx=\"18\" cy=\"-18\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"18\" y=\"-14.3\">2</text>\n",
|
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"</g>\n",
|
|
"<!-- 0->2 -->\n",
|
|
"<g class=\"edge\" id=\"edge3\">\n",
|
|
"<title>0->2</title>\n",
|
|
"<path d=\"M70.1054,-196.826C59.8191,-181.7592 46.9152,-160.8734 39,-140.7401 27.0818,-110.4247 29.2415,-101.1495 24,-69 22.6242,-60.5612 21.4371,-51.2874 20.4905,-42.9887\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"19.7218,-35.9924 23.6175,-42.6064 20.1041,-39.4714 20.4864,-42.9505 20.4864,-42.9505 20.4864,-42.9505 20.1041,-39.4714 17.3552,-43.2946 19.7218,-35.9924 19.7218,-35.9924\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"39\" y=\"-110.1701\">!a</text>\n",
|
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"</g>\n",
|
|
"<!-- 1->0 -->\n",
|
|
"<g class=\"edge\" id=\"edge9\">\n",
|
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"<title>1->0</title>\n",
|
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"<path d=\"M86,-140.7518C86,-154.0554 86,-170.261 86,-184.4358\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"86,-191.637 82.8501,-184.6369 86,-188.137 86.0001,-184.637 86.0001,-184.637 86.0001,-184.637 86,-188.137 89.1501,-184.637 86,-191.637 86,-191.637\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"86\" y=\"-162.5401\">!a & b & p</text>\n",
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"</g>\n",
|
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"<!-- 1->1 -->\n",
|
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"<g class=\"edge\" id=\"edge7\">\n",
|
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"<title>1->1</title>\n",
|
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"<path d=\"M111.37,-123.5344C121.9238,-124.2009 130.8701,-120.9794 130.8701,-113.8701 130.8701,-108.4269 125.6259,-105.2629 118.4312,-104.3778\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"111.37,-104.2058 118.4447,-101.2273 114.869,-104.2911 118.3679,-104.3764 118.3679,-104.3764 118.3679,-104.3764 114.869,-104.2911 118.2911,-107.5254 111.37,-104.2058 111.37,-104.2058\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"130.8701\" y=\"-110.1701\">!b & p</text>\n",
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"</g>\n",
|
|
"<!-- 1->2 -->\n",
|
|
"<g class=\"edge\" id=\"edge8\">\n",
|
|
"<title>1->2</title>\n",
|
|
"<path d=\"M63.7074,-98.5189C53.74,-90.6832 42.5599,-80.4015 35,-69 29.7908,-61.1437 26.0458,-51.5481 23.4206,-42.8085\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"21.5487,-36.0326 26.449,-41.941 22.4807,-39.4062 23.4128,-42.7799 23.4128,-42.7799 23.4128,-42.7799 22.4807,-39.4062 20.3765,-43.6187 21.5487,-36.0326 21.5487,-36.0326\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"35\" y=\"-57.8\">!a & !b</text>\n",
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"</g>\n",
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|
"<!-- -1 -->\n",
|
|
"<g class=\"node\" id=\"node6\">\n",
|
|
"<title>-1</title>\n",
|
|
"<ellipse cx=\"173\" cy=\"-18\" fill=\"#ffffaa\" rx=\"1.8\" ry=\"1.8\" stroke=\"#000000\"/>\n",
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|
"</g>\n",
|
|
"<!-- 1->-1 -->\n",
|
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"<g class=\"edge\" id=\"edge4\">\n",
|
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"<title>1->-1</title>\n",
|
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"<path d=\"M86.7675,-86.9417C88.2935,-75.7727 91.7063,-63.2839 99,-54 115.6814,-32.7669 148.066,-23.2637 163.8748,-19.7437\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"none\" points=\"164.3646,-22.1444 170.7471,-18.3673 163.4022,-17.3398 164.3646,-22.1444\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"99\" y=\"-57.8\">a & b & p</text>\n",
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"</g>\n",
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|
"<!-- 2->2 -->\n",
|
|
"<g class=\"edge\" id=\"edge10\">\n",
|
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"<title>2->2</title>\n",
|
|
"<path d=\"M34.6641,-25.3828C44.625,-27.0234 54,-24.5625 54,-18 54,-13.0781 48.7266,-10.4634 41.8876,-10.1558\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"34.6641,-10.6172 41.449,-7.0273 38.1569,-10.394 41.6498,-10.1709 41.6498,-10.1709 41.6498,-10.1709 38.1569,-10.394 41.8507,-13.3145 34.6641,-10.6172 34.6641,-10.6172\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"58.5\" y=\"-14.3\">1</text>\n",
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"</g>\n",
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"<!-- -1->0 -->\n",
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"<g class=\"edge\" id=\"edge5\">\n",
|
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"<title>-1->0</title>\n",
|
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"<path d=\"M173.564,-19.7969C177.0283,-31.1379 194.7654,-93.822 179,-140.7401 173.1392,-158.182 167.8646,-161.6429 154,-173.7401 141.7045,-184.4682 135.6779,-182.8414 122,-191.7401 119.1277,-193.6088 116.1809,-195.6276 113.2698,-197.6898\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"107.3797,-201.9499 111.2056,-195.2951 110.2157,-199.8987 113.0517,-197.8475 113.0517,-197.8475 113.0517,-197.8475 110.2157,-199.8987 114.8977,-200.3999 107.3797,-201.9499 107.3797,-201.9499\" stroke=\"#000000\"/>\n",
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"</g>\n",
|
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"<!-- -1->1 -->\n",
|
|
"<g class=\"edge\" id=\"edge6\">\n",
|
|
"<title>-1->1</title>\n",
|
|
"<path d=\"M172.9533,-20.1844C172.6868,-27.7353 170.9041,-53.1374 159,-69 148.4691,-83.0327 132.1479,-93.659 117.6064,-101.0393\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"111.0777,-104.2023 116.0039,-98.3154 114.2275,-102.6763 117.3773,-101.1502 117.3773,-101.1502 117.3773,-101.1502 114.2275,-102.6763 118.7508,-103.9851 111.0777,-104.2023 111.0777,-104.2023\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- -4->0 -->\n",
|
|
"<g class=\"edge\" id=\"edge12\">\n",
|
|
"<title>-4->0</title>\n",
|
|
"<path d=\"M110.382,-288.216C108.5302,-282.9294 102.8184,-266.6235 97.3886,-251.1223\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"94.9285,-244.0993 100.2156,-249.6643 96.0856,-247.4025 97.2427,-250.7057 97.2427,-250.7057 97.2427,-250.7057 96.0856,-247.4025 94.2698,-251.7471 94.9285,-244.0993 94.9285,-244.0993\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 4 -->\n",
|
|
"<g class=\"node\" id=\"node8\">\n",
|
|
"<title>4</title>\n",
|
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"<ellipse cx=\"149\" cy=\"-218.6102\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"149\" y=\"-214.9102\">4</text>\n",
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|
"</g>\n",
|
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"<!-- -4->4 -->\n",
|
|
"<g class=\"edge\" id=\"edge13\">\n",
|
|
"<title>-4->4</title>\n",
|
|
"<path d=\"M111.9393,-288.216C115.3798,-281.7542 127.586,-258.829 137.061,-241.0335\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"140.4069,-234.7494 139.8975,-242.4086 138.762,-237.8388 137.117,-240.9282 137.117,-240.9282 137.117,-240.9282 138.762,-237.8388 134.3366,-239.4478 140.4069,-234.7494 140.4069,-234.7494\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 4->3 -->\n",
|
|
"<g class=\"edge\" id=\"edge14\">\n",
|
|
"<title>4->3</title>\n",
|
|
"<path d=\"M146.6512,-236.8903C143.2787,-263.1372 137.0522,-311.5954 133.2429,-341.2416\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"132.3298,-348.3485 130.0976,-341.0041 132.7759,-344.877 133.222,-341.4055 133.222,-341.4055 133.222,-341.4055 132.7759,-344.877 136.3463,-341.807 132.3298,-348.3485 132.3298,-348.3485\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"145.5\" y=\"-286.2802\">1</text>\n",
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"</g>\n",
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"</g>\n",
|
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"</svg></div><div style='vertical-align:text-top;display:inline-block;'><svg height=\"327pt\" viewBox=\"0.00 0.00 193.79 327.48\" width=\"194pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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"<g class=\"graph\" id=\"graph0\" transform=\"scale(1 1) rotate(0) translate(4 323.4802)\">\n",
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"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-323.4802 189.7888,-323.4802 189.7888,4 -4,4\" stroke=\"transparent\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"70.3944\" y=\"-305.2802\">Fin(</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"95.3944\" y=\"-305.2802\">⓿</text>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"111.3944\" y=\"-305.2802\">)</text>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"60.3944\" y=\"-291.2802\">[co-Büchi]</text>\n",
|
|
"<!-- I -->\n",
|
|
"<!-- 0 -->\n",
|
|
"<g class=\"node\" id=\"node2\">\n",
|
|
"<title>0</title>\n",
|
|
"<g id=\"a_node2\"><a xlink:title=\"(a;a*;b)*\">\n",
|
|
"<ellipse cx=\"86\" cy=\"-218.6102\" fill=\"#ffffaa\" rx=\"26.7407\" ry=\"26.7407\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"81.5\" y=\"-222.4102\">0</text>\n",
|
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"78\" y=\"-207.4102\">⓿</text>\n",
|
|
"</a>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"<!-- I->0 -->\n",
|
|
"<g class=\"edge\" id=\"edge1\">\n",
|
|
"<title>I->0</title>\n",
|
|
"<path d=\"M86,-282.2573C86,-279.1051 86,-266.1173 86,-252.6885\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"86,-245.6757 89.1501,-252.6756 86,-249.1757 86.0001,-252.6757 86.0001,-252.6757 86.0001,-252.6757 86,-249.1757 82.8501,-252.6757 86,-245.6757 86,-245.6757\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 1 -->\n",
|
|
"<g class=\"node\" id=\"node3\">\n",
|
|
"<title>1</title>\n",
|
|
"<g id=\"a_node3\"><a xlink:title=\"a*;b;(a;a*;b)*\">\n",
|
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"<ellipse cx=\"86\" cy=\"-113.8701\" fill=\"#ffffaa\" rx=\"26.7407\" ry=\"26.7407\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"81.5\" y=\"-117.6701\">1</text>\n",
|
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"78\" y=\"-102.6701\">⓿</text>\n",
|
|
"</a>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"<!-- 0->1 -->\n",
|
|
"<g class=\"edge\" id=\"edge2\">\n",
|
|
"<title>0->1</title>\n",
|
|
"<path d=\"M77.1095,-193.098C74.411,-182.5207 72.5083,-170.0914 74,-158.7401 74.5122,-154.8426 75.2645,-150.8023 76.1468,-146.815\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"77.8518,-139.7373 79.2747,-147.2804 77.032,-143.14 76.2123,-146.5427 76.2123,-146.5427 76.2123,-146.5427 77.032,-143.14 73.1499,-145.8049 77.8518,-139.7373 77.8518,-139.7373\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"74\" y=\"-162.5401\">a</text>\n",
|
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"</g>\n",
|
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"<!-- 2 -->\n",
|
|
"<g class=\"node\" id=\"node4\">\n",
|
|
"<title>2</title>\n",
|
|
"<ellipse cx=\"18\" cy=\"-18\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"18\" y=\"-14.3\">2</text>\n",
|
|
"</g>\n",
|
|
"<!-- 0->2 -->\n",
|
|
"<g class=\"edge\" id=\"edge3\">\n",
|
|
"<title>0->2</title>\n",
|
|
"<path d=\"M70.1054,-196.826C59.8191,-181.7592 46.9152,-160.8734 39,-140.7401 27.0818,-110.4247 29.2415,-101.1495 24,-69 22.6242,-60.5612 21.4371,-51.2874 20.4905,-42.9887\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"19.7218,-35.9924 23.6175,-42.6064 20.1041,-39.4714 20.4864,-42.9505 20.4864,-42.9505 20.4864,-42.9505 20.1041,-39.4714 17.3552,-43.2946 19.7218,-35.9924 19.7218,-35.9924\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"39\" y=\"-110.1701\">!a</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1->0 -->\n",
|
|
"<g class=\"edge\" id=\"edge9\">\n",
|
|
"<title>1->0</title>\n",
|
|
"<path d=\"M86,-140.7518C86,-154.0554 86,-170.261 86,-184.4358\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"86,-191.637 82.8501,-184.6369 86,-188.137 86.0001,-184.637 86.0001,-184.637 86.0001,-184.637 86,-188.137 89.1501,-184.637 86,-191.637 86,-191.637\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"86\" y=\"-162.5401\">!a & b & p</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1->1 -->\n",
|
|
"<g class=\"edge\" id=\"edge7\">\n",
|
|
"<title>1->1</title>\n",
|
|
"<path d=\"M111.37,-123.5344C121.9238,-124.2009 130.8701,-120.9794 130.8701,-113.8701 130.8701,-108.4269 125.6259,-105.2629 118.4312,-104.3778\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"111.37,-104.2058 118.4447,-101.2273 114.869,-104.2911 118.3679,-104.3764 118.3679,-104.3764 118.3679,-104.3764 114.869,-104.2911 118.2911,-107.5254 111.37,-104.2058 111.37,-104.2058\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"130.8701\" y=\"-110.1701\">!b & p</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1->2 -->\n",
|
|
"<g class=\"edge\" id=\"edge8\">\n",
|
|
"<title>1->2</title>\n",
|
|
"<path d=\"M63.7074,-98.5189C53.74,-90.6832 42.5599,-80.4015 35,-69 29.7908,-61.1437 26.0458,-51.5481 23.4206,-42.8085\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"21.5487,-36.0326 26.449,-41.941 22.4807,-39.4062 23.4128,-42.7799 23.4128,-42.7799 23.4128,-42.7799 22.4807,-39.4062 20.3765,-43.6187 21.5487,-36.0326 21.5487,-36.0326\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"35\" y=\"-57.8\">!a & !b</text>\n",
|
|
"</g>\n",
|
|
"<!-- -1 -->\n",
|
|
"<g class=\"node\" id=\"node5\">\n",
|
|
"<title>-1</title>\n",
|
|
"<ellipse cx=\"173\" cy=\"-18\" fill=\"#ffffaa\" rx=\"1.8\" ry=\"1.8\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 1->-1 -->\n",
|
|
"<g class=\"edge\" id=\"edge4\">\n",
|
|
"<title>1->-1</title>\n",
|
|
"<path d=\"M86.7675,-86.9417C88.2935,-75.7727 91.7063,-63.2839 99,-54 115.6814,-32.7669 148.066,-23.2637 163.8748,-19.7437\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"none\" points=\"164.3646,-22.1444 170.7471,-18.3673 163.4022,-17.3398 164.3646,-22.1444\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"99\" y=\"-57.8\">a & b & p</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2->2 -->\n",
|
|
"<g class=\"edge\" id=\"edge10\">\n",
|
|
"<title>2->2</title>\n",
|
|
"<path d=\"M34.6641,-25.3828C44.625,-27.0234 54,-24.5625 54,-18 54,-13.0781 48.7266,-10.4634 41.8876,-10.1558\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"34.6641,-10.6172 41.449,-7.0273 38.1569,-10.394 41.6498,-10.1709 41.6498,-10.1709 41.6498,-10.1709 38.1569,-10.394 41.8507,-13.3145 34.6641,-10.6172 34.6641,-10.6172\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"58.5\" y=\"-14.3\">1</text>\n",
|
|
"</g>\n",
|
|
"<!-- -1->0 -->\n",
|
|
"<g class=\"edge\" id=\"edge5\">\n",
|
|
"<title>-1->0</title>\n",
|
|
"<path d=\"M173.564,-19.7969C177.0283,-31.1379 194.7654,-93.822 179,-140.7401 169.1903,-169.9339 140.2364,-191.1861 117.2137,-204.0425\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"110.8982,-207.4457 115.5662,-201.352 113.9794,-205.7853 117.0605,-204.125 117.0605,-204.125 117.0605,-204.125 113.9794,-205.7853 118.5548,-206.898 110.8982,-207.4457 110.8982,-207.4457\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- -1->1 -->\n",
|
|
"<g class=\"edge\" id=\"edge6\">\n",
|
|
"<title>-1->1</title>\n",
|
|
"<path d=\"M172.9533,-20.1844C172.6868,-27.7353 170.9041,-53.1374 159,-69 148.4691,-83.0327 132.1479,-93.659 117.6064,-101.0393\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"111.0777,-104.2023 116.0039,-98.3154 114.2275,-102.6763 117.3773,-101.1502 117.3773,-101.1502 117.3773,-101.1502 114.2275,-102.6763 118.7508,-103.9851 111.0777,-104.2023 111.0777,-104.2023\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"</svg></div><div style='vertical-align:text-top;display:inline-block;'><svg height=\"350pt\" viewBox=\"0.00 0.00 89.00 350.34\" width=\"89pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
|
|
"<g class=\"graph\" id=\"graph0\" transform=\"scale(1 1) rotate(0) translate(4 346.3401)\">\n",
|
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"<title>VWAA for GFa</title>\n",
|
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"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-346.3401 85,-346.3401 85,4 -4,4\" stroke=\"transparent\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"18\" y=\"-328.1401\">Fin(</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"43\" y=\"-328.1401\">⓿</text>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"59\" y=\"-328.1401\">)</text>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"8\" y=\"-314.1401\">[co-Büchi]</text>\n",
|
|
"<!-- I -->\n",
|
|
"<!-- 0 -->\n",
|
|
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"<title>0</title>\n",
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"</g>\n",
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"</g>\n",
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"<!-- I->0 -->\n",
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"<g class=\"edge\" id=\"edge1\">\n",
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"<title>I->0</title>\n",
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"</g>\n",
