alarsyo/spot
1
0
Fork 0
Code Issues Pull requests Projects Releases Wiki Activity
spot/tests/python/parity.ipynb
Alexandre Duret-Lutz e6c8c09fd5 tests: fix some examples 
Reported by František Blahoudek.

* tests/python/parity.ipynb: Fix examples and improve some text.
2019-04-18 14:41:03 +02:00

2091 lines
148 KiB
Text
Raw Blame History

{
"cells": [
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"from IPython.display import display\n",
"import spot\n",
"spot.setup()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Definitions and examples for parity acceptance"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In Spot a **parity acceptance** is defined by a **kind**, a **style** and a **numsets**:\n",
"+ The **kind** can be either **max** or **min**.\n",
"+ The **style** can be either **odd** or **even**.\n",
"+ The **numsets** is the number of acceptance sets used by the parity acceptance.\n",
" \n",
"Here are some examples:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"parity min odd 1 = Fin(0)\n",
"parity min odd 2 = Fin(0) & Inf(1)\n",
"parity min odd 3 = Fin(0) & (Inf(1) | Fin(2))\n",
"parity min odd 4 = Fin(0) & (Inf(1) | (Fin(2) & Inf(3)))\n",
"parity min even 1 = Inf(0)\n",
"parity min even 2 = Inf(0) | Fin(1)\n",
"parity min even 3 = Inf(0) | (Fin(1) & Inf(2))\n",
"parity min even 4 = Inf(0) | (Fin(1) & (Inf(2) | Fin(3)))\n",
"parity max odd 1 = Fin(0)\n",
"parity max odd 2 = Inf(1) | Fin(0)\n",
"parity max odd 3 = Fin(2) & (Inf(1) | Fin(0))\n",
"parity max odd 4 = Inf(3) | (Fin(2) & (Inf(1) | Fin(0)))\n",
"parity max even 1 = Inf(0)\n",
"parity max even 2 = Fin(1) & Inf(0)\n",
"parity max even 3 = Inf(2) | (Fin(1) & Inf(0))\n",
"parity max even 4 = Fin(3) & (Inf(2) | (Fin(1) & Inf(0)))\n"
]
}
],
"source": [
"for kind in ['min', 'max']:\n",
" for style in ['odd', 'even']:\n",
" for sets in range(1, 5):\n",
" name = 'parity {} {} {}'.format(kind, style, sets)\n",
" print('{:17} = {}'.format(name, spot.acc_code(name)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Change parity\n",
"\n",
"This section describes the `change_parity()` method, that allows switching between different kinds and styles."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## To toggle **style**\n",
"### A new acceptance set is introduced and all the existing sets' indexes are increased by 1.\n",
"#### Parity max odd 5 -> Parity max even\n",
"If the acceptance is a parity **max**, all the transitions that do not belong to any acceptance set will belong to the new set."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"<svg height=\"219pt\" viewBox=\"0.00 0.00 494.00 219.14\" width=\"494pt\" 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(4 215.1379)\">\n",
"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-215.1379 490,-215.1379 490,4 -4,4\" stroke=\"transparent\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"94\" y=\"-196.9379\">Fin(</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"119\" y=\"-196.9379\">❹</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"135\" y=\"-196.9379\">) &amp; (Inf(</text>\n",
"<text fill=\"#6a3d9a\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"182\" y=\"-196.9379\">❸</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"198\" y=\"-196.9379\">) | (Fin(</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"241\" y=\"-196.9379\">❷</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"257\" y=\"-196.9379\">) &amp; (Inf(</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"304\" y=\"-196.9379\">❶</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"320\" y=\"-196.9379\">) | Fin(</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"360\" y=\"-196.9379\">⓿</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"376\" y=\"-196.9379\">))))</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"185.5\" y=\"-182.9379\">[parity max odd 5]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g class=\"node\" id=\"node2\">\n",
"<title>0</title>\n",
"<ellipse cx=\"56\" cy=\"-27.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"56\" y=\"-23.4379\">0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge1\">\n",
"<title>I-&gt;0</title>\n",
"<path d=\"M1.1233,-27.1379C4.178,-27.1379 17.9448,-27.1379 30.9241,-27.1379\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"37.9807,-27.1379 30.9808,-30.288 34.4807,-27.1379 30.9807,-27.138 30.9807,-27.138 30.9807,-27.138 34.4807,-27.1379 30.9807,-23.988 37.9807,-27.1379 37.9807,-27.1379\" stroke=\"#000000\"/>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g class=\"node\" id=\"node3\">\n",
"<title>2</title>\n",
"<ellipse cx=\"187\" cy=\"-89.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"187\" y=\"-85.4379\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge2\">\n",
"<title>0-&gt;2</title>\n",
"<path d=\"M72.3264,-34.8648C95.3702,-45.7711 137.55,-65.7341 163.8289,-78.1714\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"170.4679,-81.3135 162.7932,-81.1661 167.3043,-79.8162 164.1407,-78.3189 164.1407,-78.3189 164.1407,-78.3189 167.3043,-79.8162 165.4883,-75.4717 170.4679,-81.3135 170.4679,-81.3135\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"92\" y=\"-73.9379\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g class=\"node\" id=\"node4\">\n",
"<title>3</title>\n",
"<ellipse cx=\"468\" cy=\"-50.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"468\" y=\"-46.4379\">3</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge3\">\n",
"<title>0-&gt;3</title>\n",
"<path d=\"M74.2347,-28.1558C140.1802,-31.8372 366.3929,-44.4656 442.661,-48.7233\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"449.9758,-49.1317 442.8111,-51.8865 446.4813,-48.9365 442.9867,-48.7414 442.9867,-48.7414 442.9867,-48.7414 446.4813,-48.9365 443.1623,-45.5963 449.9758,-49.1317 449.9758,-49.1317\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"223\" y=\"-57.9379\">!p0 &amp; !p1</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"244.5\" y=\"-42.9379\">❹</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g class=\"node\" id=\"node5\">\n",
"<title>1</title>\n",
"<ellipse cx=\"329.5\" cy=\"-124.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"329.5\" y=\"-120.4379\">1</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;1 -->\n",
"<g class=\"edge\" id=\"edge7\">\n",
"<title>2-&gt;1</title>\n",
"<path d=\"M194.4417,-105.7555C200.4125,-116.8719 209.9563,-130.616 223,-137.1379 249.4223,-150.349 283.9805,-142.2021 306.4535,-134.0898\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"313.0175,-131.597 307.5919,-137.027 309.7455,-132.8396 306.4735,-134.0822 306.4735,-134.0822 306.4735,-134.0822 309.7455,-132.8396 305.3552,-131.1374 313.0175,-131.597 313.0175,-131.597\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"226.5\" y=\"-146.9379\">p0 &amp; p1</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge8\">\n",
"<title>3-&gt;0</title>\n",
"<path d=\"M450.8478,-44.1499C418.3857,-33.17 345.5214,-10.2021 282,-2.1379 255.9866,1.1646 249.1499,-.1914 223,-2.1379 172.1741,-5.9211 113.3624,-16.0956 80.8517,-22.2358\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"73.9414,-23.5552 80.2264,-19.1482 77.3793,-22.8988 80.8172,-22.2423 80.8172,-22.2423 80.8172,-22.2423 77.3793,-22.8988 81.408,-25.3364 73.9414,-23.5552 73.9414,-23.5552\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"225\" y=\"-20.9379\">p0 &amp; !p1</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"244.5\" y=\"-5.9379\">❶</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge9\">\n",
"<title>3-&gt;2</title>\n",
"<path d=\"M450.1447,-52.616C401.7471,-59.3331 267.9465,-77.9033 212.0485,-85.6614\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"205.0053,-86.6389 211.5057,-82.5564 208.472,-86.1577 211.9388,-85.6765 211.9388,-85.6765 211.9388,-85.6765 208.472,-86.1577 212.3719,-88.7966 205.0053,-86.6389 205.0053,-86.6389\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"300\" y=\"-75.9379\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge4\">\n",
"<title>1-&gt;2</title>\n",
"<path d=\"M312.5568,-117.345C303.5825,-113.9337 292.3114,-109.9414 282,-107.1379 258.5876,-100.7723 231.3296,-95.8568 212.0314,-92.7832\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"205.0495,-91.6962 212.4508,-89.6606 208.5078,-92.2347 211.9662,-92.7731 211.9662,-92.7731 211.9662,-92.7731 208.5078,-92.2347 211.4815,-95.8857 205.0495,-91.6962 205.0495,-91.6962\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"225\" y=\"-125.9379\">!p0 &amp; p1</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"244.5\" y=\"-110.9379\">❹</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge6\">\n",
"<title>1-&gt;3</title>\n",
"<path d=\"M347.2795,-120.3178C368.6392,-115.1652 404.9704,-104.5683 432,-87.1379 439.2661,-82.4522 446.1681,-76.0438 451.9486,-69.8765\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"456.9202,-64.3368 454.5892,-71.6504 454.5825,-66.9417 452.2448,-69.5465 452.2448,-69.5465 452.2448,-69.5465 454.5825,-66.9417 449.9004,-67.4426 456.9202,-64.3368 456.9202,-64.3368\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"377\" y=\"-129.9379\">!p0 &amp; p1</text>\n",
"<text fill=\"#6a3d9a\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"396.5\" y=\"-114.9379\">❸</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g class=\"edge\" id=\"edge5\">\n",
"<title>1-&gt;1</title>\n",
"<path d=\"M317.5762,-137.8048C312.8066,-148.7941 316.7813,-160.1379 329.5,-160.1379 339.4365,-160.1379 344.036,-153.2142 343.2986,-144.945\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"341.4238,-137.8048 346.2483,-143.7754 342.3127,-141.1901 343.2016,-144.5754 343.2016,-144.5754 343.2016,-144.5754 342.3127,-141.1901 340.1549,-145.3754 341.4238,-137.8048 341.4238,-137.8048\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"303.5\" y=\"-163.9379\">p0 &amp; p1</text>\n",
"</g>\n",
"</g>\n",
"</svg>"
],
"text/plain": [
"<IPython.core.display.SVG object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"aut_max_odd5 = tuple(spot.automata(\"randaut -A 'parity max odd 5' -Q4 2|\"))[0]\n",
"display(aut_max_odd5.show(\".a\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The new indexes of the acceptance sets:\n",
"+ 4 -> 5\n",
"+ 3 -> 4\n",
"+ 2 -> 3\n",
"+ 1 -> 2\n",
"+ 0 -> 1\n",
"+ ∅ -> 0"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Result of Parity max odd 5 -> Parity max even 6"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"<svg height=\"249pt\" viewBox=\"0.00 0.00 494.00 249.14\" width=\"494pt\" 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(4 245.1379)\">\n",
"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-245.1379 490,-245.1379 490,4 -4,4\" stroke=\"transparent\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"61.5\" y=\"-226.9379\">Fin(</text>\n",
"<text fill=\"#e31a1c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"86.5\" y=\"-226.9379\">❺</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"102.5\" y=\"-226.9379\">) &amp; (Inf(</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"149.5\" y=\"-226.9379\">❹</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"165.5\" y=\"-226.9379\">) | (Fin(</text>\n",
"<text fill=\"#6a3d9a\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"208.5\" y=\"-226.9379\">❸</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"224.5\" y=\"-226.9379\">) &amp; (Inf(</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"271.5\" y=\"-226.9379\">❷</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"287.5\" y=\"-226.9379\">) | (Fin(</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"330.5\" y=\"-226.9379\">❶</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"346.5\" y=\"-226.9379\">) &amp; Inf(</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"389.5\" y=\"-226.9379\">⓿</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"405.5\" y=\"-226.9379\">)))))</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"182.5\" y=\"-212.9379\">[parity max even 6]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g class=\"node\" id=\"node2\">\n",
"<title>0</title>\n",
"<ellipse cx=\"56\" cy=\"-27.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"56\" y=\"-23.4379\">0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge1\">\n",
"<title>I-&gt;0</title>\n",
"<path d=\"M1.1233,-27.1379C4.178,-27.1379 17.9448,-27.1379 30.9241,-27.1379\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"37.9807,-27.1379 30.9808,-30.288 34.4807,-27.1379 30.9807,-27.138 30.9807,-27.138 30.9807,-27.138 34.4807,-27.1379 30.9807,-23.988 37.9807,-27.1379 37.9807,-27.1379\" stroke=\"#000000\"/>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g class=\"node\" id=\"node3\">\n",
"<title>2</title>\n",
"<ellipse cx=\"187\" cy=\"-89.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"187\" y=\"-85.4379\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge2\">\n",
"<title>0-&gt;2</title>\n",
"<path d=\"M72.3264,-34.8648C95.3702,-45.7711 137.55,-65.7341 163.8289,-78.1714\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"170.4679,-81.3135 162.7932,-81.1661 167.3043,-79.8162 164.1407,-78.3189 164.1407,-78.3189 164.1407,-78.3189 167.3043,-79.8162 165.4883,-75.4717 170.4679,-81.3135 170.4679,-81.3135\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"92\" y=\"-88.9379\">!p0 &amp; !p1</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"113.5\" y=\"-73.9379\">⓿</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g class=\"node\" id=\"node4\">\n",
"<title>3</title>\n",
"<ellipse cx=\"468\" cy=\"-50.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"468\" y=\"-46.4379\">3</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge3\">\n",
"<title>0-&gt;3</title>\n",
"<path d=\"M74.2347,-28.1558C140.1802,-31.8372 366.3929,-44.4656 442.661,-48.7233\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"449.9758,-49.1317 442.8111,-51.8865 446.4813,-48.9365 442.9867,-48.7414 442.9867,-48.7414 442.9867,-48.7414 446.4813,-48.9365 443.1623,-45.5963 449.9758,-49.1317 449.9758,-49.1317\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"223\" y=\"-57.9379\">!p0 &amp; !p1</text>\n",
"<text fill=\"#e31a1c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"244.5\" y=\"-42.9379\">❺</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g class=\"node\" id=\"node5\">\n",
"<title>1</title>\n",
"<ellipse cx=\"329.5\" cy=\"-139.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"329.5\" y=\"-135.4379\">1</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;1 -->\n",
"<g class=\"edge\" id=\"edge7\">\n",
"<title>2-&gt;1</title>\n",
"<path d=\"M194.4797,-105.6802C200.4685,-116.7612 210.0181,-130.4938 223,-137.1379 248.5497,-150.214 282.2643,-148.1701 304.8527,-144.5334\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"311.7712,-143.3138 305.4244,-147.6313 308.3243,-143.9215 304.8775,-144.5291 304.8775,-144.5291 304.8775,-144.5291 308.3243,-143.9215 304.3306,-141.4269 311.7712,-143.3138 311.7712,-143.3138\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"226.5\" y=\"-165.9379\">p0 &amp; p1</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"244.5\" y=\"-150.9379\">⓿</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge8\">\n",
"<title>3-&gt;0</title>\n",
"<path d=\"M450.8478,-44.1499C418.3857,-33.17 345.5214,-10.2021 282,-2.1379 255.9866,1.1646 249.1499,-.1914 223,-2.1379 172.1741,-5.9211 113.3624,-16.0956 80.8517,-22.2358\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"73.9414,-23.5552 80.2264,-19.1482 77.3793,-22.8988 80.8172,-22.2423 80.8172,-22.2423 80.8172,-22.2423 77.3793,-22.8988 81.408,-25.3364 73.9414,-23.5552 73.9414,-23.5552\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"225\" y=\"-20.9379\">p0 &amp; !p1</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"244.5\" y=\"-5.9379\">❷</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge9\">\n",
"<title>3-&gt;2</title>\n",
"<path d=\"M450.1447,-52.616C401.7471,-59.3331 267.9465,-77.9033 212.0485,-85.6614\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"205.0053,-86.6389 211.5057,-82.5564 208.472,-86.1577 211.9388,-85.6765 211.9388,-85.6765 211.9388,-85.6765 208.472,-86.1577 212.3719,-88.7966 205.0053,-86.6389 205.0053,-86.6389\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"300\" y=\"-90.9379\">!p0 &amp; !p1</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"321.5\" y=\"-75.9379\">⓿</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge4\">\n",
"<title>1-&gt;2</title>\n",
"<path d=\"M315.4073,-127.4003C306.3888,-120.4804 294.1393,-112.1285 282,-107.1379 259.4223,-97.8559 231.8402,-93.3109 212.2247,-91.1163\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"205.124,-90.3853 212.4098,-87.9688 208.6056,-90.7438 212.0872,-91.1023 212.0872,-91.1023 212.0872,-91.1023 208.6056,-90.7438 211.7646,-94.2357 205.124,-90.3853 205.124,-90.3853\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"225\" y=\"-125.9379\">!p0 &amp; p1</text>\n",
"<text fill=\"#e31a1c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"244.5\" y=\"-110.9379\">❺</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge6\">\n",
"<title>1-&gt;3</title>\n",
"<path d=\"M346.4357,-132.5855C367.5876,-123.9589 404.3546,-107.4768 432,-87.1379 438.8537,-82.0955 445.5751,-75.7045 451.3197,-69.6586\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"456.2965,-64.2518 453.8734,-71.5355 453.9261,-66.827 451.5558,-69.4021 451.5558,-69.4021 451.5558,-69.4021 453.9261,-66.827 449.2381,-67.2688 456.2965,-64.2518 456.2965,-64.2518\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"377\" y=\"-136.9379\">!p0 &amp; p1</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"396.5\" y=\"-121.9379\">❹</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g class=\"edge\" id=\"edge5\">\n",
"<title>1-&gt;1</title>\n",
"<path d=\"M317.5762,-152.8048C312.8066,-163.7941 316.7813,-175.1379 329.5,-175.1379 339.4365,-175.1379 344.036,-168.2142 343.2986,-159.945\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"341.4238,-152.8048 346.2483,-158.7754 342.3127,-156.1901 343.2016,-159.5754 343.2016,-159.5754 343.2016,-159.5754 342.3127,-156.1901 340.1549,-160.3754 341.4238,-152.8048 341.4238,-152.8048\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"303.5\" y=\"-193.9379\">p0 &amp; p1</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"321.5\" y=\"-178.9379\">⓿</text>\n",
"</g>\n",
"</g>\n",
"</svg>"
],
"text/plain": [
"<IPython.core.display.SVG object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"aut_max_odd5_to_even = spot.change_parity(aut_max_odd5, spot.parity_kind_any, spot.parity_style_even)\n",
"display(aut_max_odd5_to_even.show(\".a\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Parity min odd 5 -> Parity min even\n",
"If the acceptance is a parity **min**, the new acceptance set will not be used."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"<svg height=\"219pt\" viewBox=\"0.00 0.00 494.00 219.14\" width=\"494pt\" 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(4 215.1379)\">\n",
"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-215.1379 490,-215.1379 490,4 -4,4\" stroke=\"transparent\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"94\" y=\"-196.9379\">Fin(</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"119\" y=\"-196.9379\">⓿</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"135\" y=\"-196.9379\">) &amp; (Inf(</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"182\" y=\"-196.9379\">❶</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"198\" y=\"-196.9379\">) | (Fin(</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"241\" y=\"-196.9379\">❷</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"257\" y=\"-196.9379\">) &amp; (Inf(</text>\n",
"<text fill=\"#6a3d9a\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"304\" y=\"-196.9379\">❸</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"320\" y=\"-196.9379\">) | Fin(</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"360\" y=\"-196.9379\">❹</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"376\" y=\"-196.9379\">))))</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"186\" y=\"-182.9379\">[parity min odd 5]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g class=\"node\" id=\"node2\">\n",
"<title>0</title>\n",
"<ellipse cx=\"56\" cy=\"-27.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"56\" y=\"-23.4379\">0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge1\">\n",
"<title>I-&gt;0</title>\n",
"<path d=\"M1.1233,-27.1379C4.178,-27.1379 17.9448,-27.1379 30.9241,-27.1379\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"37.9807,-27.1379 30.9808,-30.288 34.4807,-27.1379 30.9807,-27.138 30.9807,-27.138 30.9807,-27.138 34.4807,-27.1379 30.9807,-23.988 37.9807,-27.1379 37.9807,-27.1379\" stroke=\"#000000\"/>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g class=\"node\" id=\"node3\">\n",
"<title>2</title>\n",
"<ellipse cx=\"187\" cy=\"-89.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"187\" y=\"-85.4379\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge2\">\n",
"<title>0-&gt;2</title>\n",
"<path d=\"M72.3264,-34.8648C95.3702,-45.7711 137.55,-65.7341 163.8289,-78.1714\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"170.4679,-81.3135 162.7932,-81.1661 167.3043,-79.8162 164.1407,-78.3189 164.1407,-78.3189 164.1407,-78.3189 167.3043,-79.8162 165.4883,-75.4717 170.4679,-81.3135 170.4679,-81.3135\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"92\" y=\"-73.9379\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g class=\"node\" id=\"node4\">\n",
"<title>3</title>\n",
"<ellipse cx=\"468\" cy=\"-50.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"468\" y=\"-46.4379\">3</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge3\">\n",
"<title>0-&gt;3</title>\n",
"<path d=\"M74.2347,-28.1558C140.1802,-31.8372 366.3929,-44.4656 442.661,-48.7233\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"449.9758,-49.1317 442.8111,-51.8865 446.4813,-48.9365 442.9867,-48.7414 442.9867,-48.7414 442.9867,-48.7414 446.4813,-48.9365 443.1623,-45.5963 449.9758,-49.1317 449.9758,-49.1317\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"223\" y=\"-57.9379\">!p0 &amp; !p1</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"244.5\" y=\"-42.9379\">❹</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g class=\"node\" id=\"node5\">\n",
"<title>1</title>\n",
"<ellipse cx=\"329.5\" cy=\"-124.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"329.5\" y=\"-120.4379\">1</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;1 -->\n",
"<g class=\"edge\" id=\"edge7\">\n",
"<title>2-&gt;1</title>\n",
"<path d=\"M194.4417,-105.7555C200.4125,-116.8719 209.9563,-130.616 223,-137.1379 249.4223,-150.349 283.9805,-142.2021 306.4535,-134.0898\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"313.0175,-131.597 307.5919,-137.027 309.7455,-132.8396 306.4735,-134.0822 306.4735,-134.0822 306.4735,-134.0822 309.7455,-132.8396 305.3552,-131.1374 313.0175,-131.597 313.0175,-131.597\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"226.5\" y=\"-146.9379\">p0 &amp; p1</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge8\">\n",
"<title>3-&gt;0</title>\n",
"<path d=\"M450.8478,-44.1499C418.3857,-33.17 345.5214,-10.2021 282,-2.1379 255.9866,1.1646 249.1499,-.1914 223,-2.1379 172.1741,-5.9211 113.3624,-16.0956 80.8517,-22.2358\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"73.9414,-23.5552 80.2264,-19.1482 77.3793,-22.8988 80.8172,-22.2423 80.8172,-22.2423 80.8172,-22.2423 77.3793,-22.8988 81.408,-25.3364 73.9414,-23.5552 73.9414,-23.5552\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"225\" y=\"-20.9379\">p0 &amp; !p1</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"244.5\" y=\"-5.9379\">❶</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge9\">\n",
"<title>3-&gt;2</title>\n",
"<path d=\"M450.1447,-52.616C401.7471,-59.3331 267.9465,-77.9033 212.0485,-85.6614\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"205.0053,-86.6389 211.5057,-82.5564 208.472,-86.1577 211.9388,-85.6765 211.9388,-85.6765 211.9388,-85.6765 208.472,-86.1577 212.3719,-88.7966 205.0053,-86.6389 205.0053,-86.6389\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"300\" y=\"-75.9379\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge4\">\n",
"<title>1-&gt;2</title>\n",
"<path d=\"M312.5568,-117.345C303.5825,-113.9337 292.3114,-109.9414 282,-107.1379 258.5876,-100.7723 231.3296,-95.8568 212.0314,-92.7832\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"205.0495,-91.6962 212.4508,-89.6606 208.5078,-92.2347 211.9662,-92.7731 211.9662,-92.7731 211.9662,-92.7731 208.5078,-92.2347 211.4815,-95.8857 205.0495,-91.6962 205.0495,-91.6962\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"225\" y=\"-125.9379\">!p0 &amp; p1</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"244.5\" y=\"-110.9379\">❹</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge6\">\n",
"<title>1-&gt;3</title>\n",
"<path d=\"M347.2795,-120.3178C368.6392,-115.1652 404.9704,-104.5683 432,-87.1379 439.2661,-82.4522 446.1681,-76.0438 451.9486,-69.8765\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"456.9202,-64.3368 454.5892,-71.6504 454.5825,-66.9417 452.2448,-69.5465 452.2448,-69.5465 452.2448,-69.5465 454.5825,-66.9417 449.9004,-67.4426 456.9202,-64.3368 456.9202,-64.3368\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"377\" y=\"-129.9379\">!p0 &amp; p1</text>\n",
"<text fill=\"#6a3d9a\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"396.5\" y=\"-114.9379\">❸</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g class=\"edge\" id=\"edge5\">\n",
"<title>1-&gt;1</title>\n",
"<path d=\"M317.5762,-137.8048C312.8066,-148.7941 316.7813,-160.1379 329.5,-160.1379 339.4365,-160.1379 344.036,-153.2142 343.2986,-144.945\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"341.4238,-137.8048 346.2483,-143.7754 342.3127,-141.1901 343.2016,-144.5754 343.2016,-144.5754 343.2016,-144.5754 342.3127,-141.1901 340.1549,-145.3754 341.4238,-137.8048 341.4238,-137.8048\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"303.5\" y=\"-163.9379\">p0 &amp; p1</text>\n",
"</g>\n",
"</g>\n",
"</svg>"
],
"text/plain": [
"<IPython.core.display.SVG object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"aut_min_odd5 = tuple(spot.automata(\"randaut -A 'parity min odd 5' -Q4 2|\"))[0]\n",
"display(aut_min_odd5.show(\".a\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The new indexes of the acceptance sets:\n",
"+ 4 -> 5\n",
"+ 3 -> 4\n",
"+ 2 -> 3\n",
"+ 1 -> 2\n",
"+ 0 -> 1\n",
"+ ∅ -> ∅"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Result of Parity min odd 5 -> Parity min even 6"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"<svg height=\"219pt\" viewBox=\"0.00 0.00 494.00 219.14\" width=\"494pt\" 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(4 215.1379)\">\n",
"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-215.1379 490,-215.1379 490,4 -4,4\" stroke=\"transparent\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"64.5\" y=\"-196.9379\">Inf(</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"86.5\" y=\"-196.9379\">⓿</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"102.5\" y=\"-196.9379\">) | (Fin(</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"145.5\" y=\"-196.9379\">❶</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"161.5\" y=\"-196.9379\">) &amp; (Inf(</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"208.5\" y=\"-196.9379\">❷</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"224.5\" y=\"-196.9379\">) | (Fin(</text>\n",