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"</g>\n",
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"<g class=\"edge\" id=\"edge2\">\n",
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"<g class=\"edge\" id=\"edge3\">\n",
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"<title>-1->0</title>\n",
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"</g>\n",
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"<!-- 1 -->\n",
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"<g class=\"node\" id=\"node4\">\n",
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"<title>1</title>\n",
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"<g id=\"a_node4\"><a xlink:title=\"F(a)\">\n",
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"</g>\n",
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"</g>\n",
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"<title>2</title>\n",
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"<g id=\"a_node5\"><a xlink:title=\"t\">\n",
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"</g>\n",
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"<!-- 1->2 -->\n",
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"<g class=\"edge\" id=\"edge5\">\n",
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"<title>1->2</title>\n",
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"<!-- 2->2 -->\n",
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"<g class=\"edge\" id=\"edge7\">\n",
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"<title>2->2</title>\n",
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"<path d=\"M43.6641,-25.3828C53.625,-27.0234 63,-24.5625 63,-18 63,-13.0781 57.7266,-10.4634 50.8876,-10.1558\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"63\" y=\"-14.3\">1</text>\n",
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"</g>\n",
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"</g>\n",
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"</svg></div>"
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],
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"text/plain": [
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"<IPython.core.display.HTML object>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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|
],
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|
"source": [
|
|
"display_inline(aut1, aut2, aut3, aut4, aut5, show='.bav1')"
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|
]
|
|
},
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{
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|
"cell_type": "markdown",
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"metadata": {},
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"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,
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|
"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<div style='vertical-align:text-top;display:inline-block;'><svg height=\"360pt\" viewBox=\"0.00 0.00 130.50 360.00\" width=\"130pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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"<g class=\"graph\" id=\"graph0\" transform=\"scale(.7301 .7301) rotate(0) translate(4 489.0802)\">\n",
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"<title>VWAA for FGa && GFb</title>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"52.8701\" y=\"-456.8802\">[co-Büchi]</text>\n",
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"</g>\n",
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"</g>\n",
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"</g>\n",
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"</g>\n",
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"</g>\n",
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"<title>4</title>\n",
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"<g id=\"a_node9\"><a xlink:title=\"G(a)\">\n",
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"</g>\n",
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|
"</g>\n",
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"<!-- 3->4 -->\n",
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"<title>3->4</title>\n",
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"<path d=\"M116.8701,-229.6499C116.8701,-216.005 116.8701,-199.5356 116.8701,-186.1195\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<title>-4->1</title>\n",
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"<path d=\"M26.8701,-162.9456C26.8701,-171.9744 26.8701,-206.7972 26.8701,-231.3333\" fill=\"none\" stroke=\"#000000\"/>\n",
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"</g>\n",
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"<g class=\"node\" id=\"node7\">\n",
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"<title>2</title>\n",
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"<g id=\"a_node7\"><a xlink:title=\"F(b)\">\n",
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"</g>\n",
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"</g>\n",
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"<!-- -4->2 -->\n",
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"<g class=\"edge\" id=\"edge8\">\n",
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"<title>-4->2</title>\n",
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"<title>2->2</title>\n",
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"<path d=\"M52.6914,-87.0697C63.0476,-87.533 71.7401,-84.7997 71.7401,-78.8701 71.7401,-74.4228 66.8506,-71.7735 60.0368,-70.9223\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"52.6914,-70.6704 59.7953,-67.7623 56.1893,-70.7904 59.6873,-70.9104 59.6873,-70.9104 59.6873,-70.9104 56.1893,-70.7904 59.5793,-74.0586 52.6914,-70.6704 52.6914,-70.6704\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"71.7401\" y=\"-75.1701\">!b</text>\n",
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"</g>\n",
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"<!-- T5T2 -->\n",
|
|
"<!-- 2->T5T2 -->\n",
|
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"<g class=\"edge\" id=\"edge9\">\n",
|
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"<title>2->T5T2</title>\n",
|
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"<path d=\"M26.8701,-51.8995C26.8701,-36.6517 26.8701,-18.6623 26.8701,-8.5175\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"26.8701,-1.2289 30.0202,-8.2288 26.8701,-4.7289 26.8702,-8.2289 26.8702,-8.2289 26.8702,-8.2289 26.8701,-4.7289 23.7202,-8.2289 26.8701,-1.2289 26.8701,-1.2289\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"26.8701\" y=\"-22.8\">b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4->4 -->\n",
|
|
"<g class=\"edge\" id=\"edge13\">\n",
|
|
"<title>4->4</title>\n",
|
|
"<path d=\"M133.9074,-167.1193C143.728,-168.4212 152.8701,-166.2948 152.8701,-160.7401 152.8701,-156.5741 147.7276,-154.3365 141.0134,-154.0273\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"133.9074,-154.3609 140.7519,-150.886 137.4035,-154.1967 140.8997,-154.0325 140.8997,-154.0325 140.8997,-154.0325 137.4035,-154.1967 141.0474,-157.1791 133.9074,-154.3609 133.9074,-154.3609\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"152.8701\" y=\"-157.0401\">a</text>\n",
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"</g>\n",
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"</g>\n",
|
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"</svg></div><div style='vertical-align:text-top;display:inline-block;'><svg height=\"295pt\" viewBox=\"0.00 0.00 172.05 295.08\" width=\"172pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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"<g class=\"graph\" id=\"graph0\" transform=\"scale(1 1) rotate(0) translate(4 291.0802)\">\n",
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"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-291.0802 168.052,-291.0802 168.052,4 -4,4\" stroke=\"transparent\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"59.526\" y=\"-272.8802\">Fin(</text>\n",
|
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"84.526\" y=\"-272.8802\">⓿</text>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"100.526\" y=\"-272.8802\">)</text>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"49.526\" y=\"-258.8802\">[co-Büchi]</text>\n",
|
|
"<!-- I -->\n",
|
|
"<!-- 0 -->\n",
|
|
"<g class=\"node\" id=\"node2\">\n",
|
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"<title>0</title>\n",
|
|
"<g id=\"a_node2\"><a xlink:title=\"(a;a*;b)*\">\n",
|
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"<ellipse cx=\"104.0978\" cy=\"-186.2102\" fill=\"#ffffaa\" rx=\"26.7407\" ry=\"26.7407\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"99.5978\" y=\"-190.0102\">0</text>\n",
|
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"96.0978\" y=\"-175.0102\">⓿</text>\n",
|
|
"</a>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"<!-- I->0 -->\n",
|
|
"<g class=\"edge\" id=\"edge1\">\n",
|
|
"<title>I->0</title>\n",
|
|
"<path d=\"M104.0978,-249.8573C104.0978,-246.7051 104.0978,-233.7173 104.0978,-220.2885\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"104.0978,-213.2757 107.2479,-220.2756 104.0978,-216.7757 104.0979,-220.2757 104.0979,-220.2757 104.0979,-220.2757 104.0978,-216.7757 100.9479,-220.2757 104.0978,-213.2757 104.0978,-213.2757\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 1 -->\n",
|
|
"<g class=\"node\" id=\"node3\">\n",
|
|
"<title>1</title>\n",
|
|
"<g id=\"a_node3\"><a xlink:title=\"a*;b;(a;a*;b)*\">\n",
|
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"<ellipse cx=\"46.0978\" cy=\"-81.4701\" fill=\"#ffffaa\" rx=\"26.7407\" ry=\"26.7407\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"41.5978\" y=\"-85.2701\">1</text>\n",
|
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"38.0978\" y=\"-70.2701\">⓿</text>\n",
|
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"</a>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"<!-- 0->1 -->\n",
|
|
"<g class=\"edge\" id=\"edge2\">\n",
|
|
"<title>0->1</title>\n",
|
|
"<path d=\"M78.5833,-177.23C62.6836,-170.152 43.5164,-158.565 34.0978,-141.3401 29.3095,-132.5832 29.6662,-122.1697 32.0312,-112.5025\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"34.0633,-105.6296 35.0992,-113.2355 33.0709,-108.9859 32.0785,-112.3423 32.0785,-112.3423 32.0785,-112.3423 33.0709,-108.9859 29.0577,-111.4491 34.0633,-105.6296 34.0633,-105.6296\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"34.0978\" y=\"-130.1401\">a</text>\n",
|
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"</g>\n",
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"<!-- T2T0 -->\n",
|
|
"<!-- 0->T2T0 -->\n",
|
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"<g class=\"edge\" id=\"edge3\">\n",
|
|
"<title>0->T2T0</title>\n",
|
|
"<path d=\"M116.3326,-162.1599C119.6144,-155.47 123.0856,-148.1663 126.0978,-141.3401 132.4617,-126.9181 133.7038,-123.1522 139.0978,-108.3401 141.4545,-101.8684 143.9252,-94.439 145.6804,-89.0349\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"147.8878,-82.1392 148.7537,-89.7664 146.8207,-85.4726 145.7536,-88.806 145.7536,-88.806 145.7536,-88.806 146.8207,-85.4726 142.7536,-87.8456 147.8878,-82.1392 147.8878,-82.1392\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"132.0978\" y=\"-130.1401\">!a</text>\n",
|
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"</g>\n",
|
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"<!-- 1->0 -->\n",
|
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"<g class=\"edge\" id=\"edge9\">\n",
|
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"<title>1->0</title>\n",
|
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"<path d=\"M48.0109,-108.2777C49.6408,-119.0535 52.6308,-131.2808 58.0978,-141.3401 62.8523,-150.0885 69.8828,-158.1907 77.0243,-165.0339\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"82.4713,-170.0114 75.1789,-167.6146 79.8875,-167.6503 77.3038,-165.2893 77.3038,-165.2893 77.3038,-165.2893 79.8875,-167.6503 79.4287,-162.9639 82.4713,-170.0114 82.4713,-170.0114\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"58.0978\" y=\"-130.1401\">!a & b & p</text>\n",
|
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"</g>\n",
|
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"<!-- 1->1 -->\n",
|
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"<g class=\"edge\" id=\"edge7\">\n",
|
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"<title>1->1</title>\n",
|
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"<path d=\"M71.4678,-91.1344C82.0216,-91.8009 90.9678,-88.5794 90.9678,-81.4701 90.9678,-76.0269 85.7237,-72.8629 78.529,-71.9778\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"71.4678,-71.8058 78.5425,-68.8273 74.9667,-71.8911 78.4657,-71.9764 78.4657,-71.9764 78.4657,-71.9764 74.9667,-71.8911 78.3889,-75.1254 71.4678,-71.8058 71.4678,-71.8058\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"90.9678\" y=\"-77.7701\">!b & p</text>\n",
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"</g>\n",
|
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"<!-- -1 -->\n",
|
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"<g class=\"node\" id=\"node5\">\n",
|
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"<title>-1</title>\n",
|
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"<ellipse cx=\"91.0978\" cy=\"-1.8\" fill=\"#ffffaa\" rx=\"1.8\" ry=\"1.8\" stroke=\"#000000\"/>\n",
|
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"</g>\n",
|
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"<!-- 1->-1 -->\n",
|
|
"<g class=\"edge\" id=\"edge4\">\n",
|
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"<title>1->-1</title>\n",
|
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"<path d=\"M59.3559,-57.9973C68.5351,-41.7459 80.1983,-21.0969 86.5204,-9.9041\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"none\" points=\"88.7585,-10.9232 90.0679,-3.6233 84.492,-8.5133 88.7585,-10.9232\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"78.0978\" y=\"-25.4\">a & b & p</text>\n",
|
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"</g>\n",
|
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"<!-- T2T1 -->\n",
|
|
"<!-- 1->T2T1 -->\n",
|
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"<g class=\"edge\" id=\"edge8\">\n",
|
|
"<title>1->T2T1</title>\n",
|
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"<path d=\"M24.5641,-65.0166C16.264,-57.372 7.6804,-47.548 3.0978,-36.6 -.5823,-27.8083 -.1082,-16.6437 .7987,-9.3652\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"1.9797,-2.3192 3.9291,-9.7436 1.4011,-5.771 .8225,-9.2229 .8225,-9.2229 .8225,-9.2229 1.4011,-5.771 -2.2842,-8.7021 1.9797,-2.3192 1.9797,-2.3192\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"3.0978\" y=\"-25.4\">!a & !b</text>\n",
|
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"</g>\n",
|
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"<!-- -1->0 -->\n",
|
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"<g class=\"edge\" id=\"edge5\">\n",
|
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"<title>-1->0</title>\n",
|
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"<path d=\"M92.9283,-2.0242C100.1123,-2.9935 126.7352,-7.4359 142.0978,-21.6 154.0813,-32.6487 154.4497,-38.7138 158.0978,-54.6 166.7952,-92.4741 167.1748,-108.0684 147.0978,-141.3401 142.3944,-149.1346 136.1203,-156.6654 129.8218,-163.2595\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"124.5593,-168.5635 127.2535,-161.3757 127.0244,-166.0789 129.4896,-163.5943 129.4896,-163.5943 129.4896,-163.5943 127.0244,-166.0789 131.7257,-165.813 124.5593,-168.5635 124.5593,-168.5635\" stroke=\"#000000\"/>\n",
|
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"</g>\n",
|
|
"<!-- -1->1 -->\n",
|
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"<g class=\"edge\" id=\"edge6\">\n",
|
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"<title>-1->1</title>\n",
|
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"<path d=\"M89.5259,-3.0892C86.0042,-6.0448 77.3771,-13.6679 72.0978,-21.6 66.4391,-30.102 61.5423,-40.038 57.5723,-49.3446\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"54.8476,-55.9805 54.5925,-48.3086 56.177,-52.7427 57.5064,-49.505 57.5064,-49.505 57.5064,-49.505 56.177,-52.7427 60.4204,-50.7015 54.8476,-55.9805 54.8476,-55.9805\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"</svg></div><div style='vertical-align:text-top;display:inline-block;'><svg height=\"360pt\" viewBox=\"0.00 0.00 160.14 360.00\" width=\"160pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
|
|
"<g class=\"graph\" id=\"graph0\" transform=\"scale(.8293 .8293) rotate(0) translate(4 430.0802)\">\n",
|
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"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-430.0802 189.0978,-430.0802 189.0978,4 -4,4\" stroke=\"transparent\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"70.0489\" y=\"-411.8802\">Fin(</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"95.0489\" y=\"-411.8802\">⓿</text>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"111.0489\" y=\"-411.8802\">)</text>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"60.0489\" y=\"-397.8802\">[co-Büchi]</text>\n",