"<text fill=\"#6a3d9a\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"267.5\" y=\"-196.9379\">❸</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"283.5\" y=\"-196.9379\">) &amp; (Inf(</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"330.5\" y=\"-196.9379\">❹</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"346.5\" y=\"-196.9379\">) | Fin(</text>\n",
"<text fill=\"#e31a1c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"386.5\" y=\"-196.9379\">❺</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"402.5\" y=\"-196.9379\">)))))</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"183\" y=\"-182.9379\">[parity min even 6]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g class=\"node\" id=\"node2\">\n",
"<title>0</title>\n",
"<ellipse cx=\"56\" cy=\"-27.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"56\" y=\"-23.4379\">0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge1\">\n",
"<title>I-&gt;0</title>\n",
"<path d=\"M1.1233,-27.1379C4.178,-27.1379 17.9448,-27.1379 30.9241,-27.1379\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"37.9807,-27.1379 30.9808,-30.288 34.4807,-27.1379 30.9807,-27.138 30.9807,-27.138 30.9807,-27.138 34.4807,-27.1379 30.9807,-23.988 37.9807,-27.1379 37.9807,-27.1379\" stroke=\"#000000\"/>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g class=\"node\" id=\"node3\">\n",
"<title>2</title>\n",
"<ellipse cx=\"187\" cy=\"-89.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"187\" y=\"-85.4379\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge2\">\n",
"<title>0-&gt;2</title>\n",
"<path d=\"M72.3264,-34.8648C95.3702,-45.7711 137.55,-65.7341 163.8289,-78.1714\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"170.4679,-81.3135 162.7932,-81.1661 167.3043,-79.8162 164.1407,-78.3189 164.1407,-78.3189 164.1407,-78.3189 167.3043,-79.8162 165.4883,-75.4717 170.4679,-81.3135 170.4679,-81.3135\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"92\" y=\"-73.9379\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g class=\"node\" id=\"node4\">\n",
"<title>3</title>\n",
"<ellipse cx=\"468\" cy=\"-50.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"468\" y=\"-46.4379\">3</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge3\">\n",
"<title>0-&gt;3</title>\n",
"<path d=\"M74.2347,-28.1558C140.1802,-31.8372 366.3929,-44.4656 442.661,-48.7233\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"449.9758,-49.1317 442.8111,-51.8865 446.4813,-48.9365 442.9867,-48.7414 442.9867,-48.7414 442.9867,-48.7414 446.4813,-48.9365 443.1623,-45.5963 449.9758,-49.1317 449.9758,-49.1317\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"223\" y=\"-57.9379\">!p0 &amp; !p1</text>\n",
"<text fill=\"#e31a1c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"244.5\" y=\"-42.9379\">❺</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g class=\"node\" id=\"node5\">\n",
"<title>1</title>\n",
"<ellipse cx=\"329.5\" cy=\"-124.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"329.5\" y=\"-120.4379\">1</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;1 -->\n",
"<g class=\"edge\" id=\"edge7\">\n",
"<title>2-&gt;1</title>\n",
"<path d=\"M194.4417,-105.7555C200.4125,-116.8719 209.9563,-130.616 223,-137.1379 249.4223,-150.349 283.9805,-142.2021 306.4535,-134.0898\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"313.0175,-131.597 307.5919,-137.027 309.7455,-132.8396 306.4735,-134.0822 306.4735,-134.0822 306.4735,-134.0822 309.7455,-132.8396 305.3552,-131.1374 313.0175,-131.597 313.0175,-131.597\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"226.5\" y=\"-146.9379\">p0 &amp; p1</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge8\">\n",
"<title>3-&gt;0</title>\n",
"<path d=\"M450.8478,-44.1499C418.3857,-33.17 345.5214,-10.2021 282,-2.1379 255.9866,1.1646 249.1499,-.1914 223,-2.1379 172.1741,-5.9211 113.3624,-16.0956 80.8517,-22.2358\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"73.9414,-23.5552 80.2264,-19.1482 77.3793,-22.8988 80.8172,-22.2423 80.8172,-22.2423 80.8172,-22.2423 77.3793,-22.8988 81.408,-25.3364 73.9414,-23.5552 73.9414,-23.5552\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"225\" y=\"-20.9379\">p0 &amp; !p1</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"244.5\" y=\"-5.9379\">❷</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge9\">\n",
"<title>3-&gt;2</title>\n",
"<path d=\"M450.1447,-52.616C401.7471,-59.3331 267.9465,-77.9033 212.0485,-85.6614\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"205.0053,-86.6389 211.5057,-82.5564 208.472,-86.1577 211.9388,-85.6765 211.9388,-85.6765 211.9388,-85.6765 208.472,-86.1577 212.3719,-88.7966 205.0053,-86.6389 205.0053,-86.6389\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"300\" y=\"-75.9379\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge4\">\n",
"<title>1-&gt;2</title>\n",
"<path d=\"M312.5568,-117.345C303.5825,-113.9337 292.3114,-109.9414 282,-107.1379 258.5876,-100.7723 231.3296,-95.8568 212.0314,-92.7832\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"205.0495,-91.6962 212.4508,-89.6606 208.5078,-92.2347 211.9662,-92.7731 211.9662,-92.7731 211.9662,-92.7731 208.5078,-92.2347 211.4815,-95.8857 205.0495,-91.6962 205.0495,-91.6962\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"225\" y=\"-125.9379\">!p0 &amp; p1</text>\n",
"<text fill=\"#e31a1c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"244.5\" y=\"-110.9379\">❺</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge6\">\n",
"<title>1-&gt;3</title>\n",
"<path d=\"M347.2795,-120.3178C368.6392,-115.1652 404.9704,-104.5683 432,-87.1379 439.2661,-82.4522 446.1681,-76.0438 451.9486,-69.8765\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"456.9202,-64.3368 454.5892,-71.6504 454.5825,-66.9417 452.2448,-69.5465 452.2448,-69.5465 452.2448,-69.5465 454.5825,-66.9417 449.9004,-67.4426 456.9202,-64.3368 456.9202,-64.3368\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"377\" y=\"-129.9379\">!p0 &amp; p1</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"396.5\" y=\"-114.9379\">❹</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g class=\"edge\" id=\"edge5\">\n",
"<title>1-&gt;1</title>\n",
"<path d=\"M317.5762,-137.8048C312.8066,-148.7941 316.7813,-160.1379 329.5,-160.1379 339.4365,-160.1379 344.036,-153.2142 343.2986,-144.945\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"341.4238,-137.8048 346.2483,-143.7754 342.3127,-141.1901 343.2016,-144.5754 343.2016,-144.5754 343.2016,-144.5754 342.3127,-141.1901 340.1549,-145.3754 341.4238,-137.8048 341.4238,-137.8048\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"303.5\" y=\"-163.9379\">p0 &amp; p1</text>\n",
"</g>\n",
"</g>\n",
"</svg>"
],
"text/plain": [
"<IPython.core.display.SVG object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"aut_min_odd5_to_even = spot.change_parity(aut_min_odd5, spot.parity_kind_any, spot.parity_style_even)\n",
"display(aut_min_odd5_to_even.show(\".a\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### To toggle **kind**\n",
"#### The indexes of the acceptance sets are reversed\n",
"#### Parity max odd 5 ----> Parity min:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"<svg height=\"219pt\" viewBox=\"0.00 0.00 494.00 219.14\" width=\"494pt\" 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(4 215.1379)\">\n",
"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-215.1379 490,-215.1379 490,4 -4,4\" stroke=\"transparent\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"94\" y=\"-196.9379\">Fin(</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"119\" y=\"-196.9379\">❹</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"135\" y=\"-196.9379\">) &amp; (Inf(</text>\n",
"<text fill=\"#6a3d9a\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"182\" y=\"-196.9379\">❸</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"198\" y=\"-196.9379\">) | (Fin(</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"241\" y=\"-196.9379\">❷</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"257\" y=\"-196.9379\">) &amp; (Inf(</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"304\" y=\"-196.9379\">❶</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"320\" y=\"-196.9379\">) | Fin(</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"360\" y=\"-196.9379\">⓿</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"376\" y=\"-196.9379\">))))</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"185.5\" y=\"-182.9379\">[parity max odd 5]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g class=\"node\" id=\"node2\">\n",
"<title>0</title>\n",
"<ellipse cx=\"56\" cy=\"-27.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"56\" y=\"-23.4379\">0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge1\">\n",
"<title>I-&gt;0</title>\n",
"<path d=\"M1.1233,-27.1379C4.178,-27.1379 17.9448,-27.1379 30.9241,-27.1379\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"37.9807,-27.1379 30.9808,-30.288 34.4807,-27.1379 30.9807,-27.138 30.9807,-27.138 30.9807,-27.138 34.4807,-27.1379 30.9807,-23.988 37.9807,-27.1379 37.9807,-27.1379\" stroke=\"#000000\"/>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g class=\"node\" id=\"node3\">\n",
"<title>2</title>\n",
"<ellipse cx=\"187\" cy=\"-89.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"187\" y=\"-85.4379\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge2\">\n",
"<title>0-&gt;2</title>\n",
"<path d=\"M72.3264,-34.8648C95.3702,-45.7711 137.55,-65.7341 163.8289,-78.1714\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"170.4679,-81.3135 162.7932,-81.1661 167.3043,-79.8162 164.1407,-78.3189 164.1407,-78.3189 164.1407,-78.3189 167.3043,-79.8162 165.4883,-75.4717 170.4679,-81.3135 170.4679,-81.3135\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"92\" y=\"-73.9379\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g class=\"node\" id=\"node4\">\n",
"<title>3</title>\n",
"<ellipse cx=\"468\" cy=\"-50.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"468\" y=\"-46.4379\">3</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge3\">\n",
"<title>0-&gt;3</title>\n",
"<path d=\"M74.2347,-28.1558C140.1802,-31.8372 366.3929,-44.4656 442.661,-48.7233\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"449.9758,-49.1317 442.8111,-51.8865 446.4813,-48.9365 442.9867,-48.7414 442.9867,-48.7414 442.9867,-48.7414 446.4813,-48.9365 443.1623,-45.5963 449.9758,-49.1317 449.9758,-49.1317\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"223\" y=\"-57.9379\">!p0 &amp; !p1</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"244.5\" y=\"-42.9379\">❹</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g class=\"node\" id=\"node5\">\n",
"<title>1</title>\n",
"<ellipse cx=\"329.5\" cy=\"-124.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"329.5\" y=\"-120.4379\">1</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;1 -->\n",
"<g class=\"edge\" id=\"edge7\">\n",
"<title>2-&gt;1</title>\n",
"<path d=\"M194.4417,-105.7555C200.4125,-116.8719 209.9563,-130.616 223,-137.1379 249.4223,-150.349 283.9805,-142.2021 306.4535,-134.0898\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"313.0175,-131.597 307.5919,-137.027 309.7455,-132.8396 306.4735,-134.0822 306.4735,-134.0822 306.4735,-134.0822 309.7455,-132.8396 305.3552,-131.1374 313.0175,-131.597 313.0175,-131.597\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"226.5\" y=\"-146.9379\">p0 &amp; p1</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge8\">\n",
"<title>3-&gt;0</title>\n",
"<path d=\"M450.8478,-44.1499C418.3857,-33.17 345.5214,-10.2021 282,-2.1379 255.9866,1.1646 249.1499,-.1914 223,-2.1379 172.1741,-5.9211 113.3624,-16.0956 80.8517,-22.2358\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"73.9414,-23.5552 80.2264,-19.1482 77.3793,-22.8988 80.8172,-22.2423 80.8172,-22.2423 80.8172,-22.2423 77.3793,-22.8988 81.408,-25.3364 73.9414,-23.5552 73.9414,-23.5552\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"225\" y=\"-20.9379\">p0 &amp; !p1</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"244.5\" y=\"-5.9379\">❶</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge9\">\n",
"<title>3-&gt;2</title>\n",
"<path d=\"M450.1447,-52.616C401.7471,-59.3331 267.9465,-77.9033 212.0485,-85.6614\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"205.0053,-86.6389 211.5057,-82.5564 208.472,-86.1577 211.9388,-85.6765 211.9388,-85.6765 211.9388,-85.6765 208.472,-86.1577 212.3719,-88.7966 205.0053,-86.6389 205.0053,-86.6389\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"300\" y=\"-75.9379\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge4\">\n",
"<title>1-&gt;2</title>\n",
"<path d=\"M312.5568,-117.345C303.5825,-113.9337 292.3114,-109.9414 282,-107.1379 258.5876,-100.7723 231.3296,-95.8568 212.0314,-92.7832\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"205.0495,-91.6962 212.4508,-89.6606 208.5078,-92.2347 211.9662,-92.7731 211.9662,-92.7731 211.9662,-92.7731 208.5078,-92.2347 211.4815,-95.8857 205.0495,-91.6962 205.0495,-91.6962\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"225\" y=\"-125.9379\">!p0 &amp; p1</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"244.5\" y=\"-110.9379\">❹</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge6\">\n",
"<title>1-&gt;3</title>\n",
"<path d=\"M347.2795,-120.3178C368.6392,-115.1652 404.9704,-104.5683 432,-87.1379 439.2661,-82.4522 446.1681,-76.0438 451.9486,-69.8765\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"456.9202,-64.3368 454.5892,-71.6504 454.5825,-66.9417 452.2448,-69.5465 452.2448,-69.5465 452.2448,-69.5465 454.5825,-66.9417 449.9004,-67.4426 456.9202,-64.3368 456.9202,-64.3368\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"377\" y=\"-129.9379\">!p0 &amp; p1</text>\n",
"<text fill=\"#6a3d9a\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"396.5\" y=\"-114.9379\">❸</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g class=\"edge\" id=\"edge5\">\n",
"<title>1-&gt;1</title>\n",
"<path d=\"M317.5762,-137.8048C312.8066,-148.7941 316.7813,-160.1379 329.5,-160.1379 339.4365,-160.1379 344.036,-153.2142 343.2986,-144.945\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"341.4238,-137.8048 346.2483,-143.7754 342.3127,-141.1901 343.2016,-144.5754 343.2016,-144.5754 343.2016,-144.5754 342.3127,-141.1901 340.1549,-145.3754 341.4238,-137.8048 341.4238,-137.8048\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"303.5\" y=\"-163.9379\">p0 &amp; p1</text>\n",
"</g>\n",
"</g>\n",
"</svg>"
],
"text/plain": [
"<IPython.core.display.SVG object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"aut_max_odd5 = tuple(spot.automata(\"randaut -A 'parity max odd 5' -Q4 2|\"))[0]\n",
"display(aut_max_odd5.show(\".a\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The new indexes of the acceptance sets:\n",
"+ 4 -> 0\n",
"+ 3 -> 1\n",
"+ 2 -> 2\n",
"+ 1 -> 3\n",
"+ 0 -> 4\n",
"+ ∅ -> ∅"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Result of Parity max odd 5 ----> Parity min odd 5:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"<svg height=\"219pt\" viewBox=\"0.00 0.00 494.00 219.14\" width=\"494pt\" 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(4 215.1379)\">\n",
"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-215.1379 490,-215.1379 490,4 -4,4\" stroke=\"transparent\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"94\" y=\"-196.9379\">Fin(</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"119\" y=\"-196.9379\">⓿</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"135\" y=\"-196.9379\">) &amp; (Inf(</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"182\" y=\"-196.9379\">❶</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"198\" y=\"-196.9379\">) | (Fin(</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"241\" y=\"-196.9379\">❷</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"257\" y=\"-196.9379\">) &amp; (Inf(</text>\n",
"<text fill=\"#6a3d9a\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"304\" y=\"-196.9379\">❸</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"320\" y=\"-196.9379\">) | Fin(</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"360\" y=\"-196.9379\">❹</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"376\" y=\"-196.9379\">))))</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"186\" y=\"-182.9379\">[parity min odd 5]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g class=\"node\" id=\"node2\">\n",
"<title>0</title>\n",
"<ellipse cx=\"56\" cy=\"-27.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"56\" y=\"-23.4379\">0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge1\">\n",
"<title>I-&gt;0</title>\n",
"<path d=\"M1.1233,-27.1379C4.178,-27.1379 17.9448,-27.1379 30.9241,-27.1379\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"37.9807,-27.1379 30.9808,-30.288 34.4807,-27.1379 30.9807,-27.138 30.9807,-27.138 30.9807,-27.138 34.4807,-27.1379 30.9807,-23.988 37.9807,-27.1379 37.9807,-27.1379\" stroke=\"#000000\"/>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g class=\"node\" id=\"node3\">\n",
"<title>2</title>\n",
"<ellipse cx=\"187\" cy=\"-89.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"187\" y=\"-85.4379\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge2\">\n",
"<title>0-&gt;2</title>\n",
"<path d=\"M72.3264,-34.8648C95.3702,-45.7711 137.55,-65.7341 163.8289,-78.1714\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"170.4679,-81.3135 162.7932,-81.1661 167.3043,-79.8162 164.1407,-78.3189 164.1407,-78.3189 164.1407,-78.3189 167.3043,-79.8162 165.4883,-75.4717 170.4679,-81.3135 170.4679,-81.3135\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"92\" y=\"-73.9379\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g class=\"node\" id=\"node4\">\n",
"<title>3</title>\n",
"<ellipse cx=\"468\" cy=\"-50.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"468\" y=\"-46.4379\">3</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge3\">\n",
"<title>0-&gt;3</title>\n",
"<path d=\"M74.2347,-28.1558C140.1802,-31.8372 366.3929,-44.4656 442.661,-48.7233\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"449.9758,-49.1317 442.8111,-51.8865 446.4813,-48.9365 442.9867,-48.7414 442.9867,-48.7414 442.9867,-48.7414 446.4813,-48.9365 443.1623,-45.5963 449.9758,-49.1317 449.9758,-49.1317\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"223\" y=\"-57.9379\">!p0 &amp; !p1</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"244.5\" y=\"-42.9379\">⓿</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g class=\"node\" id=\"node5\">\n",
"<title>1</title>\n",
"<ellipse cx=\"329.5\" cy=\"-124.1379\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"329.5\" y=\"-120.4379\">1</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;1 -->\n",
"<g class=\"edge\" id=\"edge7\">\n",
"<title>2-&gt;1</title>\n",
"<path d=\"M194.4417,-105.7555C200.4125,-116.8719 209.9563,-130.616 223,-137.1379 249.4223,-150.349 283.9805,-142.2021 306.4535,-134.0898\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"313.0175,-131.597 307.5919,-137.027 309.7455,-132.8396 306.4735,-134.0822 306.4735,-134.0822 306.4735,-134.0822 309.7455,-132.8396 305.3552,-131.1374 313.0175,-131.597 313.0175,-131.597\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"226.5\" y=\"-146.9379\">p0 &amp; p1</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge8\">\n",
"<title>3-&gt;0</title>\n",
"<path d=\"M450.8478,-44.1499C418.3857,-33.17 345.5214,-10.2021 282,-2.1379 255.9866,1.1646 249.1499,-.1914 223,-2.1379 172.1741,-5.9211 113.3624,-16.0956 80.8517,-22.2358\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"73.9414,-23.5552 80.2264,-19.1482 77.3793,-22.8988 80.8172,-22.2423 80.8172,-22.2423 80.8172,-22.2423 77.3793,-22.8988 81.408,-25.3364 73.9414,-23.5552 73.9414,-23.5552\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"225\" y=\"-20.9379\">p0 &amp; !p1</text>\n",
"<text fill=\"#6a3d9a\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"244.5\" y=\"-5.9379\">❸</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge9\">\n",
"<title>3-&gt;2</title>\n",
"<path d=\"M450.1447,-52.616C401.7471,-59.3331 267.9465,-77.9033 212.0485,-85.6614\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"205.0053,-86.6389 211.5057,-82.5564 208.472,-86.1577 211.9388,-85.6765 211.9388,-85.6765 211.9388,-85.6765 208.472,-86.1577 212.3719,-88.7966 205.0053,-86.6389 205.0053,-86.6389\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"300\" y=\"-75.9379\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge4\">\n",
"<title>1-&gt;2</title>\n",
"<path d=\"M312.5568,-117.345C303.5825,-113.9337 292.3114,-109.9414 282,-107.1379 258.5876,-100.7723 231.3296,-95.8568 212.0314,-92.7832\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"205.0495,-91.6962 212.4508,-89.6606 208.5078,-92.2347 211.9662,-92.7731 211.9662,-92.7731 211.9662,-92.7731 208.5078,-92.2347 211.4815,-95.8857 205.0495,-91.6962 205.0495,-91.6962\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"225\" y=\"-125.9379\">!p0 &amp; p1</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"244.5\" y=\"-110.9379\">⓿</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge6\">\n",
"<title>1-&gt;3</title>\n",
"<path d=\"M347.2795,-120.3178C368.6392,-115.1652 404.9704,-104.5683 432,-87.1379 439.2661,-82.4522 446.1681,-76.0438 451.9486,-69.8765\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"456.9202,-64.3368 454.5892,-71.6504 454.5825,-66.9417 452.2448,-69.5465 452.2448,-69.5465 452.2448,-69.5465 454.5825,-66.9417 449.9004,-67.4426 456.9202,-64.3368 456.9202,-64.3368\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"377\" y=\"-129.9379\">!p0 &amp; p1</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"396.5\" y=\"-114.9379\">❶</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;1 -->\n",
"<g class=\"edge\" id=\"edge5\">\n",
"<title>1-&gt;1</title>\n",
"<path d=\"M317.5762,-137.8048C312.8066,-148.7941 316.7813,-160.1379 329.5,-160.1379 339.4365,-160.1379 344.036,-153.2142 343.2986,-144.945\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"341.4238,-137.8048 346.2483,-143.7754 342.3127,-141.1901 343.2016,-144.5754 343.2016,-144.5754 343.2016,-144.5754 342.3127,-141.1901 340.1549,-145.3754 341.4238,-137.8048 341.4238,-137.8048\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"303.5\" y=\"-163.9379\">p0 &amp; p1</text>\n",
"</g>\n",
"</g>\n",
"</svg>"
],
"text/plain": [
"<IPython.core.display.SVG object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"aut_max_odd5_to_min = spot.change_parity(aut_max_odd5, spot.parity_kind_min, spot.parity_style_any)\n",
"display(aut_max_odd5_to_min.show(\".a\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Parity max odd 4 ----> Parity min odd:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"<svg height=\"173pt\" viewBox=\"0.00 0.00 498.00 172.81\" width=\"498pt\" 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(4 168.8065)\">\n",
"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-168.8065 494,-168.8065 494,4 -4,4\" stroke=\"transparent\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"131\" y=\"-150.6065\">Inf(</text>\n",
"<text fill=\"#6a3d9a\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"153\" y=\"-150.6065\">❸</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"169\" y=\"-150.6065\">) | (Fin(</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"212\" y=\"-150.6065\">❷</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"228\" y=\"-150.6065\">) &amp; (Inf(</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"275\" y=\"-150.6065\">❶</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"291\" y=\"-150.6065\">) | Fin(</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"331\" y=\"-150.6065\">⓿</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"347\" y=\"-150.6065\">)))</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"187.5\" y=\"-136.6065\">[parity max odd 4]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g class=\"node\" id=\"node2\">\n",
"<title>0</title>\n",
"<ellipse cx=\"56\" cy=\"-34.8065\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"56\" y=\"-31.1065\">0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge1\">\n",
"<title>I-&gt;0</title>\n",
"<path d=\"M1.1233,-34.8065C4.178,-34.8065 17.9448,-34.8065 30.9241,-34.8065\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"37.9807,-34.8065 30.9808,-37.9566 34.4807,-34.8065 30.9807,-34.8066 30.9807,-34.8066 30.9807,-34.8066 34.4807,-34.8065 30.9807,-31.6566 37.9807,-34.8065 37.9807,-34.8065\" stroke=\"#000000\"/>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g class=\"node\" id=\"node3\">\n",
"<title>2</title>\n",
"<ellipse cx=\"341\" cy=\"-54.8065\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"341\" y=\"-51.1065\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge2\">\n",
"<title>0-&gt;2</title>\n",
"<path d=\"M69.2358,-47.4757C89.0421,-65.4599 128.4234,-97.5662 169,-109.8065 223.8706,-126.3588 288.086,-91.2232 320.3183,-69.7806\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"326.326,-65.694 322.3098,-72.2357 323.4321,-67.6626 320.5381,-69.6311 320.5381,-69.6311 320.5381,-69.6311 323.4321,-67.6626 318.7664,-67.0265 326.326,-65.694 326.326,-65.694\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"169\" y=\"-117.6065\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g class=\"node\" id=\"node4\">\n",
"<title>3</title>\n",
"<ellipse cx=\"198.5\" cy=\"-34.8065\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"198.5\" y=\"-31.1065\">3</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge3\">\n",
"<title>0-&gt;3</title>\n",
"<path d=\"M74.0477,-34.8065C99.0722,-34.8065 144.4394,-34.8065 172.939,-34.8065\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"180.1487,-34.8065 173.1488,-37.9566 176.6487,-34.8065 173.1487,-34.8066 173.1487,-34.8066 173.1487,-34.8066 176.6487,-34.8065 173.1487,-31.6566 180.1487,-34.8065 180.1487,-34.8065\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"92\" y=\"-38.6065\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g class=\"node\" id=\"node5\">\n",
"<title>1</title>\n",
"<ellipse cx=\"472\" cy=\"-21.8065\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"472\" y=\"-18.1065\">1</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;1 -->\n",
"<g class=\"edge\" id=\"edge6\">\n",
"<title>2-&gt;1</title>\n",
"<path d=\"M359.1657,-52.8771C378.5155,-50.5179 409.8902,-45.816 436,-37.8065 440.3769,-36.4638 444.9261,-34.7294 449.2584,-32.8999\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"455.8317,-29.9893 450.7065,-35.7038 452.6314,-31.4064 449.4311,-32.8235 449.4311,-32.8235 449.4311,-32.8235 452.6314,-31.4064 448.1557,-29.9432 455.8317,-29.9893 455.8317,-29.9893\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"379\" y=\"-53.6065\">!p0 &amp; p1</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge7\">\n",
"<title>3-&gt;2</title>\n",