|
|
"<!-- I -->\n",
|
|
"<!-- 3 -->\n",
|
|
"<g class=\"node\" id=\"node2\">\n",
|
|
"<title>3</title>\n",
|
|
"<ellipse cx=\"148.0978\" cy=\"-334.0802\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"148.0978\" y=\"-330.3802\">3</text>\n",
|
|
"</g>\n",
|
|
"<!-- I->3 -->\n",
|
|
"<g class=\"edge\" id=\"edge1\">\n",
|
|
"<title>I->3</title>\n",
|
|
"<path d=\"M148.0978,-388.9569C148.0978,-385.9023 148.0978,-372.1354 148.0978,-359.1561\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"148.0978,-352.0995 151.2479,-359.0994 148.0978,-355.5995 148.0979,-359.0995 148.0979,-359.0995 148.0979,-359.0995 148.0978,-355.5995 144.9479,-359.0995 148.0978,-352.0995 148.0978,-352.0995\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- -4 -->\n",
|
|
"<g class=\"node\" id=\"node8\">\n",
|
|
"<title>-4</title>\n",
|
|
"<ellipse cx=\"129.0978\" cy=\"-257.5802\" fill=\"#ffffaa\" rx=\"1.8\" ry=\"1.8\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 3->-4 -->\n",
|
|
"<g class=\"edge\" id=\"edge10\">\n",
|
|
"<title>3->-4</title>\n",
|
|
"<path d=\"M143.691,-316.3373C139.8096,-300.7095 134.3178,-278.5976 131.2989,-266.4428\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"none\" points=\"133.6613,-265.7901 129.5962,-259.5871 128.9058,-266.9713 133.6613,-265.7901\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"139.0978\" y=\"-286.8802\">a</text>\n",
|
|
"</g>\n",
|
|
"<!-- 0 -->\n",
|
|
"<g class=\"node\" id=\"node3\">\n",
|
|
"<title>0</title>\n",
|
|
"<g id=\"a_node3\"><a xlink:title=\"(a;a*;b)*\">\n",
|
|
"<ellipse cx=\"104.0978\" cy=\"-186.2102\" fill=\"#ffffaa\" rx=\"26.7407\" ry=\"26.7407\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"99.5978\" y=\"-190.0102\">0</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"96.0978\" y=\"-175.0102\">⓿</text>\n",
|
|
"</a>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"<!-- 1 -->\n",
|
|
"<g class=\"node\" id=\"node4\">\n",
|
|
"<title>1</title>\n",
|
|
"<g id=\"a_node4\"><a xlink:title=\"a*;b;(a;a*;b)*\">\n",
|
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"<ellipse cx=\"46.0978\" cy=\"-81.4701\" fill=\"#ffffaa\" rx=\"26.7407\" ry=\"26.7407\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"41.5978\" y=\"-85.2701\">1</text>\n",
|
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"38.0978\" y=\"-70.2701\">⓿</text>\n",
|
|
"</a>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"<!-- 0->1 -->\n",
|
|
"<g class=\"edge\" id=\"edge2\">\n",
|
|
"<title>0->1</title>\n",
|
|
"<path d=\"M78.5833,-177.23C62.6836,-170.152 43.5164,-158.565 34.0978,-141.3401 29.3095,-132.5832 29.6662,-122.1697 32.0312,-112.5025\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"34.0633,-105.6296 35.0992,-113.2355 33.0709,-108.9859 32.0785,-112.3423 32.0785,-112.3423 32.0785,-112.3423 33.0709,-108.9859 29.0577,-111.4491 34.0633,-105.6296 34.0633,-105.6296\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"34.0978\" y=\"-130.1401\">a</text>\n",
|
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"</g>\n",
|
|
"<!-- T2T0 -->\n",
|
|
"<!-- 0->T2T0 -->\n",
|
|
"<g class=\"edge\" id=\"edge3\">\n",
|
|
"<title>0->T2T0</title>\n",
|
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"<path d=\"M116.3326,-162.1599C119.6144,-155.47 123.0856,-148.1663 126.0978,-141.3401 132.4617,-126.9181 133.7038,-123.1522 139.0978,-108.3401 141.4545,-101.8684 143.9252,-94.439 145.6804,-89.0349\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"147.8878,-82.1392 148.7537,-89.7664 146.8207,-85.4726 145.7536,-88.806 145.7536,-88.806 145.7536,-88.806 146.8207,-85.4726 142.7536,-87.8456 147.8878,-82.1392 147.8878,-82.1392\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"133.0978\" y=\"-130.1401\">!a</text>\n",
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"</g>\n",
|
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"<!-- 1->0 -->\n",
|
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"<g class=\"edge\" id=\"edge9\">\n",
|
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"<title>1->0</title>\n",
|
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"<path d=\"M48.0109,-108.2777C49.6408,-119.0535 52.6308,-131.2808 58.0978,-141.3401 62.8523,-150.0885 69.8828,-158.1907 77.0243,-165.0339\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"82.4713,-170.0114 75.1789,-167.6146 79.8875,-167.6503 77.3038,-165.2893 77.3038,-165.2893 77.3038,-165.2893 79.8875,-167.6503 79.4287,-162.9639 82.4713,-170.0114 82.4713,-170.0114\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"58.0978\" y=\"-130.1401\">!a & b & p</text>\n",
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"</g>\n",
|
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"<!-- 1->1 -->\n",
|
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"<g class=\"edge\" id=\"edge7\">\n",
|
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"<title>1->1</title>\n",
|
|
"<path d=\"M71.4678,-91.1344C82.0216,-91.8009 90.9678,-88.5794 90.9678,-81.4701 90.9678,-76.0269 85.7237,-72.8629 78.529,-71.9778\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"71.4678,-71.8058 78.5425,-68.8273 74.9667,-71.8911 78.4657,-71.9764 78.4657,-71.9764 78.4657,-71.9764 74.9667,-71.8911 78.3889,-75.1254 71.4678,-71.8058 71.4678,-71.8058\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"90.9678\" y=\"-77.7701\">!b & p</text>\n",
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"</g>\n",
|
|
"<!-- -1 -->\n",
|
|
"<g class=\"node\" id=\"node6\">\n",
|
|
"<title>-1</title>\n",
|
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"<ellipse cx=\"91.0978\" cy=\"-1.8\" fill=\"#ffffaa\" rx=\"1.8\" ry=\"1.8\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 1->-1 -->\n",
|
|
"<g class=\"edge\" id=\"edge4\">\n",
|
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"<title>1->-1</title>\n",
|
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"<path d=\"M59.3559,-57.9973C68.5351,-41.7459 80.1983,-21.0969 86.5204,-9.9041\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"none\" points=\"88.7585,-10.9232 90.0679,-3.6233 84.492,-8.5133 88.7585,-10.9232\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"79.0978\" y=\"-25.4\">a & b & p</text>\n",
|
|
"</g>\n",
|
|
"<!-- T2T1 -->\n",
|
|
"<!-- 1->T2T1 -->\n",
|
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"<g class=\"edge\" id=\"edge8\">\n",
|
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"<title>1->T2T1</title>\n",
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"<path d=\"M24.5641,-65.0166C16.264,-57.372 7.6804,-47.548 3.0978,-36.6 -.5823,-27.8083 -.1082,-16.6437 .7987,-9.3652\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"1.9797,-2.3192 3.9291,-9.7436 1.4011,-5.771 .8225,-9.2229 .8225,-9.2229 .8225,-9.2229 1.4011,-5.771 -2.2842,-8.7021 1.9797,-2.3192 1.9797,-2.3192\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"3.0978\" y=\"-25.4\">!a & !b</text>\n",
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"</g>\n",
|
|
"<!-- -1->0 -->\n",
|
|
"<g class=\"edge\" id=\"edge5\">\n",
|
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"<title>-1->0</title>\n",
|
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"<path d=\"M92.9855,-1.9898C100.3896,-2.8305 127.7918,-6.8561 143.0978,-21.6 154.5721,-32.6529 153.923,-38.9876 157.0978,-54.6 164.8212,-92.5808 167.3872,-107.723 148.0978,-141.3401 143.4246,-149.4844 136.9207,-157.2238 130.3452,-163.9103\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"125.332,-168.8074 128.1382,-161.6626 127.8357,-166.3617 130.3394,-163.9159 130.3394,-163.9159 130.3394,-163.9159 127.8357,-166.3617 132.5405,-166.1693 125.332,-168.8074 125.332,-168.8074\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- -1->1 -->\n",
|
|
"<g class=\"edge\" id=\"edge6\">\n",
|
|
"<title>-1->1</title>\n",
|
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"<path d=\"M89.5259,-3.0892C86.0042,-6.0448 77.3771,-13.6679 72.0978,-21.6 66.4391,-30.102 61.5423,-40.038 57.5723,-49.3446\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"54.8476,-55.9805 54.5925,-48.3086 56.177,-52.7427 57.5064,-49.505 57.5064,-49.505 57.5064,-49.505 56.177,-52.7427 60.4204,-50.7015 54.8476,-55.9805 54.8476,-55.9805\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- -4->0 -->\n",
|
|
"<g class=\"edge\" id=\"edge11\">\n",
|
|
"<title>-4->0</title>\n",
|
|
"<path d=\"M128.4798,-255.816C126.628,-250.5294 120.9162,-234.2235 115.4864,-218.7223\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"113.0263,-211.6993 118.3134,-217.2643 114.1834,-215.0025 115.3405,-218.3057 115.3405,-218.3057 115.3405,-218.3057 114.1834,-215.0025 112.3676,-219.3471 113.0263,-211.6993 113.0263,-211.6993\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 4 -->\n",
|
|
"<g class=\"node\" id=\"node9\">\n",
|
|
"<title>4</title>\n",
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"<ellipse cx=\"167.0978\" cy=\"-186.2102\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"167.0978\" y=\"-182.5102\">4</text>\n",
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|
"</g>\n",
|
|
"<!-- -4->4 -->\n",
|
|
"<g class=\"edge\" id=\"edge12\">\n",
|
|
"<title>-4->4</title>\n",
|
|
"<path d=\"M130.0371,-255.816C133.4776,-249.3542 145.6838,-226.429 155.1588,-208.6335\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"158.5047,-202.3494 157.9953,-210.0086 156.8597,-205.4388 155.2148,-208.5282 155.2148,-208.5282 155.2148,-208.5282 156.8597,-205.4388 152.4343,-207.0478 158.5047,-202.3494 158.5047,-202.3494\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 4->3 -->\n",
|
|
"<g class=\"edge\" id=\"edge13\">\n",
|
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"<title>4->3</title>\n",
|
|
"<path d=\"M164.7489,-204.4903C161.3764,-230.7372 155.15,-279.1954 151.3407,-308.8416\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"150.4275,-315.9485 148.1954,-308.6041 150.8736,-312.477 151.3197,-309.0055 151.3197,-309.0055 151.3197,-309.0055 150.8736,-312.477 154.444,-309.407 150.4275,-315.9485 150.4275,-315.9485\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"163.5978\" y=\"-253.8802\">1</text>\n",
|
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"</g>\n",
|
|
"</g>\n",
|
|
"</svg></div><div style='vertical-align:text-top;display:inline-block;'><svg height=\"295pt\" viewBox=\"0.00 0.00 172.05 295.08\" width=\"172pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
|
|
"<g class=\"graph\" id=\"graph0\" transform=\"scale(1 1) rotate(0) translate(4 291.0802)\">\n",
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"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-291.0802 168.052,-291.0802 168.052,4 -4,4\" stroke=\"transparent\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"59.526\" y=\"-272.8802\">Fin(</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"84.526\" y=\"-272.8802\">⓿</text>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"100.526\" y=\"-272.8802\">)</text>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"49.526\" y=\"-258.8802\">[co-Büchi]</text>\n",
|
|
"<!-- I -->\n",
|
|
"<!-- 0 -->\n",
|
|
"<g class=\"node\" id=\"node2\">\n",
|
|
"<title>0</title>\n",
|
|
"<g id=\"a_node2\"><a xlink:title=\"(a;a*;b)*\">\n",
|
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"<ellipse cx=\"104.0978\" cy=\"-186.2102\" fill=\"#ffffaa\" rx=\"26.7407\" ry=\"26.7407\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"99.5978\" y=\"-190.0102\">0</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"96.0978\" y=\"-175.0102\">⓿</text>\n",
|
|
"</a>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"<!-- I->0 -->\n",
|
|
"<g class=\"edge\" id=\"edge1\">\n",
|
|
"<title>I->0</title>\n",
|
|
"<path d=\"M104.0978,-249.8573C104.0978,-246.7051 104.0978,-233.7173 104.0978,-220.2885\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"104.0978,-213.2757 107.2479,-220.2756 104.0978,-216.7757 104.0979,-220.2757 104.0979,-220.2757 104.0979,-220.2757 104.0978,-216.7757 100.9479,-220.2757 104.0978,-213.2757 104.0978,-213.2757\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 1 -->\n",
|
|
"<g class=\"node\" id=\"node3\">\n",
|
|
"<title>1</title>\n",
|
|
"<g id=\"a_node3\"><a xlink:title=\"a*;b;(a;a*;b)*\">\n",
|
|
"<ellipse cx=\"46.0978\" cy=\"-81.4701\" fill=\"#ffffaa\" rx=\"26.7407\" ry=\"26.7407\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"41.5978\" y=\"-85.2701\">1</text>\n",
|
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"38.0978\" y=\"-70.2701\">⓿</text>\n",
|
|
"</a>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"<!-- 0->1 -->\n",
|
|
"<g class=\"edge\" id=\"edge2\">\n",
|
|
"<title>0->1</title>\n",
|
|
"<path d=\"M78.5833,-177.23C62.6836,-170.152 43.5164,-158.565 34.0978,-141.3401 29.3095,-132.5832 29.6662,-122.1697 32.0312,-112.5025\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"34.0633,-105.6296 35.0992,-113.2355 33.0709,-108.9859 32.0785,-112.3423 32.0785,-112.3423 32.0785,-112.3423 33.0709,-108.9859 29.0577,-111.4491 34.0633,-105.6296 34.0633,-105.6296\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"34.0978\" y=\"-130.1401\">a</text>\n",
|
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"</g>\n",
|
|
"<!-- T2T0 -->\n",
|
|
"<!-- 0->T2T0 -->\n",
|
|
"<g class=\"edge\" id=\"edge3\">\n",
|
|
"<title>0->T2T0</title>\n",
|
|
"<path d=\"M116.3326,-162.1599C119.6144,-155.47 123.0856,-148.1663 126.0978,-141.3401 132.4617,-126.9181 133.7038,-123.1522 139.0978,-108.3401 141.4545,-101.8684 143.9252,-94.439 145.6804,-89.0349\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"147.8878,-82.1392 148.7537,-89.7664 146.8207,-85.4726 145.7536,-88.806 145.7536,-88.806 145.7536,-88.806 146.8207,-85.4726 142.7536,-87.8456 147.8878,-82.1392 147.8878,-82.1392\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"132.0978\" y=\"-130.1401\">!a</text>\n",
|
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"</g>\n",
|
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"<!-- 1->0 -->\n",
|
|
"<g class=\"edge\" id=\"edge9\">\n",
|
|
"<title>1->0</title>\n",
|
|
"<path d=\"M48.0109,-108.2777C49.6408,-119.0535 52.6308,-131.2808 58.0978,-141.3401 62.8523,-150.0885 69.8828,-158.1907 77.0243,-165.0339\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"82.4713,-170.0114 75.1789,-167.6146 79.8875,-167.6503 77.3038,-165.2893 77.3038,-165.2893 77.3038,-165.2893 79.8875,-167.6503 79.4287,-162.9639 82.4713,-170.0114 82.4713,-170.0114\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"58.0978\" y=\"-130.1401\">!a & b & p</text>\n",
|
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"</g>\n",
|
|
"<!-- 1->1 -->\n",
|
|
"<g class=\"edge\" id=\"edge7\">\n",
|
|
"<title>1->1</title>\n",
|
|
"<path d=\"M71.4678,-91.1344C82.0216,-91.8009 90.9678,-88.5794 90.9678,-81.4701 90.9678,-76.0269 85.7237,-72.8629 78.529,-71.9778\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"71.4678,-71.8058 78.5425,-68.8273 74.9667,-71.8911 78.4657,-71.9764 78.4657,-71.9764 78.4657,-71.9764 74.9667,-71.8911 78.3889,-75.1254 71.4678,-71.8058 71.4678,-71.8058\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"90.9678\" y=\"-77.7701\">!b & p</text>\n",
|
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"</g>\n",
|
|
"<!-- -1 -->\n",
|
|
"<g class=\"node\" id=\"node5\">\n",
|
|
"<title>-1</title>\n",
|
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"<ellipse cx=\"91.0978\" cy=\"-1.8\" fill=\"#ffffaa\" rx=\"1.8\" ry=\"1.8\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 1->-1 -->\n",
|
|
"<g class=\"edge\" id=\"edge4\">\n",
|
|
"<title>1->-1</title>\n",
|
|
"<path d=\"M59.3559,-57.9973C68.5351,-41.7459 80.1983,-21.0969 86.5204,-9.9041\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"none\" points=\"88.7585,-10.9232 90.0679,-3.6233 84.492,-8.5133 88.7585,-10.9232\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"78.0978\" y=\"-25.4\">a & b & p</text>\n",
|
|
"</g>\n",
|
|
"<!-- T2T1 -->\n",
|
|
"<!-- 1->T2T1 -->\n",
|
|
"<g class=\"edge\" id=\"edge8\">\n",
|
|
"<title>1->T2T1</title>\n",
|
|
"<path d=\"M24.5641,-65.0166C16.264,-57.372 7.6804,-47.548 3.0978,-36.6 -.5823,-27.8083 -.1082,-16.6437 .7987,-9.3652\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"1.9797,-2.3192 3.9291,-9.7436 1.4011,-5.771 .8225,-9.2229 .8225,-9.2229 .8225,-9.2229 1.4011,-5.771 -2.2842,-8.7021 1.9797,-2.3192 1.9797,-2.3192\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"3.0978\" y=\"-25.4\">!a & !b</text>\n",
|
|
"</g>\n",
|
|
"<!-- -1->0 -->\n",
|
|
"<g class=\"edge\" id=\"edge5\">\n",
|
|
"<title>-1->0</title>\n",
|
|
"<path d=\"M92.9283,-2.0242C100.1123,-2.9935 126.7352,-7.4359 142.0978,-21.6 154.0813,-32.6487 154.4497,-38.7138 158.0978,-54.6 166.7952,-92.4741 167.1748,-108.0684 147.0978,-141.3401 142.3944,-149.1346 136.1203,-156.6654 129.8218,-163.2595\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"124.5593,-168.5635 127.2535,-161.3757 127.0244,-166.0789 129.4896,-163.5943 129.4896,-163.5943 129.4896,-163.5943 127.0244,-166.0789 131.7257,-165.813 124.5593,-168.5635 124.5593,-168.5635\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- -1->1 -->\n",