"<path d=\"M216.5477,-37.3395C241.7097,-40.871 287.4385,-47.2891 315.9073,-51.2847\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"323.0988,-52.294 315.7289,-54.4405 319.6328,-51.8075 316.1668,-51.321 316.1668,-51.321 316.1668,-51.321 319.6328,-51.8075 316.6046,-48.2016 323.0988,-52.294 323.0988,-52.294\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"246\" y=\"-52.6065\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge8\">\n",
"<title>3-&gt;3</title>\n",
"<path d=\"M186.2539,-48.4735C181.3555,-59.4627 185.4375,-70.8065 198.5,-70.8065 208.7051,-70.8065 213.4289,-63.8828 212.6715,-55.6136\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"210.7461,-48.4735 215.61,-54.4119 211.6574,-51.8528 212.5687,-55.2321 212.5687,-55.2321 212.5687,-55.2321 211.6574,-51.8528 209.5273,-56.0522 210.7461,-48.4735 210.7461,-48.4735\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"171\" y=\"-89.6065\">p0 &amp; !p1</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"190.5\" y=\"-74.6065\">⓿</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge4\">\n",
"<title>1-&gt;0</title>\n",
"<path d=\"M455.0183,-15.5417C449.0859,-13.6427 442.3273,-11.7983 436,-10.8065 323.3123,6.8572 222.0648,-1.5549 169,-7.8065 137.9101,-11.4692 102.9839,-20.6148 80.3002,-27.2488\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"73.3859,-29.3043 79.198,-24.2901 76.7408,-28.3069 80.0957,-27.3095 80.0957,-27.3095 80.0957,-27.3095 76.7408,-28.3069 80.9933,-30.3289 73.3859,-29.3043 73.3859,-29.3043\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"248\" y=\"-19.6065\">!p0 &amp; p1</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"259.5\" y=\"-5.6065\">⓿</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"275.5\" y=\"-5.6065\">❷</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge5\">\n",
"<title>1-&gt;2</title>\n",
"<path d=\"M454.1457,-18.3787C434.5137,-15.42 402.3872,-13.001 377,-22.8065 369.8625,-25.5633 363.2281,-30.4374 357.6491,-35.5631\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"352.4423,-40.7036 355.2106,-33.544 354.933,-38.2446 357.4237,-35.7856 357.4237,-35.7856 357.4237,-35.7856 354.933,-38.2446 359.6368,-38.0273 352.4423,-40.7036 352.4423,-40.7036\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"377\" y=\"-26.6065\">!p0 &amp; !p1</text>\n",
"</g>\n",
"</g>\n",
"</svg>"
],
"text/plain": [
"<IPython.core.display.SVG object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"aut_max_odd4 = tuple(spot.automata(\"randaut -A 'parity max odd 4' -Q4 2|\"))[0]\n",
"display(aut_max_odd4.show(\".a\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The new indexes of the acceptance sets:\n",
"+ 3 -> 0\n",
"+ 2 -> 1\n",
"+ 1 -> 2\n",
"+ 0 -> 3\n",
"+ ∅ -> ∅"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Result of Parity max odd 4 ----> Parity min even 4:\n",
"\n",
"If the **numsets** is even and the **kind** is toggled, then the **style** will be toggled too."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"<svg height=\"176pt\" viewBox=\"0.00 0.00 498.00 175.85\" width=\"498pt\" 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(4 171.8479)\">\n",
"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-171.8479 494,-171.8479 494,4 -4,4\" stroke=\"transparent\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"131\" y=\"-153.6479\">Inf(</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"153\" y=\"-153.6479\">⓿</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"169\" y=\"-153.6479\">) | (Fin(</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"212\" y=\"-153.6479\">❶</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"228\" y=\"-153.6479\">) &amp; (Inf(</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"275\" y=\"-153.6479\">❷</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"291\" y=\"-153.6479\">) | Fin(</text>\n",
"<text fill=\"#6a3d9a\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"331\" y=\"-153.6479\">❸</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"347\" y=\"-153.6479\">)))</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"185\" y=\"-139.6479\">[parity min even 4]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g class=\"node\" id=\"node2\">\n",
"<title>0</title>\n",
"<ellipse cx=\"56\" cy=\"-37.8479\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"56\" y=\"-34.1479\">0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge1\">\n",
"<title>I-&gt;0</title>\n",
"<path d=\"M1.1233,-37.8479C4.178,-37.8479 17.9448,-37.8479 30.9241,-37.8479\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"37.9807,-37.8479 30.9808,-40.998 34.4807,-37.848 30.9807,-37.848 30.9807,-37.848 30.9807,-37.848 34.4807,-37.848 30.9807,-34.698 37.9807,-37.8479 37.9807,-37.8479\" stroke=\"#000000\"/>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g class=\"node\" id=\"node3\">\n",
"<title>2</title>\n",
"<ellipse cx=\"341\" cy=\"-57.8479\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"341\" y=\"-54.1479\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge2\">\n",
"<title>0-&gt;2</title>\n",
"<path d=\"M69.2358,-50.5171C89.0421,-68.5014 128.4234,-100.6076 169,-112.8479 223.8706,-129.4002 288.086,-94.2646 320.3183,-72.822\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"326.326,-68.7355 322.3098,-75.2771 323.4321,-70.704 320.5381,-72.6725 320.5381,-72.6725 320.5381,-72.6725 323.4321,-70.704 318.7664,-70.068 326.326,-68.7355 326.326,-68.7355\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"169\" y=\"-120.6479\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g class=\"node\" id=\"node4\">\n",
"<title>3</title>\n",
"<ellipse cx=\"198.5\" cy=\"-37.8479\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"198.5\" y=\"-34.1479\">3</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge3\">\n",
"<title>0-&gt;3</title>\n",
"<path d=\"M74.0477,-37.8479C99.0722,-37.8479 144.4394,-37.8479 172.939,-37.8479\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"180.1487,-37.8479 173.1488,-40.998 176.6487,-37.848 173.1487,-37.848 173.1487,-37.848 173.1487,-37.848 176.6487,-37.848 173.1487,-34.698 180.1487,-37.8479 180.1487,-37.8479\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"92\" y=\"-41.6479\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g class=\"node\" id=\"node5\">\n",
"<title>1</title>\n",
"<ellipse cx=\"472\" cy=\"-24.8479\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"472\" y=\"-21.1479\">1</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;1 -->\n",
"<g class=\"edge\" id=\"edge6\">\n",
"<title>2-&gt;1</title>\n",
"<path d=\"M359.1657,-55.9185C378.5155,-53.5593 409.8902,-48.8574 436,-40.8479 440.3769,-39.5053 444.9261,-37.7709 449.2584,-35.9414\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"455.8317,-33.0308 450.7065,-38.7452 452.6314,-34.4479 449.4311,-35.8649 449.4311,-35.8649 449.4311,-35.8649 452.6314,-34.4479 448.1557,-32.9847 455.8317,-33.0308 455.8317,-33.0308\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"379\" y=\"-56.6479\">!p0 &amp; p1</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge7\">\n",
"<title>3-&gt;2</title>\n",
"<path d=\"M216.5477,-40.381C241.7097,-43.9125 287.4385,-50.3305 315.9073,-54.3262\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"323.0988,-55.3355 315.7289,-57.4819 319.6328,-54.849 316.1668,-54.3625 316.1668,-54.3625 316.1668,-54.3625 319.6328,-54.849 316.6046,-51.2431 323.0988,-55.3355 323.0988,-55.3355\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"246\" y=\"-55.6479\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge8\">\n",
"<title>3-&gt;3</title>\n",
"<path d=\"M186.2539,-51.5149C181.3555,-62.5042 185.4375,-73.8479 198.5,-73.8479 208.7051,-73.8479 213.4289,-66.9243 212.6715,-58.6551\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"210.7461,-51.5149 215.61,-57.4534 211.6574,-54.8942 212.5687,-58.2735 212.5687,-58.2735 212.5687,-58.2735 211.6574,-54.8942 209.5273,-59.0937 210.7461,-51.5149 210.7461,-51.5149\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"171\" y=\"-92.6479\">p0 &amp; !p1</text>\n",
"<text fill=\"#6a3d9a\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"190.5\" y=\"-77.6479\">❸</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge4\">\n",
"<title>1-&gt;0</title>\n",
"<path d=\"M455.0135,-18.6138C449.0806,-16.7173 442.323,-14.8665 436,-13.8479 318.8364,5.0264 286.8591,3.0371 169,-10.8479 137.9101,-14.5107 102.9839,-23.6562 80.3002,-30.2903\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"73.3859,-32.3458 79.198,-27.3316 76.7408,-31.3484 80.0957,-30.351 80.0957,-30.351 80.0957,-30.351 76.7408,-31.3484 80.9933,-33.3704 73.3859,-32.3458 73.3859,-32.3458\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"248\" y=\"-21.6479\">!p0 &amp; p1</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"267.5\" y=\"-6.6479\">❶</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge5\">\n",
"<title>1-&gt;2</title>\n",
"<path d=\"M454.1457,-21.4202C434.5137,-18.4615 402.3872,-16.0425 377,-25.8479 369.8625,-28.6047 363.2281,-33.4788 357.6491,-38.6046\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"352.4423,-43.745 355.2106,-36.5855 354.933,-41.2861 357.4237,-38.8271 357.4237,-38.8271 357.4237,-38.8271 354.933,-41.2861 359.6368,-41.0687 352.4423,-43.745 352.4423,-43.745\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"377\" y=\"-29.6479\">!p0 &amp; !p1</text>\n",
"</g>\n",
"</g>\n",
"</svg>"
],
"text/plain": [
"<IPython.core.display.SVG object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"aut_max_odd4_to_min = spot.change_parity(aut_max_odd4, spot.parity_kind_min, spot.parity_style_any)\n",
"display(aut_max_odd4_to_min.show(\".a\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To keep the same **style** a new acceptance set is introduced, thus the **style** is toggled once again.\n",
"<br>\n",
"The new indexes of the acceptance sets are:\n",
"\n",
"+ 3 -> 0 -> 1\n",
"+ 2 -> 1 -> 2\n",
"+ 1 -> 2 -> 3\n",
"+ 0 -> 3 -> 4\n",
"+ ∅ -> ∅ -> 0 (as the resulting automaton is a parity min)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Result of Parity max odd 4 ----> Parity min even 5:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"<svg height=\"176pt\" viewBox=\"0.00 0.00 498.00 175.85\" width=\"498pt\" 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(4 171.8479)\">\n",
"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-171.8479 494,-171.8479 494,4 -4,4\" stroke=\"transparent\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"96\" y=\"-153.6479\">Fin(</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"121\" y=\"-153.6479\">⓿</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"137\" y=\"-153.6479\">) &amp; (Inf(</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"184\" y=\"-153.6479\">❶</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"200\" y=\"-153.6479\">) | (Fin(</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"243\" y=\"-153.6479\">❷</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"259\" y=\"-153.6479\">) &amp; (Inf(</text>\n",
"<text fill=\"#6a3d9a\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"306\" y=\"-153.6479\">❸</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"322\" y=\"-153.6479\">) | Fin(</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"362\" y=\"-153.6479\">❹</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"378\" y=\"-153.6479\">))))</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"188\" y=\"-139.6479\">[parity min odd 5]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g class=\"node\" id=\"node2\">\n",
"<title>0</title>\n",
"<ellipse cx=\"56\" cy=\"-37.8479\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"56\" y=\"-34.1479\">0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge1\">\n",
"<title>I-&gt;0</title>\n",
"<path d=\"M1.1233,-37.8479C4.178,-37.8479 17.9448,-37.8479 30.9241,-37.8479\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"37.9807,-37.8479 30.9808,-40.998 34.4807,-37.848 30.9807,-37.848 30.9807,-37.848 30.9807,-37.848 34.4807,-37.848 30.9807,-34.698 37.9807,-37.8479 37.9807,-37.8479\" stroke=\"#000000\"/>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g class=\"node\" id=\"node3\">\n",
"<title>2</title>\n",
"<ellipse cx=\"341\" cy=\"-57.8479\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"341\" y=\"-54.1479\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge2\">\n",
"<title>0-&gt;2</title>\n",
"<path d=\"M69.2358,-50.5171C89.0421,-68.5014 128.4234,-100.6076 169,-112.8479 223.8706,-129.4002 288.086,-94.2646 320.3183,-72.822\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"326.326,-68.7355 322.3098,-75.2771 323.4321,-70.704 320.5381,-72.6725 320.5381,-72.6725 320.5381,-72.6725 323.4321,-70.704 318.7664,-70.068 326.326,-68.7355 326.326,-68.7355\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"169\" y=\"-120.6479\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g class=\"node\" id=\"node4\">\n",
"<title>3</title>\n",
"<ellipse cx=\"198.5\" cy=\"-37.8479\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"198.5\" y=\"-34.1479\">3</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge3\">\n",
"<title>0-&gt;3</title>\n",
"<path d=\"M74.0477,-37.8479C99.0722,-37.8479 144.4394,-37.8479 172.939,-37.8479\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"180.1487,-37.8479 173.1488,-40.998 176.6487,-37.848 173.1487,-37.848 173.1487,-37.848 173.1487,-37.848 176.6487,-37.848 173.1487,-34.698 180.1487,-37.8479 180.1487,-37.8479\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"92\" y=\"-41.6479\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g class=\"node\" id=\"node5\">\n",
"<title>1</title>\n",
"<ellipse cx=\"472\" cy=\"-24.8479\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"472\" y=\"-21.1479\">1</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;1 -->\n",
"<g class=\"edge\" id=\"edge6\">\n",
"<title>2-&gt;1</title>\n",
"<path d=\"M359.1657,-55.9185C378.5155,-53.5593 409.8902,-48.8574 436,-40.8479 440.3769,-39.5053 444.9261,-37.7709 449.2584,-35.9414\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"455.8317,-33.0308 450.7065,-38.7452 452.6314,-34.4479 449.4311,-35.8649 449.4311,-35.8649 449.4311,-35.8649 452.6314,-34.4479 448.1557,-32.9847 455.8317,-33.0308 455.8317,-33.0308\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"379\" y=\"-56.6479\">!p0 &amp; p1</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge7\">\n",
"<title>3-&gt;2</title>\n",
"<path d=\"M216.5477,-40.381C241.7097,-43.9125 287.4385,-50.3305 315.9073,-54.3262\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"323.0988,-55.3355 315.7289,-57.4819 319.6328,-54.849 316.1668,-54.3625 316.1668,-54.3625 316.1668,-54.3625 319.6328,-54.849 316.6046,-51.2431 323.0988,-55.3355 323.0988,-55.3355\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"246\" y=\"-55.6479\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge8\">\n",
"<title>3-&gt;3</title>\n",
"<path d=\"M186.2539,-51.5149C181.3555,-62.5042 185.4375,-73.8479 198.5,-73.8479 208.7051,-73.8479 213.4289,-66.9243 212.6715,-58.6551\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"210.7461,-51.5149 215.61,-57.4534 211.6574,-54.8942 212.5687,-58.2735 212.5687,-58.2735 212.5687,-58.2735 211.6574,-54.8942 209.5273,-59.0937 210.7461,-51.5149 210.7461,-51.5149\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"171\" y=\"-92.6479\">p0 &amp; !p1</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"190.5\" y=\"-77.6479\">❹</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge4\">\n",
"<title>1-&gt;0</title>\n",
"<path d=\"M455.0135,-18.6138C449.0806,-16.7173 442.323,-14.8665 436,-13.8479 318.8364,5.0264 286.8591,3.0371 169,-10.8479 137.9101,-14.5107 102.9839,-23.6562 80.3002,-30.2903\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"73.3859,-32.3458 79.198,-27.3316 76.7408,-31.3484 80.0957,-30.351 80.0957,-30.351 80.0957,-30.351 76.7408,-31.3484 80.9933,-33.3704 73.3859,-32.3458 73.3859,-32.3458\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"248\" y=\"-21.6479\">!p0 &amp; p1</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"267.5\" y=\"-6.6479\">❷</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge5\">\n",
"<title>1-&gt;2</title>\n",
"<path d=\"M454.1457,-21.4202C434.5137,-18.4615 402.3872,-16.0425 377,-25.8479 369.8625,-28.6047 363.2281,-33.4788 357.6491,-38.6046\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"352.4423,-43.745 355.2106,-36.5855 354.933,-41.2861 357.4237,-38.8271 357.4237,-38.8271 357.4237,-38.8271 354.933,-41.2861 359.6368,-41.0687 352.4423,-43.745 352.4423,-43.745\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"377\" y=\"-29.6479\">!p0 &amp; !p1</text>\n",
"</g>\n",
"</g>\n",
"</svg>"
],
"text/plain": [
"<IPython.core.display.SVG object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"aut_max_odd4_to_min_bis = spot.change_parity(aut_max_odd4, spot.parity_kind_min, spot.parity_style_same)\n",
"display(aut_max_odd4_to_min_bis.show(\".a\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Colorize parity\n",
"\n",
"People working with parity automata usually expect all states (or edges) to be part of some acceptance set. This constraints, which come in addition to the use of a parity acceptance, is what the HOA format call \"colored\".\n",
"\n",
"A *parity automaton* is a *colored* automaton with *parity acceptance*.\n",
"\n",
"Coloring an automaton can be done with the `colorize_parity()` function.\n",
"\n",
"## Parity max\n",
"Transitions with multiple acceptance sets are purified by keeping only the set with the greatest index.\n",
"<br>\n",
"If there is a transition that do not belong to any acceptance set, a new acceptance set is introduced at the least significant place.\n",
"<br>\n",
"The least significant place of a parity max acceptance is where the indexes are the lowest, so all the existing acceptance sets' indexes will be shifted.\n",
"#### Colorize parity max odd 4"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"<svg height=\"173pt\" viewBox=\"0.00 0.00 498.00 172.81\" width=\"498pt\" 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(4 168.8065)\">\n",
"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-168.8065 494,-168.8065 494,4 -4,4\" stroke=\"transparent\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"131\" y=\"-150.6065\">Inf(</text>\n",
"<text fill=\"#6a3d9a\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"153\" y=\"-150.6065\">❸</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"169\" y=\"-150.6065\">) | (Fin(</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"212\" y=\"-150.6065\">❷</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"228\" y=\"-150.6065\">) &amp; (Inf(</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"275\" y=\"-150.6065\">❶</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"291\" y=\"-150.6065\">) | Fin(</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"331\" y=\"-150.6065\">⓿</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"347\" y=\"-150.6065\">)))</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"187.5\" y=\"-136.6065\">[parity max odd 4]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g class=\"node\" id=\"node2\">\n",
"<title>0</title>\n",
"<ellipse cx=\"56\" cy=\"-34.8065\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"56\" y=\"-31.1065\">0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge1\">\n",
"<title>I-&gt;0</title>\n",
"<path d=\"M1.1233,-34.8065C4.178,-34.8065 17.9448,-34.8065 30.9241,-34.8065\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"37.9807,-34.8065 30.9808,-37.9566 34.4807,-34.8065 30.9807,-34.8066 30.9807,-34.8066 30.9807,-34.8066 34.4807,-34.8065 30.9807,-31.6566 37.9807,-34.8065 37.9807,-34.8065\" stroke=\"#000000\"/>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g class=\"node\" id=\"node3\">\n",
"<title>2</title>\n",
"<ellipse cx=\"341\" cy=\"-54.8065\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"341\" y=\"-51.1065\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge2\">\n",
"<title>0-&gt;2</title>\n",
"<path d=\"M69.2358,-47.4757C89.0421,-65.4599 128.4234,-97.5662 169,-109.8065 223.8706,-126.3588 288.086,-91.2232 320.3183,-69.7806\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"326.326,-65.694 322.3098,-72.2357 323.4321,-67.6626 320.5381,-69.6311 320.5381,-69.6311 320.5381,-69.6311 323.4321,-67.6626 318.7664,-67.0265 326.326,-65.694 326.326,-65.694\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"169\" y=\"-117.6065\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g class=\"node\" id=\"node4\">\n",
"<title>3</title>\n",
"<ellipse cx=\"198.5\" cy=\"-34.8065\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"198.5\" y=\"-31.1065\">3</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge3\">\n",
"<title>0-&gt;3</title>\n",
"<path d=\"M74.0477,-34.8065C99.0722,-34.8065 144.4394,-34.8065 172.939,-34.8065\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"180.1487,-34.8065 173.1488,-37.9566 176.6487,-34.8065 173.1487,-34.8066 173.1487,-34.8066 173.1487,-34.8066 176.6487,-34.8065 173.1487,-31.6566 180.1487,-34.8065 180.1487,-34.8065\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"92\" y=\"-38.6065\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g class=\"node\" id=\"node5\">\n",
"<title>1</title>\n",
"<ellipse cx=\"472\" cy=\"-21.8065\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"472\" y=\"-18.1065\">1</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;1 -->\n",
"<g class=\"edge\" id=\"edge6\">\n",
"<title>2-&gt;1</title>\n",
"<path d=\"M359.1657,-52.8771C378.5155,-50.5179 409.8902,-45.816 436,-37.8065 440.3769,-36.4638 444.9261,-34.7294 449.2584,-32.8999\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"455.8317,-29.9893 450.7065,-35.7038 452.6314,-31.4064 449.4311,-32.8235 449.4311,-32.8235 449.4311,-32.8235 452.6314,-31.4064 448.1557,-29.9432 455.8317,-29.9893 455.8317,-29.9893\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"379\" y=\"-53.6065\">!p0 &amp; p1</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge7\">\n",
"<title>3-&gt;2</title>\n",
"<path d=\"M216.5477,-37.3395C241.7097,-40.871 287.4385,-47.2891 315.9073,-51.2847\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"323.0988,-52.294 315.7289,-54.4405 319.6328,-51.8075 316.1668,-51.321 316.1668,-51.321 316.1668,-51.321 319.6328,-51.8075 316.6046,-48.2016 323.0988,-52.294 323.0988,-52.294\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"246\" y=\"-52.6065\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge8\">\n",
"<title>3-&gt;3</title>\n",
"<path d=\"M186.2539,-48.4735C181.3555,-59.4627 185.4375,-70.8065 198.5,-70.8065 208.7051,-70.8065 213.4289,-63.8828 212.6715,-55.6136\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"210.7461,-48.4735 215.61,-54.4119 211.6574,-51.8528 212.5687,-55.2321 212.5687,-55.2321 212.5687,-55.2321 211.6574,-51.8528 209.5273,-56.0522 210.7461,-48.4735 210.7461,-48.4735\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"171\" y=\"-89.6065\">p0 &amp; !p1</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"190.5\" y=\"-74.6065\">⓿</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge4\">\n",
"<title>1-&gt;0</title>\n",
"<path d=\"M455.0183,-15.5417C449.0859,-13.6427 442.3273,-11.7983 436,-10.8065 323.3123,6.8572 222.0648,-1.5549 169,-7.8065 137.9101,-11.4692 102.9839,-20.6148 80.3002,-27.2488\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"73.3859,-29.3043 79.198,-24.2901 76.7408,-28.3069 80.0957,-27.3095 80.0957,-27.3095 80.0957,-27.3095 76.7408,-28.3069 80.9933,-30.3289 73.3859,-29.3043 73.3859,-29.3043\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"248\" y=\"-19.6065\">!p0 &amp; p1</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"259.5\" y=\"-5.6065\">⓿</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"275.5\" y=\"-5.6065\">❷</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge5\">\n",
"<title>1-&gt;2</title>\n",
"<path d=\"M454.1457,-18.3787C434.5137,-15.42 402.3872,-13.001 377,-22.8065 369.8625,-25.5633 363.2281,-30.4374 357.6491,-35.5631\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"352.4423,-40.7036 355.2106,-33.544 354.933,-38.2446 357.4237,-35.7856 357.4237,-35.7856 357.4237,-35.7856 354.933,-38.2446 359.6368,-38.0273 352.4423,-40.7036 352.4423,-40.7036\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"377\" y=\"-26.6065\">!p0 &amp; !p1</text>\n",
"</g>\n",
"</g>\n",
"</svg>"
],
"text/plain": [
"<IPython.core.display.SVG object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"aut_max_odd4 = tuple(spot.automata(\"randaut -A 'parity max odd 4' -Q4 2|\"))[0]\n",
"display(aut_max_odd4.show(\".a\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The new acceptance sets are:\n",
"+ ∅ -> 0\n",
"+ 0 -> 1\n",
"+ 1 -> 2\n",
"+ 2 -> 3\n",
"+ 3 -> 4\n",
"\n",
"#### The result of colorizing the given parity max odd 4 is"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"<svg height=\"192pt\" viewBox=\"0.00 0.00 498.00 192.01\" width=\"498pt\" 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(4 188.0072)\">\n",
"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-188.0072 494,-188.0072 494,4 -4,4\" stroke=\"transparent\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"98\" y=\"-169.8072\">Inf(</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"120\" y=\"-169.8072\">❹</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"136\" y=\"-169.8072\">) | (Fin(</text>\n",
"<text fill=\"#6a3d9a\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"179\" y=\"-169.8072\">❸</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"195\" y=\"-169.8072\">) &amp; (Inf(</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"242\" y=\"-169.8072\">❷</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"258\" y=\"-169.8072\">) | (Fin(</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"301\" y=\"-169.8072\">❶</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"317\" y=\"-169.8072\">) &amp; Inf(</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"360\" y=\"-169.8072\">⓿</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"376\" y=\"-169.8072\">))))</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"184.5\" y=\"-155.8072\">[parity max even 5]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g class=\"node\" id=\"node2\">\n",
"<title>0</title>\n",
"<ellipse cx=\"56\" cy=\"-36.0072\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"56\" y=\"-32.3072\">0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge1\">\n",
"<title>I-&gt;0</title>\n",
"<path d=\"M1.1233,-36.0072C4.178,-36.0072 17.9448,-36.0072 30.9241,-36.0072\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"37.9807,-36.0072 30.9808,-39.1573 34.4807,-36.0073 30.9807,-36.0073 30.9807,-36.0073 30.9807,-36.0073 34.4807,-36.0073 30.9807,-32.8573 37.9807,-36.0072 37.9807,-36.0072\" stroke=\"#000000\"/>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g class=\"node\" id=\"node3\">\n",
"<title>2</title>\n",
"<ellipse cx=\"341\" cy=\"-67.0072\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"341\" y=\"-63.3072\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge2\">\n",
"<title>0-&gt;2</title>\n",