|
|
"<g class=\"edge\" id=\"edge6\">\n",
|
|
"<title>-1->1</title>\n",
|
|
"<path d=\"M89.5259,-3.0892C86.0042,-6.0448 77.3771,-13.6679 72.0978,-21.6 66.4391,-30.102 61.5423,-40.038 57.5723,-49.3446\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"54.8476,-55.9805 54.5925,-48.3086 56.177,-52.7427 57.5064,-49.505 57.5064,-49.505 57.5064,-49.505 56.177,-52.7427 60.4204,-50.7015 54.8476,-55.9805 54.8476,-55.9805\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"</svg></div><div style='vertical-align:text-top;display:inline-block;'><svg height=\"315pt\" viewBox=\"0.00 0.00 89.00 315.34\" width=\"89pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
|
|
"<g class=\"graph\" id=\"graph0\" transform=\"scale(1 1) rotate(0) translate(4 311.3401)\">\n",
|
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"<title>VWAA for GFa</title>\n",
|
|
"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-311.3401 85,-311.3401 85,4 -4,4\" stroke=\"transparent\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"18\" y=\"-293.1401\">Fin(</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"43\" y=\"-293.1401\">⓿</text>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"59\" y=\"-293.1401\">)</text>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"8\" y=\"-279.1401\">[co-Büchi]</text>\n",
|
|
"<!-- I -->\n",
|
|
"<!-- 0 -->\n",
|
|
"<g class=\"node\" id=\"node2\">\n",
|
|
"<title>0</title>\n",
|
|
"<g id=\"a_node2\"><a xlink:title=\"GF(a)\">\n",
|
|
"<ellipse cx=\"27\" cy=\"-215.3401\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"27\" y=\"-211.6401\">0</text>\n",
|
|
"</a>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"<!-- I->0 -->\n",
|
|
"<g class=\"edge\" id=\"edge1\">\n",
|
|
"<title>I->0</title>\n",
|
|
"<path d=\"M27,-270.2168C27,-267.1622 27,-253.3953 27,-240.416\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"27,-233.3594 30.1501,-240.3593 27,-236.8594 27.0001,-240.3594 27.0001,-240.3594 27.0001,-240.3594 27,-236.8594 23.8501,-240.3594 27,-233.3594 27,-233.3594\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- -1 -->\n",
|
|
"<g class=\"node\" id=\"node3\">\n",
|
|
"<title>-1</title>\n",
|
|
"<ellipse cx=\"27\" cy=\"-144.5401\" fill=\"#ffffaa\" rx=\"1.8\" ry=\"1.8\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 0->-1 -->\n",
|
|
"<g class=\"edge\" id=\"edge2\">\n",
|
|
"<title>0->-1</title>\n",
|
|
"<path d=\"M19.4823,-198.7216C15.9291,-188.7122 13.0463,-175.7388 16,-164.3401 17.1245,-160.0006 19.4288,-155.5995 21.6392,-152.0523\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"none\" points=\"23.675,-153.4158 25.6364,-146.2635 19.6428,-150.6316 23.675,-153.4158\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"16\" y=\"-168.1401\">1</text>\n",
|
|
"</g>\n",
|
|
"<!-- -1->0 -->\n",
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}
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],
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"source": [
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"display_inline(aut1, aut2, aut3, aut4, aut5, show='.bav1u')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
|
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"Let's make sure that option `u` and `s` (to display SCCs) work well together:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"outputs": [
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"</svg></div><div style='vertical-align:text-top;display:inline-block;'><svg height=\"360pt\" viewBox=\"0.00 0.00 179.53 360.00\" width=\"180pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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"<g class=\"graph\" id=\"graph0\" transform=\"scale(.8673 .8673) rotate(0) translate(4 411.0802)\">\n",
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"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-411.0802 203,-411.0802 203,4 -4,4\" stroke=\"transparent\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"77\" y=\"-392.8802\">Fin(</text>\n",
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"102\" y=\"-392.8802\">⓿</text>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"118\" y=\"-392.8802\">)</text>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"67\" y=\"-378.8802\">[co-Büchi]</text>\n",
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"<g class=\"cluster\" id=\"clust2\">\n",
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"<title>cluster_1</title>\n",
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"<polygon fill=\"none\" points=\"8,-8 8,-341.0802 169,-341.0802 169,-8 8,-8\" stroke=\"#ff0000\"/>\n",
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"</g>\n",
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"<!-- I -->\n",
|
|
"<!-- 0 -->\n",
|
|
"<g class=\"node\" id=\"node2\">\n",
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"<title>0</title>\n",
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"<g id=\"a_node2\"><a xlink:title=\"(a;a*;b)*\">\n",
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"<ellipse cx=\"106\" cy=\"-306.2102\" fill=\"#ffffaa\" rx=\"26.7407\" ry=\"26.7407\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"101.5\" y=\"-310.0102\">0</text>\n",
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"98\" y=\"-295.0102\">⓿</text>\n",
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"</a>\n",
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"</g>\n",
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|
"</g>\n",
|
|
"<!-- I->0 -->\n",
|
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"<g class=\"edge\" id=\"edge1\">\n",
|
|
"<title>I->0</title>\n",
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"<path d=\"M106,-369.8573C106,-366.7051 106,-353.7173 106,-340.2885\" fill=\"none\" stroke=\"#000000\"/>\n",
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|
"</g>\n",
|
|
"<!-- 1 -->\n",
|
|
"<g class=\"node\" id=\"node3\">\n",
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|
"<title>1</title>\n",
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"<g id=\"a_node3\"><a xlink:title=\"a*;b;(a;a*;b)*\">\n",
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"<ellipse cx=\"57\" cy=\"-149.4701\" fill=\"#ffffaa\" rx=\"26.7407\" ry=\"26.7407\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"52.5\" y=\"-153.2701\">1</text>\n",
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"49\" y=\"-138.2701\">⓿</text>\n",
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"</a>\n",
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"</g>\n",
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|
"</g>\n",
|
|
"<!-- 0->1 -->\n",
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"<g class=\"edge\" id=\"edge2\">\n",
|
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"<title>0->1</title>\n",
|
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"<path d=\"M86.4316,-287.4874C72.6785,-272.8753 55.4545,-251.2641 48,-228.3401 43.2021,-213.5856 44.3645,-196.5554 47.1729,-182.1044\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"48.6649,-175.2388 50.2565,-182.7481 47.9216,-178.659 47.1783,-182.0791 47.1783,-182.0791 47.1783,-182.0791 47.9216,-178.659 44.1001,-181.4102 48.6649,-175.2388 48.6649,-175.2388\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"48\" y=\"-217.1401\">a</text>\n",
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"</g>\n",
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"<!-- T2T0 -->\n",
|
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"<!-- 0->T2T0 -->\n",
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"<g class=\"edge\" id=\"edge3\">\n",
|
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"<title>0->T2T0</title>\n",
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"<path d=\"M128.5017,-291.3846C139.5056,-283.3843 152.4097,-272.8084 162,-261.3401 170.6524,-250.9933 177.4487,-236.7133 181.0819,-228.1655\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"183.7702,-221.4658 184.0868,-229.1354 182.4668,-224.714 181.1634,-227.9623 181.1634,-227.9623 181.1634,-227.9623 182.4668,-224.714 178.2399,-226.7892 183.7702,-221.4658 183.7702,-221.4658\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"171\" y=\"-250.1401\">!a</text>\n",
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"</g>\n",
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"<!-- 1->0 -->\n",
|
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"<g class=\"edge\" id=\"edge9\">\n",
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"<title>1->0</title>\n",
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"<path d=\"M65.0219,-175.1304C73.4257,-202.0124 86.6511,-244.3172 95.7932,-273.5609\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"97.9086,-280.3277 92.8134,-274.5865 96.8643,-276.9872 95.8199,-273.6466 95.8199,-273.6466 95.8199,-273.6466 96.8643,-276.9872 98.8264,-272.7067 97.9086,-280.3277 97.9086,-280.3277\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"81\" y=\"-217.1401\">!a & b & p</text>\n",
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"</g>\n",
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"<!-- 1->1 -->\n",
|
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"<g class=\"edge\" id=\"edge7\">\n",
|
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"<title>1->1</title>\n",
|
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"<path d=\"M82.8213,-157.6697C93.1776,-158.133 101.8701,-155.3997 101.8701,-149.4701 101.8701,-145.0228 96.9805,-142.3735 90.1667,-141.5223\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"82.8213,-141.2704 89.9252,-138.3623 86.3193,-141.3904 89.8172,-141.5104 89.8172,-141.5104 89.8172,-141.5104 86.3193,-141.3904 89.7092,-144.6586 82.8213,-141.2704 82.8213,-141.2704\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"101.8701\" y=\"-145.7701\">!b & p</text>\n",
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"</g>\n",
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"<!-- -1 -->\n",
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"<g class=\"node\" id=\"node4\">\n",
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"<title>-1</title>\n",
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"<ellipse cx=\"136\" cy=\"-17.8\" fill=\"#ffffaa\" rx=\"1.8\" ry=\"1.8\" stroke=\"#000000\"/>\n",
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"</g>\n",
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"<!-- 1->-1 -->\n",
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"<g class=\"edge\" id=\"edge4\">\n",
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"<title>1->-1</title>\n",
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"<path d=\"M55.1797,-122.4764C55.1599,-102.6694 58.0055,-75.9602 71,-56.6 84.5864,-36.3579 112.612,-25.0787 127.0175,-20.4016\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"none\" points=\"127.9711,-22.6737 133.9761,-18.3214 126.5676,-17.979 127.9711,-22.6737\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"71\" y=\"-60.4\">a & b & p</text>\n",
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"</g>\n",
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"<!-- T2T1 -->\n",
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"<!-- 1->T2T1 -->\n",
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"<g class=\"edge\" id=\"edge8\">\n",
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"<title>1->T2T1</title>\n",
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"<path d=\"M81.5322,-138.5002C98.8424,-130.2595 122.2022,-118.1063 141,-104.6 155.7932,-93.971 170.7592,-78.5941 178.5364,-70.175\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"183.4465,-64.7351 181.0946,-72.042 181.1014,-67.3333 178.7563,-69.9314 178.7563,-69.9314 178.7563,-69.9314 181.1014,-67.3333 176.4179,-67.8208 183.4465,-64.7351 183.4465,-64.7351\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"158\" y=\"-93.4\">!a & !b</text>\n",
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"</g>\n",
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"<!-- -1->0 -->\n",
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"<g class=\"edge\" id=\"edge5\">\n",
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"<title>-1->0</title>\n",
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"<path d=\"M137.2903,-19.1076C142.2754,-24.3042 160,-44.1814 160,-64.1 160,-220.8401 160,-220.8401 160,-220.8401 160,-244.4744 145.0352,-266.8835 130.8613,-282.8077\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"126.1076,-287.9518 128.545,-280.6729 128.483,-285.3813 130.8584,-282.8108 130.8584,-282.8108 130.8584,-282.8108 128.483,-285.3813 133.1719,-284.9487 126.1076,-287.9518 126.1076,-287.9518\" stroke=\"#000000\"/>\n",
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"</g>\n",
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"<!-- -1->1 -->\n",
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"<g class=\"edge\" id=\"edge6\">\n",
|
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"<title>-1->1</title>\n",
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"<path d=\"M136.2856,-19.9788C137.1778,-27.5338 139.3783,-53.1514 131,-71.6 120.6765,-94.3317 100.9149,-114.5828 84.4087,-128.7318\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"78.9541,-133.291 82.3049,-126.3848 81.6396,-131.0464 84.3251,-128.8017 84.3251,-128.8017 84.3251,-128.8017 81.6396,-131.0464 86.3452,-131.2186 78.9541,-133.291 78.9541,-133.291\" stroke=\"#000000\"/>\n",
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"</g>\n",
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"</g>\n",
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"</svg></div><div style='vertical-align:text-top;display:inline-block;'><svg height=\"360pt\" viewBox=\"0.00 0.00 164.42 360.00\" width=\"164pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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"<g class=\"graph\" id=\"graph0\" transform=\"scale(.5872 .5872) rotate(0) translate(4 609.0802)\">\n",
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"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-609.0802 276,-609.0802 276,4 -4,4\" stroke=\"transparent\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"113.5\" y=\"-590.8802\">Fin(</text>\n",
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"138.5\" y=\"-590.8802\">⓿</text>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"154.5\" y=\"-590.8802\">)</text>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"103.5\" y=\"-576.8802\">[co-Büchi]</text>\n",
|
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"<g class=\"cluster\" id=\"clust2\">\n",
|
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"<title>cluster_1</title>\n",
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"<polygon fill=\"none\" points=\"81,-8 81,-362.0802 242,-362.0802 242,-8 81,-8\" stroke=\"#ff0000\"/>\n",
|
|
"</g>\n",
|
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"<g class=\"cluster\" id=\"clust3\">\n",
|
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"<title>cluster_2</title>\n",
|
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"<polygon fill=\"none\" points=\"8,-205.3401 8,-539.0802 73,-539.0802 73,-205.3401 8,-205.3401\" stroke=\"#00ff00\"/>\n",
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"</g>\n",
|
|
"<!-- I -->\n",
|
|
"<!-- 3 -->\n",
|
|
"<g class=\"node\" id=\"node2\">\n",
|
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"<title>3</title>\n",
|
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"<ellipse cx=\"41\" cy=\"-513.0802\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"41\" y=\"-509.3802\">3</text>\n",
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|
"</g>\n",
|
|
"<!-- I->3 -->\n",
|
|
"<g class=\"edge\" id=\"edge1\">\n",
|
|
"<title>I->3</title>\n",
|
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"<path d=\"M41,-567.9569C41,-564.9023 41,-551.1354 41,-538.1561\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"41,-531.0995 44.1501,-538.0994 41,-534.5995 41.0001,-538.0995 41.0001,-538.0995 41.0001,-538.0995 41,-534.5995 37.8501,-538.0995 41,-531.0995 41,-531.0995\" stroke=\"#000000\"/>\n",
|
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"</g>\n",
|
|
"<!-- -4 -->\n",
|
|
"<g class=\"node\" id=\"node6\">\n",
|
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"<title>-4</title>\n",
|
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"<ellipse cx=\"18\" cy=\"-398.5802\" fill=\"#ffffaa\" rx=\"1.8\" ry=\"1.8\" stroke=\"#000000\"/>\n",
|
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"</g>\n",
|
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"<!-- 3->-4 -->\n",
|
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"<g class=\"edge\" id=\"edge10\">\n",
|
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"<title>3->-4</title>\n",
|
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"<path d=\"M37.4063,-495.1896C32.4118,-470.3257 23.5611,-426.2646 19.7862,-407.4725\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"none\" points=\"22.1607,-406.8524 18.38,-400.4721 17.3567,-407.8175 22.1607,-406.8524\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"30\" y=\"-446.8802\">a</text>\n",