"<path d=\"M68.592,-49.5021C75.1885,-56.1405 83.6223,-63.9875 92,-70.0072 123.486,-92.6311 131.3832,-101.6165 169,-111.0072 228.2142,-125.7895 249.3842,-117.1414 305,-92.0072 310.5819,-89.4846 316.213,-86.0765 321.3104,-82.5891\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"327.0143,-78.5073 323.155,-85.1427 324.168,-80.5442 321.3218,-82.581 321.3218,-82.581 321.3218,-82.581 324.168,-80.5442 319.4886,-80.0194 327.0143,-78.5073 327.0143,-78.5073\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"169\" y=\"-136.8072\">!p0 &amp; !p1</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"190.5\" y=\"-121.8072\">⓿</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g class=\"node\" id=\"node4\">\n",
"<title>3</title>\n",
"<ellipse cx=\"198.5\" cy=\"-36.0072\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"198.5\" y=\"-32.3072\">3</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge3\">\n",
"<title>0-&gt;3</title>\n",
"<path d=\"M74.0477,-36.0072C99.0722,-36.0072 144.4394,-36.0072 172.939,-36.0072\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"180.1487,-36.0072 173.1488,-39.1573 176.6487,-36.0072 173.1487,-36.0073 173.1487,-36.0073 173.1487,-36.0073 176.6487,-36.0072 173.1487,-32.8573 180.1487,-36.0072 180.1487,-36.0072\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"92\" y=\"-54.8072\">!p0 &amp; !p1</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"113.5\" y=\"-39.8072\">⓿</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g class=\"node\" id=\"node5\">\n",
"<title>1</title>\n",
"<ellipse cx=\"472\" cy=\"-23.0072\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"472\" y=\"-19.3072\">1</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;1 -->\n",
"<g class=\"edge\" id=\"edge6\">\n",
"<title>2-&gt;1</title>\n",
"<path d=\"M359.3459,-67.5236C379.1227,-67.4055 411.1106,-65.2254 436,-54.0072 442.7675,-50.957 449.226,-46.2199 454.7564,-41.3592\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"459.9545,-36.515 456.981,-43.5918 457.394,-38.9012 454.8335,-41.2874 454.8335,-41.2874 454.8335,-41.2874 457.394,-38.9012 452.6859,-38.9829 459.9545,-36.515 459.9545,-36.515\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"379\" y=\"-84.8072\">!p0 &amp; p1</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"398.5\" y=\"-69.8072\">⓿</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge7\">\n",
"<title>3-&gt;2</title>\n",
"<path d=\"M216.2596,-39.8707C241.433,-45.347 287.5999,-55.3903 316.1587,-61.6031\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"323.0166,-63.095 315.5069,-64.6849 319.5966,-62.351 316.1766,-61.6069 316.1766,-61.6069 316.1766,-61.6069 319.5966,-62.351 316.8462,-58.5289 323.0166,-63.095 323.0166,-63.095\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"246\" y=\"-76.8072\">!p0 &amp; !p1</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"267.5\" y=\"-61.8072\">⓿</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge8\">\n",
"<title>3-&gt;3</title>\n",
"<path d=\"M186.2539,-49.6742C181.3555,-60.6635 185.4375,-72.0072 198.5,-72.0072 208.7051,-72.0072 213.4289,-65.0835 212.6715,-56.8143\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"210.7461,-49.6742 215.61,-55.6126 211.6574,-53.0535 212.5687,-56.4328 212.5687,-56.4328 212.5687,-56.4328 211.6574,-53.0535 209.5273,-57.2529 210.7461,-49.6742 210.7461,-49.6742\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"171\" y=\"-90.8072\">p0 &amp; !p1</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"190.5\" y=\"-75.8072\">❶</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge4\">\n",
"<title>1-&gt;0</title>\n",
"<path d=\"M455.0647,-16.1533C449.136,-14.0801 442.3679,-12.072 436,-11.0072 322.3531,7.9964 221.7801,-2.7891 169,-9.0072 137.9101,-12.6699 102.9839,-21.8155 80.3002,-28.4495\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"73.3859,-30.5051 79.198,-25.4908 76.7408,-29.5076 80.0957,-28.5102 80.0957,-28.5102 80.0957,-28.5102 76.7408,-29.5076 80.9933,-31.5296 73.3859,-30.5051 73.3859,-30.5051\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"248\" y=\"-20.8072\">!p0 &amp; p1</text>\n",
"<text fill=\"#6a3d9a\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"267.5\" y=\"-5.8072\">❸</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge5\">\n",
"<title>1-&gt;2</title>\n",
"<path d=\"M454.2068,-18.9471C434.345,-15.3493 401.747,-12.2917 377,-24.0072 367.6034,-28.4557 359.7823,-36.6744 353.8572,-44.7442\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"349.7011,-50.8213 351.0526,-43.265 351.6769,-47.9323 353.6527,-45.0433 353.6527,-45.0433 353.6527,-45.0433 351.6769,-47.9323 356.2528,-46.8215 349.7011,-50.8213 349.7011,-50.8213\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"377\" y=\"-42.8072\">!p0 &amp; !p1</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"398.5\" y=\"-27.8072\">⓿</text>\n",
"</g>\n",
"</g>\n",
"</svg>"
],
"text/plain": [
"<IPython.core.display.SVG object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"aut_max_odd4_colored = spot.colorize_parity(aut_max_odd4, False)\n",
"display(aut_max_odd4_colored.show(\".a\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can notice that the **style** has been toggled.\n",
"<br>\n",
"To prevent colorize_parity from this we can add one extra acceptance set in the acceptance condition.\n",
"\n",
"The new acceptance sets are now:\n",
"+ ∅ -> 1\n",
"+ 0 -> 2\n",
"+ 1 -> 3\n",
"+ 2 -> 4\n",
"+ 3 -> 5\n",
"#### The result of colorizing the given parity max odd 4 without changing the style is"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"<svg height=\"192pt\" viewBox=\"0.00 0.00 498.00 192.01\" width=\"498pt\" 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(4 188.0072)\">\n",
"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-188.0072 494,-188.0072 494,4 -4,4\" stroke=\"transparent\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"66.5\" y=\"-169.8072\">Inf(</text>\n",
"<text fill=\"#e31a1c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"88.5\" y=\"-169.8072\">❺</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"104.5\" y=\"-169.8072\">) | (Fin(</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"147.5\" y=\"-169.8072\">❹</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"163.5\" y=\"-169.8072\">) &amp; (Inf(</text>\n",
"<text fill=\"#6a3d9a\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"210.5\" y=\"-169.8072\">❸</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"226.5\" y=\"-169.8072\">) | (Fin(</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"269.5\" y=\"-169.8072\">❷</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"285.5\" y=\"-169.8072\">) &amp; (Inf(</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"332.5\" y=\"-169.8072\">❶</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"348.5\" y=\"-169.8072\">) | Fin(</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"388.5\" y=\"-169.8072\">⓿</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"404.5\" y=\"-169.8072\">)))))</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"187.5\" y=\"-155.8072\">[parity max odd 6]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g class=\"node\" id=\"node2\">\n",
"<title>0</title>\n",
"<ellipse cx=\"56\" cy=\"-36.0072\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"56\" y=\"-32.3072\">0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge1\">\n",
"<title>I-&gt;0</title>\n",
"<path d=\"M1.1233,-36.0072C4.178,-36.0072 17.9448,-36.0072 30.9241,-36.0072\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"37.9807,-36.0072 30.9808,-39.1573 34.4807,-36.0073 30.9807,-36.0073 30.9807,-36.0073 30.9807,-36.0073 34.4807,-36.0073 30.9807,-32.8573 37.9807,-36.0072 37.9807,-36.0072\" stroke=\"#000000\"/>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g class=\"node\" id=\"node3\">\n",
"<title>2</title>\n",
"<ellipse cx=\"341\" cy=\"-67.0072\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"341\" y=\"-63.3072\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge2\">\n",
"<title>0-&gt;2</title>\n",
"<path d=\"M68.592,-49.5021C75.1885,-56.1405 83.6223,-63.9875 92,-70.0072 123.486,-92.6311 131.3832,-101.6165 169,-111.0072 228.2142,-125.7895 249.3842,-117.1414 305,-92.0072 310.5819,-89.4846 316.213,-86.0765 321.3104,-82.5891\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"327.0143,-78.5073 323.155,-85.1427 324.168,-80.5442 321.3218,-82.581 321.3218,-82.581 321.3218,-82.581 324.168,-80.5442 319.4886,-80.0194 327.0143,-78.5073 327.0143,-78.5073\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"169\" y=\"-136.8072\">!p0 &amp; !p1</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"190.5\" y=\"-121.8072\">❶</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g class=\"node\" id=\"node4\">\n",
"<title>3</title>\n",
"<ellipse cx=\"198.5\" cy=\"-36.0072\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"198.5\" y=\"-32.3072\">3</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge3\">\n",
"<title>0-&gt;3</title>\n",
"<path d=\"M74.0477,-36.0072C99.0722,-36.0072 144.4394,-36.0072 172.939,-36.0072\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"180.1487,-36.0072 173.1488,-39.1573 176.6487,-36.0072 173.1487,-36.0073 173.1487,-36.0073 173.1487,-36.0073 176.6487,-36.0072 173.1487,-32.8573 180.1487,-36.0072 180.1487,-36.0072\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"92\" y=\"-54.8072\">!p0 &amp; !p1</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"113.5\" y=\"-39.8072\">❶</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g class=\"node\" id=\"node5\">\n",
"<title>1</title>\n",
"<ellipse cx=\"472\" cy=\"-23.0072\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"472\" y=\"-19.3072\">1</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;1 -->\n",
"<g class=\"edge\" id=\"edge6\">\n",
"<title>2-&gt;1</title>\n",
"<path d=\"M359.3459,-67.5236C379.1227,-67.4055 411.1106,-65.2254 436,-54.0072 442.7675,-50.957 449.226,-46.2199 454.7564,-41.3592\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"459.9545,-36.515 456.981,-43.5918 457.394,-38.9012 454.8335,-41.2874 454.8335,-41.2874 454.8335,-41.2874 457.394,-38.9012 452.6859,-38.9829 459.9545,-36.515 459.9545,-36.515\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"379\" y=\"-84.8072\">!p0 &amp; p1</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"398.5\" y=\"-69.8072\">❶</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge7\">\n",
"<title>3-&gt;2</title>\n",
"<path d=\"M216.2596,-39.8707C241.433,-45.347 287.5999,-55.3903 316.1587,-61.6031\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"323.0166,-63.095 315.5069,-64.6849 319.5966,-62.351 316.1766,-61.6069 316.1766,-61.6069 316.1766,-61.6069 319.5966,-62.351 316.8462,-58.5289 323.0166,-63.095 323.0166,-63.095\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"246\" y=\"-76.8072\">!p0 &amp; !p1</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"267.5\" y=\"-61.8072\">❶</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge8\">\n",
"<title>3-&gt;3</title>\n",
"<path d=\"M186.2539,-49.6742C181.3555,-60.6635 185.4375,-72.0072 198.5,-72.0072 208.7051,-72.0072 213.4289,-65.0835 212.6715,-56.8143\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"210.7461,-49.6742 215.61,-55.6126 211.6574,-53.0535 212.5687,-56.4328 212.5687,-56.4328 212.5687,-56.4328 211.6574,-53.0535 209.5273,-57.2529 210.7461,-49.6742 210.7461,-49.6742\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"171\" y=\"-90.8072\">p0 &amp; !p1</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"190.5\" y=\"-75.8072\">❷</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge4\">\n",
"<title>1-&gt;0</title>\n",
"<path d=\"M455.0647,-16.1533C449.136,-14.0801 442.3679,-12.072 436,-11.0072 322.3531,7.9964 221.7801,-2.7891 169,-9.0072 137.9101,-12.6699 102.9839,-21.8155 80.3002,-28.4495\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"73.3859,-30.5051 79.198,-25.4908 76.7408,-29.5076 80.0957,-28.5102 80.0957,-28.5102 80.0957,-28.5102 76.7408,-29.5076 80.9933,-31.5296 73.3859,-30.5051 73.3859,-30.5051\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"248\" y=\"-20.8072\">!p0 &amp; p1</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"267.5\" y=\"-5.8072\">❹</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge5\">\n",
"<title>1-&gt;2</title>\n",
"<path d=\"M454.2068,-18.9471C434.345,-15.3493 401.747,-12.2917 377,-24.0072 367.6034,-28.4557 359.7823,-36.6744 353.8572,-44.7442\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"349.7011,-50.8213 351.0526,-43.265 351.6769,-47.9323 353.6527,-45.0433 353.6527,-45.0433 353.6527,-45.0433 351.6769,-47.9323 356.2528,-46.8215 349.7011,-50.8213 349.7011,-50.8213\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"377\" y=\"-42.8072\">!p0 &amp; !p1</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"398.5\" y=\"-27.8072\">❶</text>\n",
"</g>\n",
"</g>\n",
"</svg>"
],
"text/plain": [
"<IPython.core.display.SVG object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"aut_max_odd4_colored_bis = spot.colorize_parity(aut_max_odd4, True)\n",
"display(aut_max_odd4_colored_bis.show(\".a\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Parity min\n",
"Transitions with multiple acceptance sets are purified by keeping only the set with the lowest index.\n",
"<br>\n",
"If there is a transition that do not belong to any acceptance set, a new acceptance set is introduced at the least significant place.\n",
"<br>\n",
"The least significant place of a parity min acceptance is where the indexes are the greatest.\n",
"#### Colorize parity min odd 4"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"<svg height=\"173pt\" viewBox=\"0.00 0.00 498.00 172.81\" width=\"498pt\" 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(4 168.8065)\">\n",