|
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"</g>\n",
|
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"<!-- 0 -->\n",
|
|
"<g class=\"node\" id=\"node3\">\n",
|
|
"<title>0</title>\n",
|
|
"<g id=\"a_node3\"><a xlink:title=\"(a;a*;b)*\">\n",
|
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"<ellipse cx=\"150\" cy=\"-327.2102\" fill=\"#ffffaa\" rx=\"26.7407\" ry=\"26.7407\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"145.5\" y=\"-331.0102\">0</text>\n",
|
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"142\" y=\"-316.0102\">⓿</text>\n",
|
|
"</a>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"<!-- 1 -->\n",
|
|
"<g class=\"node\" id=\"node4\">\n",
|
|
"<title>1</title>\n",
|
|
"<g id=\"a_node4\"><a xlink:title=\"a*;b;(a;a*;b)*\">\n",
|
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"<ellipse cx=\"130\" cy=\"-149.4701\" fill=\"#ffffaa\" rx=\"26.7407\" ry=\"26.7407\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"125.5\" y=\"-153.2701\">1</text>\n",
|
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"122\" y=\"-138.2701\">⓿</text>\n",
|
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"</a>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"<!-- 0->1 -->\n",
|
|
"<g class=\"edge\" id=\"edge2\">\n",
|
|
"<title>0->1</title>\n",
|
|
"<path d=\"M138.4064,-302.9466C131.8661,-287.8938 124.3508,-267.939 121,-249.3401 117.5326,-230.0944 119.44,-224.8333 121,-205.3401 121.5761,-198.142 122.5632,-190.4717 123.6779,-183.1937\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"124.8247,-176.0785 126.8207,-183.4906 124.2677,-179.5339 123.7108,-182.9893 123.7108,-182.9893 123.7108,-182.9893 124.2677,-179.5339 120.6009,-182.4881 124.8247,-176.0785 124.8247,-176.0785\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"121\" y=\"-227.6401\">a</text>\n",
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"</g>\n",
|
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"<!-- T2T0 -->\n",
|
|
"<!-- 0->T2T0 -->\n",
|
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"<g class=\"edge\" id=\"edge3\">\n",
|
|
"<title>0->T2T0</title>\n",
|
|
"<path d=\"M175.5952,-318.9426C194.1775,-311.8092 218.8015,-299.8619 235,-282.3401 246.6271,-269.7631 252.7107,-250.0865 255.3459,-239.2173\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"256.8566,-232.1677 258.4698,-239.6724 256.1232,-235.59 255.3897,-239.0123 255.3897,-239.0123 255.3897,-239.0123 256.1232,-235.59 252.3097,-238.3522 256.8566,-232.1677 256.8566,-232.1677\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"245\" y=\"-271.1401\">!a</text>\n",
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"</g>\n",
|
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"<!-- 1->0 -->\n",
|
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"<g class=\"edge\" id=\"edge9\">\n",
|
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"<title>1->0</title>\n",
|
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"<path d=\"M133.0333,-176.4272C136.5512,-207.6902 142.3552,-259.2705 146.1782,-293.2461\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"146.9624,-300.2153 143.0494,-293.6114 146.571,-296.7372 146.1796,-293.2592 146.1796,-293.2592 146.1796,-293.2592 146.571,-296.7372 149.3099,-292.9069 146.9624,-300.2153 146.9624,-300.2153\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"141\" y=\"-227.6401\">!a & b & p</text>\n",
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"</g>\n",
|
|
"<!-- 1->1 -->\n",
|
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"<g class=\"edge\" id=\"edge7\">\n",
|
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"<title>1->1</title>\n",
|
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"<path d=\"M155.8213,-157.6697C166.1776,-158.133 174.8701,-155.3997 174.8701,-149.4701 174.8701,-145.0228 169.9805,-142.3735 163.1667,-141.5223\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"155.8213,-141.2704 162.9252,-138.3623 159.3193,-141.3904 162.8172,-141.5104 162.8172,-141.5104 162.8172,-141.5104 159.3193,-141.3904 162.7092,-144.6586 155.8213,-141.2704 155.8213,-141.2704\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"174.8701\" y=\"-145.7701\">!b & p</text>\n",
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"</g>\n",
|
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"<!-- -1 -->\n",
|
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"<g class=\"node\" id=\"node5\">\n",
|
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"<title>-1</title>\n",
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"<ellipse cx=\"209\" cy=\"-17.8\" fill=\"#ffffaa\" rx=\"1.8\" ry=\"1.8\" stroke=\"#000000\"/>\n",
|
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"</g>\n",
|
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"<!-- 1->-1 -->\n",
|
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"<g class=\"edge\" id=\"edge4\">\n",
|
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"<title>1->-1</title>\n",
|
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"<path d=\"M128.1797,-122.4764C128.1599,-102.6694 131.0055,-75.9602 144,-56.6 157.5864,-36.3579 185.612,-25.0787 200.0175,-20.4016\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"none\" points=\"200.9711,-22.6737 206.9761,-18.3214 199.5676,-17.979 200.9711,-22.6737\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"144\" y=\"-60.4\">a & b & p</text>\n",
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"</g>\n",
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"<!-- T2T1 -->\n",
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"<!-- 1->T2T1 -->\n",
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"<g class=\"edge\" id=\"edge8\">\n",
|
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"<title>1->T2T1</title>\n",
|
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"<path d=\"M154.5322,-138.5002C171.8424,-130.2595 195.2022,-118.1063 214,-104.6 228.7932,-93.971 243.7592,-78.5941 251.5364,-70.175\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"231\" y=\"-93.4\">!a & !b</text>\n",
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"</g>\n",
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"<!-- -1->0 -->\n",
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"<g class=\"edge\" id=\"edge5\">\n",
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"<title>-1->0</title>\n",
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"<path d=\"M210.2903,-19.1076C215.2754,-24.3042 233,-44.1814 233,-64.1 233,-231.3401 233,-231.3401 233,-231.3401 233,-265.0302 203.3409,-292.7 179.4818,-309.5083\" fill=\"none\" stroke=\"#000000\"/>\n",
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"</g>\n",
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"<!-- -1->1 -->\n",
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"<g class=\"edge\" id=\"edge6\">\n",
|
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"<title>-1->1</title>\n",
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"<path d=\"M209.2856,-19.9788C210.1778,-27.5338 212.3783,-53.1514 204,-71.6 193.6765,-94.3317 173.9149,-114.5828 157.4087,-128.7318\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"151.9541,-133.291 155.3049,-126.3848 154.6396,-131.0464 157.3251,-128.8017 157.3251,-128.8017 157.3251,-128.8017 154.6396,-131.0464 159.3452,-131.2186 151.9541,-133.291 151.9541,-133.291\" stroke=\"#000000\"/>\n",
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"</g>\n",
|
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"<!-- -4->0 -->\n",
|
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"<g class=\"edge\" id=\"edge11\">\n",
|
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"<title>-4->0</title>\n",
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"<path d=\"M19.866,-397.5713C30.5744,-391.7815 84.9603,-362.376 119.9489,-343.4583\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"126.2414,-340.056 121.5821,-346.1563 123.1626,-341.7207 120.0838,-343.3854 120.0838,-343.3854 120.0838,-343.3854 123.1626,-341.7207 118.5856,-340.6144 126.2414,-340.056 126.2414,-340.056\" stroke=\"#000000\"/>\n",
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"</g>\n",
|
|
"<!-- 4 -->\n",
|
|
"<g class=\"node\" id=\"node7\">\n",
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|
"<title>4</title>\n",
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"<ellipse cx=\"41\" cy=\"-231.3401\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"41\" y=\"-227.6401\">4</text>\n",
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"</g>\n",
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"<!-- -4->4 -->\n",
|
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"<g class=\"edge\" id=\"edge12\">\n",
|
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"<title>-4->4</title>\n",
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"<path d=\"M18.2583,-396.702C20.1291,-383.0988 31.6956,-298.9953 37.5755,-256.2409\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"38.5359,-249.2576 40.7027,-256.6215 38.059,-252.7249 37.5821,-256.1923 37.5821,-256.1923 37.5821,-256.1923 38.059,-252.7249 34.4614,-255.7631 38.5359,-249.2576 38.5359,-249.2576\" stroke=\"#000000\"/>\n",
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|
"</g>\n",
|
|
"<!-- 4->3 -->\n",
|
|
"<g class=\"edge\" id=\"edge13\">\n",
|
|
"<title>4->3</title>\n",
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"<path d=\"M41,-249.6071C41,-298.4414 41,-432.089 41,-487.9838\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"41,-495.0275 37.8501,-488.0275 41,-491.5275 41.0001,-488.0275 41.0001,-488.0275 41.0001,-488.0275 41,-491.5275 44.1501,-488.0276 41,-495.0275 41,-495.0275\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"45.5\" y=\"-394.8802\">1</text>\n",
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"</g>\n",
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|
"</g>\n",
|
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"</svg></div><div style='vertical-align:text-top;display:inline-block;'><svg height=\"360pt\" viewBox=\"0.00 0.00 179.53 360.00\" width=\"180pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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"<g class=\"graph\" id=\"graph0\" transform=\"scale(.8673 .8673) rotate(0) translate(4 411.0802)\">\n",
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"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-411.0802 203,-411.0802 203,4 -4,4\" stroke=\"transparent\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"77\" y=\"-392.8802\">Fin(</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"102\" y=\"-392.8802\">⓿</text>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"118\" y=\"-392.8802\">)</text>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"67\" y=\"-378.8802\">[co-Büchi]</text>\n",
|
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"<g class=\"cluster\" id=\"clust2\">\n",
|
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"<title>cluster_1</title>\n",
|
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"<polygon fill=\"none\" points=\"8,-8 8,-341.0802 169,-341.0802 169,-8 8,-8\" stroke=\"#ff0000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- I -->\n",
|
|
"<!-- 0 -->\n",
|
|
"<g class=\"node\" id=\"node2\">\n",
|
|
"<title>0</title>\n",
|
|
"<g id=\"a_node2\"><a xlink:title=\"(a;a*;b)*\">\n",
|
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"<ellipse cx=\"106\" cy=\"-306.2102\" fill=\"#ffffaa\" rx=\"26.7407\" ry=\"26.7407\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"101.5\" y=\"-310.0102\">0</text>\n",
|
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"98\" y=\"-295.0102\">⓿</text>\n",
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"</a>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"<!-- I->0 -->\n",
|
|
"<g class=\"edge\" id=\"edge1\">\n",
|
|
"<title>I->0</title>\n",
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"<path d=\"M106,-369.8573C106,-366.7051 106,-353.7173 106,-340.2885\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"106,-333.2757 109.1501,-340.2756 106,-336.7757 106.0001,-340.2757 106.0001,-340.2757 106.0001,-340.2757 106,-336.7757 102.8501,-340.2757 106,-333.2757 106,-333.2757\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 1 -->\n",
|
|
"<g class=\"node\" id=\"node3\">\n",
|
|
"<title>1</title>\n",
|
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"<g id=\"a_node3\"><a xlink:title=\"a*;b;(a;a*;b)*\">\n",
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"<ellipse cx=\"57\" cy=\"-149.4701\" fill=\"#ffffaa\" rx=\"26.7407\" ry=\"26.7407\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"52.5\" y=\"-153.2701\">1</text>\n",
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"49\" y=\"-138.2701\">⓿</text>\n",
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"</a>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"<!-- 0->1 -->\n",
|
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"<g class=\"edge\" id=\"edge2\">\n",
|
|
"<title>0->1</title>\n",
|
|
"<path d=\"M86.4316,-287.4874C72.6785,-272.8753 55.4545,-251.2641 48,-228.3401 43.2021,-213.5856 44.3645,-196.5554 47.1729,-182.1044\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"48.6649,-175.2388 50.2565,-182.7481 47.9216,-178.659 47.1783,-182.0791 47.1783,-182.0791 47.1783,-182.0791 47.9216,-178.659 44.1001,-181.4102 48.6649,-175.2388 48.6649,-175.2388\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"48\" y=\"-217.1401\">a</text>\n",
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"</g>\n",
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"<!-- T2T0 -->\n",
|
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"<!-- 0->T2T0 -->\n",
|
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"<g class=\"edge\" id=\"edge3\">\n",
|
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"<title>0->T2T0</title>\n",
|
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"<path d=\"M128.5017,-291.3846C139.5056,-283.3843 152.4097,-272.8084 162,-261.3401 170.6524,-250.9933 177.4487,-236.7133 181.0819,-228.1655\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"183.7702,-221.4658 184.0868,-229.1354 182.4668,-224.714 181.1634,-227.9623 181.1634,-227.9623 181.1634,-227.9623 182.4668,-224.714 178.2399,-226.7892 183.7702,-221.4658 183.7702,-221.4658\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"171\" y=\"-250.1401\">!a</text>\n",
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"</g>\n",
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"<!-- 1->0 -->\n",
|
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"<g class=\"edge\" id=\"edge9\">\n",
|
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"<title>1->0</title>\n",
|
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"<path d=\"M65.0219,-175.1304C73.4257,-202.0124 86.6511,-244.3172 95.7932,-273.5609\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"97.9086,-280.3277 92.8134,-274.5865 96.8643,-276.9872 95.8199,-273.6466 95.8199,-273.6466 95.8199,-273.6466 96.8643,-276.9872 98.8264,-272.7067 97.9086,-280.3277 97.9086,-280.3277\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"81\" y=\"-217.1401\">!a & b & p</text>\n",
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"</g>\n",
|
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"<!-- 1->1 -->\n",
|
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"<g class=\"edge\" id=\"edge7\">\n",
|
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"<title>1->1</title>\n",
|
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"<path d=\"M82.8213,-157.6697C93.1776,-158.133 101.8701,-155.3997 101.8701,-149.4701 101.8701,-145.0228 96.9805,-142.3735 90.1667,-141.5223\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"82.8213,-141.2704 89.9252,-138.3623 86.3193,-141.3904 89.8172,-141.5104 89.8172,-141.5104 89.8172,-141.5104 86.3193,-141.3904 89.7092,-144.6586 82.8213,-141.2704 82.8213,-141.2704\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"101.8701\" y=\"-145.7701\">!b & p</text>\n",
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"</g>\n",
|
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"<!-- -1 -->\n",
|
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"<g class=\"node\" id=\"node4\">\n",
|
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"<title>-1</title>\n",
|
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"<ellipse cx=\"136\" cy=\"-17.8\" fill=\"#ffffaa\" rx=\"1.8\" ry=\"1.8\" stroke=\"#000000\"/>\n",
|
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"</g>\n",
|
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"<!-- 1->-1 -->\n",
|
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"<g class=\"edge\" id=\"edge4\">\n",
|
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"<title>1->-1</title>\n",
|
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"<path d=\"M55.1797,-122.4764C55.1599,-102.6694 58.0055,-75.9602 71,-56.6 84.5864,-36.3579 112.612,-25.0787 127.0175,-20.4016\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"none\" points=\"127.9711,-22.6737 133.9761,-18.3214 126.5676,-17.979 127.9711,-22.6737\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"71\" y=\"-60.4\">a & b & p</text>\n",
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"</g>\n",
|
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"<!-- T2T1 -->\n",
|
|
"<!-- 1->T2T1 -->\n",
|
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"<g class=\"edge\" id=\"edge8\">\n",
|
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"<title>1->T2T1</title>\n",
|
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"<path d=\"M81.5322,-138.5002C98.8424,-130.2595 122.2022,-118.1063 141,-104.6 155.7932,-93.971 170.7592,-78.5941 178.5364,-70.175\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"183.4465,-64.7351 181.0946,-72.042 181.1014,-67.3333 178.7563,-69.9314 178.7563,-69.9314 178.7563,-69.9314 181.1014,-67.3333 176.4179,-67.8208 183.4465,-64.7351 183.4465,-64.7351\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"158\" y=\"-93.4\">!a & !b</text>\n",
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"</g>\n",
|
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"<!-- -1->0 -->\n",
|
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"<g class=\"edge\" id=\"edge5\">\n",
|
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"<title>-1->0</title>\n",
|
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"<path d=\"M137.2903,-19.1076C142.2754,-24.3042 160,-44.1814 160,-64.1 160,-220.8401 160,-220.8401 160,-220.8401 160,-244.4744 145.0352,-266.8835 130.8613,-282.8077\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"126.1076,-287.9518 128.545,-280.6729 128.483,-285.3813 130.8584,-282.8108 130.8584,-282.8108 130.8584,-282.8108 128.483,-285.3813 133.1719,-284.9487 126.1076,-287.9518 126.1076,-287.9518\" stroke=\"#000000\"/>\n",
|
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"</g>\n",
|
|
"<!-- -1->1 -->\n",
|
|
"<g class=\"edge\" id=\"edge6\">\n",
|
|
"<title>-1->1</title>\n",
|
|
"<path d=\"M136.2856,-19.9788C137.1778,-27.5338 139.3783,-53.1514 131,-71.6 120.6765,-94.3317 100.9149,-114.5828 84.4087,-128.7318\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"78.9541,-133.291 82.3049,-126.3848 81.6396,-131.0464 84.3251,-128.8017 84.3251,-128.8017 84.3251,-128.8017 81.6396,-131.0464 86.3452,-131.2186 78.9541,-133.291 78.9541,-133.291\" stroke=\"#000000\"/>\n",
|
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"</g>\n",
|
|
"</g>\n",
|
|
"</svg></div><div style='vertical-align:text-top;display:inline-block;'><svg height=\"353pt\" viewBox=\"0.00 0.00 121.00 353.34\" width=\"121pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
|
|
"<g class=\"graph\" id=\"graph0\" transform=\"scale(1 1) rotate(0) translate(4 349.3401)\">\n",
|
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"<title>VWAA for GFa</title>\n",
|
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"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-349.3401 117,-349.3401 117,4 -4,4\" stroke=\"transparent\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"34\" y=\"-331.1401\">Fin(</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"59\" y=\"-331.1401\">⓿</text>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"75\" y=\"-331.1401\">)</text>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"24\" y=\"-317.1401\">[co-Büchi]</text>\n",
|
|
"<g class=\"cluster\" id=\"clust2\">\n",
|
|
"<title>cluster_1</title>\n",
|
|
"<polygon fill=\"none\" points=\"8,-44 8,-113.7401 105,-113.7401 105,-44 8,-44\" stroke=\"#ff0000\"/>\n",
|
|
"</g>\n",
|
|
"<g class=\"cluster\" id=\"clust3\">\n",
|
|
"<title>cluster_2</title>\n",
|
|
"<polygon fill=\"none\" points=\"13,-134.7401 13,-279.3401 76,-279.3401 76,-134.7401 13,-134.7401\" stroke=\"#00ff00\"/>\n",
|
|
"</g>\n",
|
|
"<!-- I -->\n",
|
|
"<!-- 0 -->\n",
|
|
"<g class=\"node\" id=\"node2\">\n",
|
|
"<title>0</title>\n",
|
|
"<g id=\"a_node2\"><a xlink:title=\"GF(a)\">\n",
|
|
"<ellipse cx=\"45\" cy=\"-253.3401\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"45\" y=\"-249.6401\">0</text>\n",
|
|
"</a>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"<!-- I->0 -->\n",
|
|
"<g class=\"edge\" id=\"edge1\">\n",
|
|
"<title>I->0</title>\n",
|
|
"<path d=\"M45,-308.2168C45,-305.1622 45,-291.3953 45,-278.416\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"45,-271.3594 48.1501,-278.3593 45,-274.8594 45.0001,-278.3594 45.0001,-278.3594 45.0001,-278.3594 45,-274.8594 41.8501,-278.3594 45,-271.3594 45,-271.3594\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- -1 -->\n",
|
|
"<g class=\"node\" id=\"node4\">\n",
|
|
"<title>-1</title>\n",
|
|
"<ellipse cx=\"43\" cy=\"-144.5401\" fill=\"#ffffaa\" rx=\"1.8\" ry=\"1.8\" stroke=\"#000000\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 0->-1 -->\n",
|
|
"<g class=\"edge\" id=\"edge2\">\n",
|
|
"<title>0->-1</title>\n",
|
|
"<path d=\"M44.6607,-234.8837C44.228,-211.3414 43.4964,-171.543 43.1682,-153.6882\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"none\" points=\"45.6154,-153.5076 43.037,-146.5538 40.7162,-153.5977 45.6154,-153.5076\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"47.5\" y=\"-187.1401\">1</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1 -->\n",
|
|
"<g class=\"node\" id=\"node3\">\n",
|
|
"<title>1</title>\n",
|
|
"<g id=\"a_node3\"><a xlink:title=\"F(a)\">\n",
|
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"<ellipse cx=\"43\" cy=\"-78.8701\" fill=\"#ffffaa\" rx=\"26.7407\" ry=\"26.7407\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"38.5\" y=\"-82.6701\">1</text>\n",
|
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"35\" y=\"-67.6701\">⓿</text>\n",
|
|
"</a>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"<!-- 1->1 -->\n",
|
|
"<g class=\"edge\" id=\"edge6\">\n",
|
|
"<title>1->1</title>\n",
|
|
"<path d=\"M68.8213,-87.0697C79.1776,-87.533 87.8701,-84.7997 87.8701,-78.8701 87.8701,-74.4228 82.9805,-71.7735 76.1667,-70.9223\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"68.8213,-70.6704 75.9252,-67.7623 72.3193,-70.7904 75.8172,-70.9104 75.8172,-70.9104 75.8172,-70.9104 72.3193,-70.7904 75.7092,-74.0586 68.8213,-70.6704 68.8213,-70.6704\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"92.3701\" y=\"-75.1701\">1</text>\n",
|
|
"</g>\n",
|
|
"<!-- T2T1 -->\n",
|
|
"<!-- 1->T2T1 -->\n",
|
|
"<g class=\"edge\" id=\"edge5\">\n",
|
|
"<title>1->T2T1</title>\n",
|
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"<path d=\"M43,-51.8995C43,-36.6517 43,-18.6623 43,-8.5175\" fill=\"none\" stroke=\"#000000\"/>\n",
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}
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],
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"source": [
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"display_inline(aut1, aut2, aut3, aut4, aut5, show='.bav1us')"
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]
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},
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{
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"source": [
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"## Alternation removal"
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]
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},
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"source": [
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"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",
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"\n",
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"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",
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"\n",
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"The next cell shows this two-step process on our first example automaton."
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]
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},
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"<g id=\"edge1\" class=\"edge\">\n",
|
|
"<title>I->0</title>\n",
|
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"<path fill=\"none\" stroke=\"#000000\" d=\"M115,-480.8767C115,-477.822 115,-464.0552 115,-451.0759\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"115,-444.0193 118.1501,-451.0192 115,-447.5193 115.0001,-451.0193 115.0001,-451.0193 115.0001,-451.0193 115,-447.5193 111.8501,-451.0193 115,-444.0193 115,-444.0193\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 1 -->\n",
|
|
"<g id=\"node3\" class=\"node\">\n",
|
|
"<title>1</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"115\" cy=\"-324\" rx=\"27\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"105\" y=\"-320.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1,3</text>\n",
|
|
"</g>\n",
|
|
"<!-- 0->1 -->\n",
|
|
"<g id=\"edge2\" class=\"edge\">\n",
|
|
"<title>0->1</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M115,-407.7644C115,-391.5192 115,-367.5825 115,-349.4527\"/>\n",
|
|
"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"115,-342.0777 118.1501,-349.0776 115,-345.5777 115.0001,-349.0777 115.0001,-349.0777 115.0001,-349.0777 115,-345.5777 111.8501,-349.0777 115,-342.0777 115,-342.0777\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"118.5\" y=\"-378.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"115\" y=\"-363.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1->1 -->\n",
|
|
"<g id=\"edge3\" class=\"edge\">\n",
|
|
"<title>1->1</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M138.6146,-333.1461C149.9731,-334.2753 160,-331.2266 160,-324 160,-318.3542 153.8801,-315.2585 145.7865,-314.7126\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"138.6146,-314.8539 145.5512,-311.5666 142.1139,-314.7849 145.6132,-314.7159 145.6132,-314.7159 145.6132,-314.7159 142.1139,-314.7849 145.6753,-317.8653 138.6146,-314.8539 138.6146,-314.8539\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"163.5\" y=\"-327.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"160\" 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",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"27\" cy=\"-120\" rx=\"27\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"17\" y=\"-116.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1,4</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1->2 -->\n",
|
|
"<g id=\"edge4\" class=\"edge\">\n",
|
|
"<title>1->2</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M97.5786,-309.9733C80.044,-294.758 53.8143,-268.7592 41,-240 27.403,-209.4843 25.306,-170.4884 25.6624,-145.3775\"/>\n",
|
|
"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"25.831,-138.3686 28.8117,-145.4423 25.7468,-141.8676 25.6626,-145.3666 25.6626,-145.3666 25.6626,-145.3666 25.7468,-141.8676 22.5135,-145.2908 25.831,-138.3686 25.831,-138.3686\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"41\" y=\"-225.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"42\" y=\"-211.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
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"<text text-anchor=\"start\" x=\"58\" 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",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"115\" cy=\"-222\" rx=\"30.5947\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"99.5\" y=\"-218.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1,2,3</text>\n",
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|
"</g>\n",
|
|
"<!-- 1->3 -->\n",
|
|
"<g id=\"edge5\" class=\"edge\">\n",
|
|
"<title>1->3</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M105.0803,-306.978C102.2054,-301.1557 99.4518,-294.4746 98,-288 95.0826,-274.9898 95.0826,-271.0102 98,-258 98.9107,-253.9386 100.3336,-249.796 101.9774,-245.8351\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"104.9008,-239.387 104.8792,-247.0631 103.4555,-242.5747 102.0103,-245.7624 102.0103,-245.7624 102.0103,-245.7624 103.4555,-242.5747 99.1414,-244.4617 104.9008,-239.387 104.9008,-239.387\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"98\" y=\"-269.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4 -->\n",
|
|
"<g id=\"node6\" class=\"node\">\n",
|
|
"<title>4</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"116\" cy=\"-18\" rx=\"30.5947\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"100.5\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1,2,4</text>\n",
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"</g>\n",
|
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"<!-- 1->4 -->\n",
|
|
"<g id=\"edge6\" class=\"edge\">\n",
|
|
"<title>1->4</title>\n",
|
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"<path fill=\"none\" stroke=\"#000000\" d=\"M132.3877,-310.0906C149.76,-294.9709 175.3679,-269.0491 186,-240 196.7051,-210.7515 184.2203,-134.2183 173,-102 164.8436,-78.5795 148.4315,-55.526 135.3041,-39.5126\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"130.6377,-33.9438 137.5481,-37.286 132.8857,-36.6265 135.1337,-39.3091 135.1337,-39.3091 135.1337,-39.3091 132.8857,-36.6265 132.7192,-41.3323 130.6377,-33.9438 130.6377,-33.9438\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"189\" y=\"-174.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & !b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"199.5\" y=\"-159.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2->2 -->\n",
|
|
"<g id=\"edge7\" class=\"edge\">\n",
|
|
"<title>2->2</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M50.6146,-129.1461C61.9731,-130.2753 72,-127.2266 72,-120 72,-114.3542 65.8801,-111.2585 57.7865,-110.7126\"/>\n",
|
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"50.6146,-110.8539 57.5512,-107.5666 54.1139,-110.7849 57.6132,-110.7159 57.6132,-110.7159 57.6132,-110.7159 54.1139,-110.7849 57.6753,-113.8653 50.6146,-110.8539 50.6146,-110.8539\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"72\" y=\"-123.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"73\" y=\"-109.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
|
"<text text-anchor=\"start\" x=\"89\" y=\"-109.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2->4 -->\n",
|
|
"<g id=\"edge8\" class=\"edge\">\n",
|
|
"<title>2->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M23.9747,-102.0388C22.5753,-87.7014 23.0216,-67.7983 33,-54 43.8723,-38.9657 62.3829,-30.1409 79.168,-24.9962\"/>\n",
|
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"86.2286,-23.0093 80.3437,-27.9378 82.8595,-23.9574 79.4903,-24.9056 79.4903,-24.9056 79.4903,-24.9056 82.8595,-23.9574 78.637,-21.8734 86.2286,-23.0093 86.2286,-23.0093\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"33\" y=\"-72.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & !b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"43.5\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->1 -->\n",
|
|
"<g id=\"edge9\" class=\"edge\">\n",
|
|
"<title>3->1</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M115,-240.0777C115,-256.2729 115,-280.2033 115,-298.3707\"/>\n",
|
|
"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"115,-305.7644 111.8501,-298.7644 115,-302.2644 115.0001,-298.7644 115.0001,-298.7644 115.0001,-298.7644 115,-302.2644 118.1501,-298.7645 115,-305.7644 115,-305.7644\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"118.5\" y=\"-276.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"115\" y=\"-261.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->2 -->\n",
|
|
"<g id=\"edge10\" class=\"edge\">\n",
|
|
"<title>3->2</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M100.8613,-205.6119C85.8029,-188.158 61.9096,-160.4634 45.3957,-141.3223\"/>\n",
|
|
"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"40.5256,-135.6774 47.4833,-138.9198 42.8119,-138.3275 45.0983,-140.9775 45.0983,-140.9775 45.0983,-140.9775 42.8119,-138.3275 42.7132,-143.0352 40.5256,-135.6774 40.5256,-135.6774\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"82\" y=\"-174.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"83\" y=\"-160.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
|
"<text text-anchor=\"start\" x=\"99\" y=\"-160.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->3 -->\n",
|
|
"<g id=\"edge11\" class=\"edge\">\n",
|
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"<title>3->3</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M141.4663,-231.2285C153.3068,-232.1074 163.5473,-229.0313 163.5473,-222 163.5473,-216.4519 157.1714,-213.3663 148.6645,-212.7432\"/>\n",
|
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"141.4663,-212.7715 148.4539,-209.5939 144.9663,-212.7577 148.4663,-212.7439 148.4663,-212.7439 148.4663,-212.7439 144.9663,-212.7577 148.4787,-215.8939 141.4663,-212.7715 141.4663,-212.7715\"/>\n",
|
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"<text text-anchor=\"start\" x=\"163.5473\" y=\"-218.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->4 -->\n",
|
|
"<g id=\"edge12\" class=\"edge\">\n",
|
|
"<title>3->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M119.2339,-203.7334C125.7871,-172.7507 136.7627,-107.9983 128,-54 127.38,-50.1795 126.4126,-46.2165 125.2899,-42.3777\"/>\n",
|
|
"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"123.1427,-35.6595 128.2743,-41.3683 124.2082,-38.9934 125.2738,-42.3273 125.2738,-42.3273 125.2738,-42.3273 124.2082,-38.9934 122.2733,-43.2863 123.1427,-35.6595 123.1427,-35.6595\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"132\" y=\"-123.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & !b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"142.5\" y=\"-108.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4->2 -->\n",
|
|
"<g id=\"edge13\" class=\"edge\">\n",
|
|
"<title>4->2</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M105.7988,-35.1873C97.1507,-49.0758 83.9569,-68.7524 70,-84 64.1452,-90.3963 57.1597,-96.6992 50.5388,-102.1997\"/>\n",
|
|
"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"45.0959,-106.6157 48.5471,-99.7592 47.8139,-104.4105 50.5318,-102.2053 50.5318,-102.2053 50.5318,-102.2053 47.8139,-104.4105 52.5165,-104.6515 45.0959,-106.6157 45.0959,-106.6157\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"94\" y=\"-72.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"95\" y=\"-58.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
|
"<text text-anchor=\"start\" x=\"111\" y=\"-58.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4->4 -->\n",
|
|
"<g id=\"edge14\" class=\"edge\">\n",
|
|
"<title>4->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M142.4663,-27.2285C154.3068,-28.1074 164.5473,-25.0313 164.5473,-18 164.5473,-12.4519 158.1714,-9.3663 149.6645,-8.7432\"/>\n",
|
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"142.4663,-8.7715 149.4539,-5.5939 145.9663,-8.7577 149.4663,-8.7439 149.4663,-8.7439 149.4663,-8.7439 145.9663,-8.7577 149.4787,-11.8939 142.4663,-8.7715 142.4663,-8.7715\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"164.5473\" y=\"-21.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & !b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"175.0473\" 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",
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|
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
|
|
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
|
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"<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n",
|
|
" -->\n",
|
|
"<!-- Pages: 1 -->\n",
|
|
"<svg width=\"178pt\" height=\"360pt\"\n",
|
|
" viewBox=\"0.00 0.00 178.13 360.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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"<g id=\"graph0\" class=\"graph\" transform=\"scale(.7484 .7484) rotate(0) translate(4 477)\">\n",
|
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"<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-477 234,-477 234,4 -4,4\"/>\n",
|
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"<text text-anchor=\"start\" x=\"94\" y=\"-458.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">Inf(</text>\n",
|
|
"<text text-anchor=\"start\" x=\"116\" y=\"-458.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
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"<text text-anchor=\"start\" x=\"132\" y=\"-458.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">)</text>\n",
|
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"<text text-anchor=\"start\" x=\"92\" y=\"-444.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">[Büchi]</text>\n",
|
|
"<!-- I -->\n",
|
|
"<!-- 0 -->\n",
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"<g id=\"node2\" class=\"node\">\n",
|
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"<title>0</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"115\" cy=\"-381\" rx=\"27\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"115\" y=\"-377.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">0</text>\n",
|
|
"</g>\n",
|
|
"<!-- I->0 -->\n",
|
|
"<g id=\"edge1\" class=\"edge\">\n",
|
|
"<title>I->0</title>\n",
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"<path fill=\"none\" stroke=\"#000000\" d=\"M115,-435.8767C115,-432.822 115,-419.0552 115,-406.0759\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"115,-399.0193 118.1501,-406.0192 115,-402.5193 115.0001,-406.0193 115.0001,-406.0193 115.0001,-406.0193 115,-402.5193 111.8501,-406.0193 115,-399.0193 115,-399.0193\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 1 -->\n",
|
|
"<g id=\"node3\" class=\"node\">\n",
|
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"<title>1</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"115\" cy=\"-294\" rx=\"27\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"start\" x=\"105\" y=\"-290.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1,3</text>\n",
|
|
"</g>\n",
|
|
"<!-- 0->1 -->\n",
|
|
"<g id=\"edge2\" class=\"edge\">\n",
|
|
"<title>0->1</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M115,-362.9735C115,-350.2586 115,-333.0603 115,-319.0183\"/>\n",
|
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"115,-312.0034 118.1501,-319.0033 115,-315.5034 115.0001,-319.0034 115.0001,-319.0034 115.0001,-319.0034 115,-315.5034 111.8501,-319.0034 115,-312.0034 115,-312.0034\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"119.5\" y=\"-333.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1->1 -->\n",
|
|
"<g id=\"edge3\" class=\"edge\">\n",
|
|
"<title>1->1</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M139.5325,-301.752C150.5078,-302.4902 160,-299.9063 160,-294 160,-289.478 154.4359,-286.9035 146.902,-286.2764\"/>\n",
|
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"139.5325,-286.248 146.5446,-283.1251 143.0324,-286.2616 146.5324,-286.2751 146.5324,-286.2751 146.5324,-286.2751 143.0324,-286.2616 146.5202,-289.4251 139.5325,-286.248 139.5325,-286.248\"/>\n",
|
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"<text text-anchor=\"start\" x=\"160\" y=\"-290.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">b</text>\n",
|
|
"</g>\n",
|
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"<!-- 2 -->\n",
|
|
"<g id=\"node4\" class=\"node\">\n",
|
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"<title>2</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"27\" cy=\"-120\" rx=\"27\" ry=\"18\"/>\n",
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"<text text-anchor=\"start\" x=\"17\" y=\"-116.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1,4</text>\n",
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"</g>\n",
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"<!-- 1->2 -->\n",
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"<g id=\"edge4\" class=\"edge\">\n",
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"<title>1->2</title>\n",
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],
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]
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"metadata": {},
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}
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],
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"source": [
|
|
"nba1t = spot.remove_alternation(aut1, True)\n",
|
|
"nba1 = spot.scc_filter(nba1t, True)\n",
|
|
"display_inline(aut1.show('.bav1u'), nba1t, nba1)"
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|
]
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|
},
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{
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"cell_type": "markdown",
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"metadata": {},
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"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."
|
|
]
|
|
},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"<title>2->2</title>\n",
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"</g>\n",
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"<!-- 3->0 -->\n",
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"<g id=\"edge9\" class=\"edge\">\n",
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"<title>3->0</title>\n",
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"<text text-anchor=\"start\" x=\"172.2965\" y=\"-188.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a & b & p</text>\n",
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"</g>\n",
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"<!-- 3->1 -->\n",
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"<g id=\"edge10\" class=\"edge\">\n",
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"<title>3->1</title>\n",
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"<text text-anchor=\"start\" x=\"10.2965\" y=\"-144.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & !b & p</text>\n",
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"</g>\n",
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"<title>3->2</title>\n",
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"<path fill=\"none\" stroke=\"#000000\" d=\"M100.2965,-86.9735C100.2965,-74.2586 100.2965,-57.0603 100.2965,-43.0183\"/>\n",
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"</g>\n",
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"<!-- 3->3 -->\n",
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"<text text-anchor=\"start\" x=\"152.7435\" y=\"-101.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & b & p</text>\n",
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"</g>\n",
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"</g>\n",
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"</svg>\n",
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"<!-- I->0 -->\n",
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"</g>\n",
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"<title>0->1</title>\n",
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"<!-- 1->0 -->\n",
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"<g id=\"edge3\" class=\"edge\">\n",
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"<title>1->0</title>\n",
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"<path fill=\"none\" stroke=\"#000000\" d=\"M198.3029,-501.0777C198.1441,-517.2729 197.9095,-541.2033 197.7314,-559.3707\"/>\n",
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"<g id=\"node4\" class=\"node\">\n",
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"<title>2</title>\n",
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"</g>\n",
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"<title>1->2</title>\n",
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"<path fill=\"none\" stroke=\"#000000\" d=\"M198.4801,-464.7644C198.4801,-448.5192 198.4801,-424.5825 198.4801,-406.4527\"/>\n",
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"</g>\n",
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"<title>2->3</title>\n",
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"<path fill=\"none\" stroke=\"#000000\" d=\"M182.6052,-366.0132C176.1631,-359.7072 168.7727,-352.1783 162.4801,-345 151.4051,-332.3661 152.7445,-325.3116 139.4801,-315 126.8853,-305.2089 111.226,-297.5555 96.8524,-291.871\"/>\n",
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"<title>4</title>\n",
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"<text text-anchor=\"start\" x=\"176.4801\" y=\"-101.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">0,4,~1</text>\n",
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"</g>\n",
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"<!-- 2->4 -->\n",
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"<g id=\"edge6\" class=\"edge\">\n",
|
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"<title>2->4</title>\n",
|
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"<path fill=\"none\" stroke=\"#000000\" d=\"M212.1839,-364.839C216.3299,-358.9724 220.3469,-352.0455 222.4801,-345 226.3439,-332.2388 222.5567,-328.3331 222.4801,-315 222.0357,-237.6628 243.3166,-214.89 220.4801,-141 219.0793,-136.4675 216.909,-131.9803 214.434,-127.7919\"/>\n",
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"<text text-anchor=\"start\" x=\"229.4801\" y=\"-231.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & !b & p</text>\n",
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"</g>\n",
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"<g id=\"edge7\" class=\"edge\">\n",
|
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"<title>3->0</title>\n",
|
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"<path fill=\"none\" stroke=\"#000000\" d=\"M53.0145,-296.971C51.7563,-310.4285 51.262,-329.1668 55.4801,-345 79.2975,-434.4008 146.6852,-524.0674 179.3214,-563.7846\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"183.8751,-569.2761 176.982,-565.8984 181.641,-566.5819 179.4068,-563.8877 179.4068,-563.8877 179.4068,-563.8877 181.641,-566.5819 181.8316,-561.8769 183.8751,-569.2761 183.8751,-569.2761\"/>\n",
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"<text text-anchor=\"start\" x=\"97.4801\" y=\"-435.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a & !b</text>\n",
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"</g>\n",
|
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"<!-- 3->2 -->\n",
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"<g id=\"edge8\" class=\"edge\">\n",
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"<title>3->2</title>\n",
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"<path fill=\"none\" stroke=\"#000000\" d=\"M55.1305,-297.0216C55.8315,-311.7878 59.217,-332.2569 71.4801,-345 84.1486,-358.1643 130.3003,-368.8951 163.3133,-375.1173\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"170.558,-376.4508 163.1034,-378.2815 167.1158,-375.8171 163.6736,-375.1835 163.6736,-375.1835 163.6736,-375.1835 167.1158,-375.8171 164.2439,-372.0856 170.558,-376.4508 170.558,-376.4508\"/>\n",
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"<text text-anchor=\"start\" x=\"71.4801\" y=\"-326.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & !b & p</text>\n",
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"</g>\n",
|
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"<!-- 5 -->\n",
|
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"<g id=\"node7\" class=\"node\">\n",
|
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"<title>5</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"109.4801\" cy=\"-18\" rx=\"28.6953\" ry=\"18\"/>\n",
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"</g>\n",
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"<!-- 3->5 -->\n",
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"<g id=\"edge9\" class=\"edge\">\n",
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"<title>3->5</title>\n",
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"<path fill=\"none\" stroke=\"#000000\" d=\"M41.1276,-262.0067C20.9583,-235.9647 -11.6044,-184.6153 4.4801,-141 20.5563,-97.4072 59.7241,-58.7761 85.4119,-36.9077\"/>\n",
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"<text text-anchor=\"start\" x=\"4.4801\" y=\"-144.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a & b & p</text>\n",
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"<!-- 6 -->\n",
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"<g id=\"node8\" class=\"node\">\n",
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"<title>6</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"97.4801\" cy=\"-192\" rx=\"41.6928\" ry=\"18\"/>\n",
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"<text text-anchor=\"start\" x=\"73.4801\" y=\"-188.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">3,~1,~0</text>\n",
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"</g>\n",
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"<!-- 3->6 -->\n",
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"<g id=\"edge10\" class=\"edge\">\n",
|
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"<title>3->6</title>\n",
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"<path fill=\"none\" stroke=\"#000000\" d=\"M80.8033,-264.4247C88.2207,-258.7655 95.4226,-251.5624 99.4801,-243 103.178,-235.1965 103.7707,-225.9436 103.0864,-217.4757\"/>\n",
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"<title>4->0</title>\n",
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"</g>\n",
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"<!-- 4->2 -->\n",
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"<g id=\"edge12\" class=\"edge\">\n",
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"<title>4->2</title>\n",
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"</g>\n",
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"<title>1->3</title>\n",
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"<title>3->0</title>\n",
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"<title>3->3</title>\n",
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"nba2, nba3, nba4, nba5 = [spot.scc_filter(spot.remove_alternation(a, True), True) for a in (aut2, aut3, aut4, aut5)]\n",
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"display_inline(nba2, nba3, nba4, nba5)"
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"The following demonstrate that very weak (non-alternating) Büchi automata can be complemented via alternation removal."
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]
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},
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"</g>\n",
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"<!-- 0->1 -->\n",
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"<g class=\"edge\" id=\"edge2\">\n",
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"<title>0->1</title>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"38\" y=\"-345.8802\">a</text>\n",
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"</g>\n",
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"</g>\n",
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"<g class=\"edge\" id=\"edge6\">\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"54\" y=\"-302.3802\">!b</text>\n",
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"</g>\n",
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"<!-- 2 -->\n",
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"<g class=\"node\" id=\"node5\">\n",
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"<title>2</title>\n",
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"24\" y=\"-213.0102\">⓿</text>\n",
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"</g>\n",
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"<title>-1->2</title>\n",
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"</g>\n",
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"<g class=\"node\" id=\"node6\">\n",
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"<title>3</title>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"126\" y=\"-220.5102\">3</text>\n",
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"</g>\n",
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"<!-- -1->3 -->\n",
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"<g class=\"edge\" id=\"edge5\">\n",
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"<title>-1->3</title>\n",
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"<path d=\"M87.8146,-304.3703C91.2692,-297.1182 104.991,-268.3129 114.9992,-247.3034\" fill=\"none\" stroke=\"#000000\"/>\n",
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"</g>\n",
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"<!-- 2->2 -->\n",
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"<g class=\"edge\" id=\"edge7\">\n",
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"<title>2->2</title>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"76.8701\" y=\"-220.5102\">!b</text>\n",
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"</g>\n",
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"<!-- T5T2 -->\n",
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"<!-- 2->T5T2 -->\n",
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"<g class=\"edge\" id=\"edge8\">\n",
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"<title>2->T5T2</title>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"32\" y=\"-168.1401\">b</text>\n",
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"</g>\n",
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"<!-- T5T3 -->\n",
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"<!-- 3->T5T3 -->\n",
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"<g class=\"edge\" id=\"edge9\">\n",
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"<title>3->T5T3</title>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"109\" y=\"-168.1401\">a</text>\n",
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"</g>\n",
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"<g class=\"node\" id=\"node9\">\n",
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"</g>\n",
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"<title>3->-4</title>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"127\" y=\"-168.1401\">!a</text>\n",
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"</g>\n",
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"<g class=\"edge\" id=\"edge11\">\n",
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"<title>-4->3</title>\n",
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"<path d=\"M139.0993,-146.4396C139.3415,-151.7017 139.8169,-166.9002 138,-179.3401 137.0073,-186.1373 135.3464,-193.3793 133.5721,-200.0174\" fill=\"none\" stroke=\"#000000\"/>\n",
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"</g>\n",
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"<!-- 4 -->\n",
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"<g class=\"node\" id=\"node10\">\n",
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"<title>4</title>\n",
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"</g>\n",
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"<g class=\"edge\" id=\"edge12\">\n",
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"<title>-4->4</title>\n",
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"</g>\n",
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"<!-- 4->4 -->\n",
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"<g class=\"edge\" id=\"edge13\">\n",
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"<title>4->4</title>\n",
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"<path d=\"M164.8213,-87.0697C175.1776,-87.533 183.8701,-84.7997 183.8701,-78.8701 183.8701,-74.4228 178.9805,-71.7735 172.1667,-70.9223\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"183.8701\" y=\"-75.1701\">!a & !b</text>\n",
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"</g>\n",
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"<!-- T5T4 -->\n",
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"<!-- 4->T5T4 -->\n",
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"<g class=\"edge\" id=\"edge14\">\n",
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"<title>4->T5T4</title>\n",
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"<path d=\"M139,-51.8995C139,-36.6517 139,-18.6623 139,-8.5175\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"139\" y=\"-22.8\">a | b</text>\n",
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"</g>\n",
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"</g>\n",
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"</svg></div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
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" -->\n",
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" viewBox=\"0.00 0.00 280.08 360.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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"<g id=\"graph0\" class=\"graph\" transform=\"scale(.7073 .7073) rotate(0) translate(4 505)\">\n",
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"<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-505 392,-505 392,4 -4,4\"/>\n",
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"<text text-anchor=\"start\" x=\"147\" y=\"-486.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">Inf(</text>\n",
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"<text text-anchor=\"start\" x=\"169\" y=\"-486.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
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"<text text-anchor=\"start\" x=\"185\" y=\"-486.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">)&Inf(</text>\n",
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"<text text-anchor=\"start\" x=\"221\" y=\"-486.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"<text text-anchor=\"start\" x=\"237\" y=\"-486.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">)</text>\n",
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"<!-- I -->\n",
|
|
"<!-- 0 -->\n",
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"<g id=\"node2\" class=\"node\">\n",
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"<title>0</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"69\" cy=\"-409\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"69\" y=\"-405.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">0</text>\n",
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"</g>\n",
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"<!-- I->0 -->\n",
|
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"<g id=\"edge1\" class=\"edge\">\n",
|
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"<title>I->0</title>\n",
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"<path fill=\"none\" stroke=\"#000000\" d=\"M69,-463.8767C69,-460.822 69,-447.0552 69,-434.0759\"/>\n",
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"</g>\n",
|
|
"<!-- 1 -->\n",
|
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"<g id=\"node3\" class=\"node\">\n",
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"<title>1</title>\n",
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"<text text-anchor=\"middle\" x=\"18\" y=\"-303.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1</text>\n",
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"</g>\n",
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"<!-- 0->1 -->\n",
|
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"<g id=\"edge2\" class=\"edge\">\n",
|
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"<title>0->1</title>\n",
|
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"<path fill=\"none\" stroke=\"#000000\" d=\"M60.806,-392.6119C52.3298,-375.6595 39.0233,-349.0465 29.4966,-329.9931\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"26.1737,-323.3474 32.1217,-328.1996 27.739,-326.4779 29.3042,-329.6084 29.3042,-329.6084 29.3042,-329.6084 27.739,-326.4779 26.4868,-331.0171 26.1737,-323.3474 26.1737,-323.3474\"/>\n",
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"<text text-anchor=\"start\" x=\"62.5\" y=\"-361.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a</text>\n",
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"<text text-anchor=\"start\" x=\"50\" y=\"-347.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
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"<text text-anchor=\"start\" x=\"66\" y=\"-347.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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|
"</g>\n",
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"<!-- 2 -->\n",
|
|
"<g id=\"node4\" class=\"node\">\n",
|
|
"<title>2</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"122\" cy=\"-307\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"122\" y=\"-303.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">2</text>\n",
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"</g>\n",
|
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"<!-- 0->2 -->\n",
|
|
"<g id=\"edge3\" class=\"edge\">\n",
|
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"<title>0->2</title>\n",
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"<path fill=\"none\" stroke=\"#000000\" d=\"M77.5154,-392.6119C86.415,-375.4844 100.4385,-348.4957 110.3581,-329.4052\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"113.6805,-323.0111 113.2481,-330.675 112.0667,-326.1169 110.4529,-329.2226 110.4529,-329.2226 110.4529,-329.2226 112.0667,-326.1169 107.6577,-327.7702 113.6805,-323.0111 113.6805,-323.0111\"/>\n",
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"<text text-anchor=\"start\" x=\"103.5\" y=\"-361.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a</text>\n",
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"</g>\n",
|
|
"<!-- 1->1 -->\n",
|
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"<g id=\"edge4\" class=\"edge\">\n",
|
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"<title>1->1</title>\n",
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"<path fill=\"none\" stroke=\"#000000\" d=\"M34.6641,-314.3828C44.625,-316.0234 54,-313.5625 54,-307 54,-302.0781 48.7266,-299.4634 41.8876,-299.1558\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"34.6641,-299.6172 41.449,-296.0273 38.1569,-299.394 41.6498,-299.1709 41.6498,-299.1709 41.6498,-299.1709 38.1569,-299.394 41.8507,-302.3145 34.6641,-299.6172 34.6641,-299.6172\"/>\n",
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"<text text-anchor=\"start\" x=\"63.5\" y=\"-310.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!b</text>\n",
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"</g>\n",
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|
"<!-- 3 -->\n",
|
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"<g id=\"node5\" class=\"node\">\n",
|
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"<title>3</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"114\" cy=\"-18\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"114\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">3</text>\n",
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"</g>\n",
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"<!-- 2->3 -->\n",
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"<g id=\"edge5\" class=\"edge\">\n",
|
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"<title>2->3</title>\n",
|
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"<path fill=\"none\" stroke=\"#000000\" d=\"M111.1321,-292.1353C106.9052,-285.848 102.2966,-278.3002 99,-271 82.4421,-234.3339 79.6104,-223.8383 74,-184 65.8176,-125.8982 77.7857,-109.4398 97,-54 98.5151,-49.6285 100.4001,-45.0818 102.3581,-40.7504\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"105.4521,-34.1772 105.3209,-41.8522 103.9615,-37.3439 102.4709,-40.5106 102.4709,-40.5106 102.4709,-40.5106 103.9615,-37.3439 99.6208,-39.169 105.4521,-34.1772 105.4521,-34.1772\"/>\n",
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"<text text-anchor=\"start\" x=\"74\" y=\"-172.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & b</text>\n",
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"<text text-anchor=\"start\" x=\"91\" y=\"-158.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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|
"</g>\n",
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"<!-- 4 -->\n",
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"<g id=\"node6\" class=\"node\">\n",
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|
"<title>4</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"168\" cy=\"-118\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"168\" y=\"-114.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">4</text>\n",
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"</g>\n",
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"<!-- 2->4 -->\n",
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"<g id=\"edge6\" class=\"edge\">\n",
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"<title>2->4</title>\n",
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"<path fill=\"none\" stroke=\"#000000\" d=\"M114.3235,-290.6052C105.5847,-269.6095 93.7669,-232.316 104,-202 112.9556,-175.4686 134.0061,-150.6953 149.5316,-135.0263\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"154.5595,-130.0721 151.7842,-137.229 152.0664,-132.5286 149.5733,-134.9852 149.5733,-134.9852 149.5733,-134.9852 152.0664,-132.5286 147.3625,-132.7414 154.5595,-130.0721 154.5595,-130.0721\"/>\n",
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"<text text-anchor=\"start\" x=\"104\" y=\"-223.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a & b</text>\n",
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"<text text-anchor=\"start\" x=\"114.5\" y=\"-208.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
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"</g>\n",
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"<!-- 5 -->\n",
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"<g id=\"node7\" class=\"node\">\n",
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"<title>5</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"336\" cy=\"-118\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"336\" y=\"-114.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">5</text>\n",
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"</g>\n",
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"<!-- 2->5 -->\n",
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"<g id=\"edge7\" class=\"edge\">\n",
|
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"<title>2->5</title>\n",
|
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"<path fill=\"none\" stroke=\"#000000\" d=\"M139.3336,-300.9028C166.1019,-290.875 218.1497,-268.8882 254,-238 286.2495,-210.2142 311.605,-166.9367 325.1476,-140.6522\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"328.3331,-134.3556 327.9839,-142.0238 326.7531,-137.4787 325.1731,-140.6018 325.1731,-140.6018 325.1731,-140.6018 326.7531,-137.4787 322.3623,-139.1797 328.3331,-134.3556 328.3331,-134.3556\"/>\n",
|
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"<text text-anchor=\"start\" x=\"286\" y=\"-223.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & !b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"296.5\" 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",
|
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"<title>6</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"168\" cy=\"-220\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"168\" y=\"-216.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">6</text>\n",
|
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"</g>\n",
|
|
"<!-- 2->6 -->\n",
|
|
"<g id=\"edge8\" class=\"edge\">\n",
|
|
"<title>2->6</title>\n",
|
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"<path fill=\"none\" stroke=\"#000000\" d=\"M130.4371,-291.0429C137.6541,-277.3933 148.1209,-257.5975 156.1737,-242.3671\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"159.4606,-236.1506 158.9733,-243.8113 157.8246,-239.2447 156.1886,-242.3389 156.1886,-242.3389 156.1886,-242.3389 157.8246,-239.2447 153.4039,-240.8665 159.4606,-236.1506 159.4606,-236.1506\"/>\n",
|
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"<text text-anchor=\"start\" x=\"147\" y=\"-259.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a & !b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->3 -->\n",
|
|
"<g id=\"edge9\" class=\"edge\">\n",
|
|
"<title>3->3</title>\n",
|
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"<path fill=\"none\" stroke=\"#000000\" d=\"M129.916,-26.6334C140.1504,-28.8856 150,-26.0078 150,-18 150,-11.869 144.2263,-8.7452 136.9268,-8.6284\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"129.916,-9.3666 136.5477,-5.5008 133.3968,-9 136.8775,-8.6335 136.8775,-8.6335 136.8775,-8.6335 133.3968,-9 137.2074,-11.7662 129.916,-9.3666 129.916,-9.3666\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"161.5\" y=\"-21.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"150\" y=\"-7.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
|
"<text text-anchor=\"start\" x=\"166\" y=\"-7.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"</g>\n",
|
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"<!-- 4->3 -->\n",
|
|
"<g id=\"edge10\" class=\"edge\">\n",
|
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"<title>4->3</title>\n",
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"<path fill=\"none\" stroke=\"#000000\" d=\"M159.324,-101.9333C150.3491,-85.3132 136.2599,-59.2221 126.1728,-40.5423\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"122.6545,-34.0269 128.7523,-38.6895 124.3175,-37.1065 125.9806,-40.1862 125.9806,-40.1862 125.9806,-40.1862 124.3175,-37.1065 123.2089,-41.6829 122.6545,-34.0269 122.6545,-34.0269\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"159.5\" y=\"-71.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">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->4 -->\n",
|
|
"<g id=\"edge11\" class=\"edge\">\n",
|
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"<title>4->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M185.7817,-122.4941C195.3149,-123.2578 204,-121.7598 204,-118 204,-115.2389 199.3161,-113.6976 193.0521,-113.3761\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"185.7817,-113.5059 192.7243,-110.2313 189.2812,-113.4434 192.7806,-113.3808 192.7806,-113.3808 192.7806,-113.3808 189.2812,-113.4434 192.8369,-116.5303 185.7817,-113.5059 185.7817,-113.5059\"/>\n",
|
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"<text text-anchor=\"start\" x=\"204\" y=\"-121.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a & !b</text>\n",
|
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"<text text-anchor=\"start\" x=\"216.5\" y=\"-106.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
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|
"</g>\n",
|
|
"<!-- 4->4 -->\n",
|
|
"<g id=\"edge12\" class=\"edge\">\n",
|
|
"<title>4->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M185.0174,-124.4905C209.3485,-129.8803 245,-127.7168 245,-118 245,-109.1942 215.7198,-106.5917 192.1203,-110.1928\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"185.0174,-111.5095 191.326,-107.1363 188.4588,-110.8715 191.9002,-110.2335 191.9002,-110.2335 191.9002,-110.2335 188.4588,-110.8715 192.4744,-113.3307 185.0174,-111.5095 185.0174,-111.5095\"/>\n",
|
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"<text text-anchor=\"start\" x=\"245\" y=\"-121.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a & b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"247.5\" y=\"-107.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
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"<text text-anchor=\"start\" x=\"263.5\" y=\"-107.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->3 -->\n",
|
|
"<g id=\"edge13\" class=\"edge\">\n",
|
|
"<title>5->3</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M321.1759,-107.3876C317.3021,-104.819 313.0694,-102.1865 309,-100 249.8571,-68.2231 175.7422,-40.0144 138.1989,-26.4825\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"131.1931,-23.9751 138.8452,-23.3682 134.4884,-25.1545 137.7837,-26.3339 137.7837,-26.3339 137.7837,-26.3339 134.4884,-25.1545 136.7222,-29.2997 131.1931,-23.9751 131.1931,-23.9751\"/>\n",
|
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"<text text-anchor=\"start\" x=\"283.5\" y=\"-71.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"272\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
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"<text text-anchor=\"start\" x=\"288\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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|
"</g>\n",
|
|
"<!-- 5->5 -->\n",
|
|
"<g id=\"edge14\" class=\"edge\">\n",
|
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"<title>5->5</title>\n",
|
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"<path fill=\"none\" stroke=\"#000000\" d=\"M351.916,-126.6334C362.1504,-128.8856 372,-126.0078 372,-118 372,-111.869 366.2263,-108.7452 358.9268,-108.6284\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"351.916,-109.3666 358.5477,-105.5008 355.3968,-109 358.8775,-108.6335 358.8775,-108.6335 358.8775,-108.6335 355.3968,-109 359.2074,-111.7662 351.916,-109.3666 351.916,-109.3666\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"373.5\" y=\"-121.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"372\" y=\"-106.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->3 -->\n",
|
|
"<g id=\"edge15\" class=\"edge\">\n",
|
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"<title>6->3</title>\n",
|
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"<path fill=\"none\" stroke=\"#000000\" d=\"M154.9131,-207.5268C139.9793,-192.2977 116.409,-164.9691 107,-136 96.946,-105.045 102.0356,-67.1566 107.3642,-42.8056\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"109.0091,-35.7056 110.4979,-43.236 108.2192,-39.1153 107.4292,-42.525 107.4292,-42.525 107.4292,-42.525 108.2192,-39.1153 104.3604,-41.814 109.0091,-35.7056 109.0091,-35.7056\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"107\" y=\"-121.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & 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->4 -->\n",
|
|
"<g id=\"edge16\" class=\"edge\">\n",
|
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"<title>6->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M168,-201.7644C168,-185.5192 168,-161.5825 168,-143.4527\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"168,-136.0777 171.1501,-143.0776 168,-139.5777 168.0001,-143.0777 168.0001,-143.0777 168.0001,-143.0777 168,-139.5777 164.8501,-143.0777 168,-136.0777 168,-136.0777\"/>\n",
|
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"<text text-anchor=\"start\" x=\"168\" y=\"-172.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a & b</text>\n",
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"<text text-anchor=\"start\" x=\"170.5\" y=\"-158.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
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"</g>\n",
|
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"<!-- 6->5 -->\n",
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|
"<g id=\"edge17\" class=\"edge\">\n",
|
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"<title>6->5</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M181.5924,-207.8275C198.322,-193.3609 228.0796,-169.2651 257,-154 278.6285,-142.5838 287.0924,-146.8711 309,-136 311.0691,-134.9733 313.1679,-133.8137 315.234,-132.5902\"/>\n",
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|
|
"<text text-anchor=\"start\" x=\"257\" y=\"-172.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & !b</text>\n",
|
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"<text text-anchor=\"start\" x=\"267.5\" y=\"-157.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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|
"</g>\n",
|
|
"<!-- 6->6 -->\n",
|
|
"<g id=\"edge18\" class=\"edge\">\n",
|
|
"<title>6->6</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M184.6641,-227.3828C194.625,-229.0234 204,-226.5625 204,-220 204,-215.0781 198.7266,-212.4634 191.8876,-212.1558\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"184.6641,-212.6172 191.449,-209.0273 188.1569,-212.394 191.6498,-212.1709 191.6498,-212.1709 191.6498,-212.1709 188.1569,-212.394 191.8507,-215.3145 184.6641,-212.6172 184.6641,-212.6172\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"204\" y=\"-216.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a & !b</text>\n",
|
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"</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": {
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"display_name": "Python 3",
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"language": "python",
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|
"name": "python3"
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|
},
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"language_info": {
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|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
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|
"file_extension": ".py",
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|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.7.3rc1"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
|