"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-168.8065 494,-168.8065 494,4 -4,4\" stroke=\"transparent\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"128\" y=\"-150.6065\">Fin(</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"153\" y=\"-150.6065\">⓿</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"169\" y=\"-150.6065\">) &amp; (Inf(</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"216\" y=\"-150.6065\">❶</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"232\" y=\"-150.6065\">) | (Fin(</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"275\" y=\"-150.6065\">❷</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"291\" y=\"-150.6065\">) &amp; Inf(</text>\n",
"<text fill=\"#6a3d9a\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"334\" y=\"-150.6065\">❸</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"350\" y=\"-150.6065\">)))</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"188\" y=\"-136.6065\">[parity min odd 4]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g class=\"node\" id=\"node2\">\n",
"<title>0</title>\n",
"<ellipse cx=\"56\" cy=\"-34.8065\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"56\" y=\"-31.1065\">0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge1\">\n",
"<title>I-&gt;0</title>\n",
"<path d=\"M1.1233,-34.8065C4.178,-34.8065 17.9448,-34.8065 30.9241,-34.8065\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"37.9807,-34.8065 30.9808,-37.9566 34.4807,-34.8065 30.9807,-34.8066 30.9807,-34.8066 30.9807,-34.8066 34.4807,-34.8065 30.9807,-31.6566 37.9807,-34.8065 37.9807,-34.8065\" stroke=\"#000000\"/>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g class=\"node\" id=\"node3\">\n",
"<title>2</title>\n",
"<ellipse cx=\"341\" cy=\"-54.8065\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"341\" y=\"-51.1065\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge2\">\n",
"<title>0-&gt;2</title>\n",
"<path d=\"M69.2358,-47.4757C89.0421,-65.4599 128.4234,-97.5662 169,-109.8065 223.8706,-126.3588 288.086,-91.2232 320.3183,-69.7806\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"326.326,-65.694 322.3098,-72.2357 323.4321,-67.6626 320.5381,-69.6311 320.5381,-69.6311 320.5381,-69.6311 323.4321,-67.6626 318.7664,-67.0265 326.326,-65.694 326.326,-65.694\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"169\" y=\"-117.6065\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g class=\"node\" id=\"node4\">\n",
"<title>3</title>\n",
"<ellipse cx=\"198.5\" cy=\"-34.8065\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"198.5\" y=\"-31.1065\">3</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge3\">\n",
"<title>0-&gt;3</title>\n",
"<path d=\"M74.0477,-34.8065C99.0722,-34.8065 144.4394,-34.8065 172.939,-34.8065\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"180.1487,-34.8065 173.1488,-37.9566 176.6487,-34.8065 173.1487,-34.8066 173.1487,-34.8066 173.1487,-34.8066 176.6487,-34.8065 173.1487,-31.6566 180.1487,-34.8065 180.1487,-34.8065\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"92\" y=\"-38.6065\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g class=\"node\" id=\"node5\">\n",
"<title>1</title>\n",
"<ellipse cx=\"472\" cy=\"-21.8065\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"472\" y=\"-18.1065\">1</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;1 -->\n",
"<g class=\"edge\" id=\"edge6\">\n",
"<title>2-&gt;1</title>\n",
"<path d=\"M359.1657,-52.8771C378.5155,-50.5179 409.8902,-45.816 436,-37.8065 440.3769,-36.4638 444.9261,-34.7294 449.2584,-32.8999\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"455.8317,-29.9893 450.7065,-35.7038 452.6314,-31.4064 449.4311,-32.8235 449.4311,-32.8235 449.4311,-32.8235 452.6314,-31.4064 448.1557,-29.9432 455.8317,-29.9893 455.8317,-29.9893\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"379\" y=\"-53.6065\">!p0 &amp; p1</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge7\">\n",
"<title>3-&gt;2</title>\n",
"<path d=\"M216.5477,-37.3395C241.7097,-40.871 287.4385,-47.2891 315.9073,-51.2847\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"323.0988,-52.294 315.7289,-54.4405 319.6328,-51.8075 316.1668,-51.321 316.1668,-51.321 316.1668,-51.321 319.6328,-51.8075 316.6046,-48.2016 323.0988,-52.294 323.0988,-52.294\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"246\" y=\"-52.6065\">!p0 &amp; !p1</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge8\">\n",
"<title>3-&gt;3</title>\n",
"<path d=\"M186.2539,-48.4735C181.3555,-59.4627 185.4375,-70.8065 198.5,-70.8065 208.7051,-70.8065 213.4289,-63.8828 212.6715,-55.6136\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"210.7461,-48.4735 215.61,-54.4119 211.6574,-51.8528 212.5687,-55.2321 212.5687,-55.2321 212.5687,-55.2321 211.6574,-51.8528 209.5273,-56.0522 210.7461,-48.4735 210.7461,-48.4735\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"171\" y=\"-89.6065\">p0 &amp; !p1</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"190.5\" y=\"-74.6065\">⓿</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge4\">\n",
"<title>1-&gt;0</title>\n",
"<path d=\"M455.0183,-15.5417C449.0859,-13.6427 442.3273,-11.7983 436,-10.8065 323.3123,6.8572 222.0648,-1.5549 169,-7.8065 137.9101,-11.4692 102.9839,-20.6148 80.3002,-27.2488\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"73.3859,-29.3043 79.198,-24.2901 76.7408,-28.3069 80.0957,-27.3095 80.0957,-27.3095 80.0957,-27.3095 76.7408,-28.3069 80.9933,-30.3289 73.3859,-29.3043 73.3859,-29.3043\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"248\" y=\"-19.6065\">!p0 &amp; p1</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"259.5\" y=\"-5.6065\">⓿</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"275.5\" y=\"-5.6065\">❷</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge5\">\n",
"<title>1-&gt;2</title>\n",
"<path d=\"M454.1457,-18.3787C434.5137,-15.42 402.3872,-13.001 377,-22.8065 369.8625,-25.5633 363.2281,-30.4374 357.6491,-35.5631\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"352.4423,-40.7036 355.2106,-33.544 354.933,-38.2446 357.4237,-35.7856 357.4237,-35.7856 357.4237,-35.7856 354.933,-38.2446 359.6368,-38.0273 352.4423,-40.7036 352.4423,-40.7036\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"377\" y=\"-26.6065\">!p0 &amp; !p1</text>\n",
"</g>\n",
"</g>\n",
"</svg>"
],
"text/plain": [
"<IPython.core.display.SVG object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"aut_min_odd4 = tuple(spot.automata(\"randaut -A 'parity min odd 4' -Q4 2|\"))[0]\n",
"display(aut_min_odd4.show(\".a\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The new acceptance sets are:\n",
"+ ∅ -> 4\n",
"+ 0 -> 0\n",
"+ 1 -> 1\n",
"+ 2 -> 2\n",
"+ 3 -> 3\n",
"\n",
"#### The result of colorizing the given parity max odd 4 is"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"<svg height=\"192pt\" viewBox=\"0.00 0.00 498.00 192.01\" width=\"498pt\" 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(4 188.0072)\">\n",
"<polygon fill=\"#ffffff\" points=\"-4,4 -4,-188.0072 494,-188.0072 494,4 -4,4\" stroke=\"transparent\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"96\" y=\"-169.8072\">Fin(</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"121\" y=\"-169.8072\">⓿</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"137\" y=\"-169.8072\">) &amp; (Inf(</text>\n",
"<text fill=\"#ff4da0\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"184\" y=\"-169.8072\">❶</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"200\" y=\"-169.8072\">) | (Fin(</text>\n",
"<text fill=\"#ff7f00\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"243\" y=\"-169.8072\">❷</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"259\" y=\"-169.8072\">) &amp; (Inf(</text>\n",
"<text fill=\"#6a3d9a\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"306\" y=\"-169.8072\">❸</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"322\" y=\"-169.8072\">) | Fin(</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"362\" y=\"-169.8072\">❹</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"378\" y=\"-169.8072\">))))</text>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"188\" y=\"-155.8072\">[parity min odd 5]</text>\n",
"<!-- I -->\n",
"<!-- 0 -->\n",
"<g class=\"node\" id=\"node2\">\n",
"<title>0</title>\n",
"<ellipse cx=\"56\" cy=\"-36.0072\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"56\" y=\"-32.3072\">0</text>\n",
"</g>\n",
"<!-- I&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge1\">\n",
"<title>I-&gt;0</title>\n",
"<path d=\"M1.1233,-36.0072C4.178,-36.0072 17.9448,-36.0072 30.9241,-36.0072\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"37.9807,-36.0072 30.9808,-39.1573 34.4807,-36.0073 30.9807,-36.0073 30.9807,-36.0073 30.9807,-36.0073 34.4807,-36.0073 30.9807,-32.8573 37.9807,-36.0072 37.9807,-36.0072\" stroke=\"#000000\"/>\n",
"</g>\n",
"<!-- 2 -->\n",
"<g class=\"node\" id=\"node3\">\n",
"<title>2</title>\n",
"<ellipse cx=\"341\" cy=\"-67.0072\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"341\" y=\"-63.3072\">2</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge2\">\n",
"<title>0-&gt;2</title>\n",
"<path d=\"M68.592,-49.5021C75.1885,-56.1405 83.6223,-63.9875 92,-70.0072 123.486,-92.6311 131.3832,-101.6165 169,-111.0072 228.2142,-125.7895 249.3842,-117.1414 305,-92.0072 310.5819,-89.4846 316.213,-86.0765 321.3104,-82.5891\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"327.0143,-78.5073 323.155,-85.1427 324.168,-80.5442 321.3218,-82.581 321.3218,-82.581 321.3218,-82.581 324.168,-80.5442 319.4886,-80.0194 327.0143,-78.5073 327.0143,-78.5073\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"169\" y=\"-136.8072\">!p0 &amp; !p1</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"190.5\" y=\"-121.8072\">❹</text>\n",
"</g>\n",
"<!-- 3 -->\n",
"<g class=\"node\" id=\"node4\">\n",
"<title>3</title>\n",
"<ellipse cx=\"198.5\" cy=\"-36.0072\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"198.5\" y=\"-32.3072\">3</text>\n",
"</g>\n",
"<!-- 0&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge3\">\n",
"<title>0-&gt;3</title>\n",
"<path d=\"M74.0477,-36.0072C99.0722,-36.0072 144.4394,-36.0072 172.939,-36.0072\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"180.1487,-36.0072 173.1488,-39.1573 176.6487,-36.0072 173.1487,-36.0073 173.1487,-36.0073 173.1487,-36.0073 176.6487,-36.0072 173.1487,-32.8573 180.1487,-36.0072 180.1487,-36.0072\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"92\" y=\"-54.8072\">!p0 &amp; !p1</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"113.5\" y=\"-39.8072\">❹</text>\n",
"</g>\n",
"<!-- 1 -->\n",
"<g class=\"node\" id=\"node5\">\n",
"<title>1</title>\n",
"<ellipse cx=\"472\" cy=\"-23.0072\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"472\" y=\"-19.3072\">1</text>\n",
"</g>\n",
"<!-- 2&#45;&gt;1 -->\n",
"<g class=\"edge\" id=\"edge6\">\n",
"<title>2-&gt;1</title>\n",
"<path d=\"M359.3459,-67.5236C379.1227,-67.4055 411.1106,-65.2254 436,-54.0072 442.7675,-50.957 449.226,-46.2199 454.7564,-41.3592\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"459.9545,-36.515 456.981,-43.5918 457.394,-38.9012 454.8335,-41.2874 454.8335,-41.2874 454.8335,-41.2874 457.394,-38.9012 452.6859,-38.9829 459.9545,-36.515 459.9545,-36.515\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"379\" y=\"-84.8072\">!p0 &amp; p1</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"398.5\" y=\"-69.8072\">❹</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge7\">\n",
"<title>3-&gt;2</title>\n",
"<path d=\"M216.2596,-39.8707C241.433,-45.347 287.5999,-55.3903 316.1587,-61.6031\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"323.0166,-63.095 315.5069,-64.6849 319.5966,-62.351 316.1766,-61.6069 316.1766,-61.6069 316.1766,-61.6069 319.5966,-62.351 316.8462,-58.5289 323.0166,-63.095 323.0166,-63.095\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"246\" y=\"-76.8072\">!p0 &amp; !p1</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"267.5\" y=\"-61.8072\">❹</text>\n",
"</g>\n",
"<!-- 3&#45;&gt;3 -->\n",
"<g class=\"edge\" id=\"edge8\">\n",
"<title>3-&gt;3</title>\n",
"<path d=\"M186.2539,-49.6742C181.3555,-60.6635 185.4375,-72.0072 198.5,-72.0072 208.7051,-72.0072 213.4289,-65.0835 212.6715,-56.8143\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"210.7461,-49.6742 215.61,-55.6126 211.6574,-53.0535 212.5687,-56.4328 212.5687,-56.4328 212.5687,-56.4328 211.6574,-53.0535 209.5273,-57.2529 210.7461,-49.6742 210.7461,-49.6742\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"171\" y=\"-90.8072\">p0 &amp; !p1</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"190.5\" y=\"-75.8072\">⓿</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;0 -->\n",
"<g class=\"edge\" id=\"edge4\">\n",
"<title>1-&gt;0</title>\n",
"<path d=\"M455.0647,-16.1533C449.136,-14.0801 442.3679,-12.072 436,-11.0072 322.3531,7.9964 221.7801,-2.7891 169,-9.0072 137.9101,-12.6699 102.9839,-21.8155 80.3002,-28.4495\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"73.3859,-30.5051 79.198,-25.4908 76.7408,-29.5076 80.0957,-28.5102 80.0957,-28.5102 80.0957,-28.5102 76.7408,-29.5076 80.9933,-31.5296 73.3859,-30.5051 73.3859,-30.5051\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"248\" y=\"-20.8072\">!p0 &amp; p1</text>\n",
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"267.5\" y=\"-5.8072\">⓿</text>\n",
"</g>\n",
"<!-- 1&#45;&gt;2 -->\n",
"<g class=\"edge\" id=\"edge5\">\n",
"<title>1-&gt;2</title>\n",
"<path d=\"M454.2068,-18.9471C434.345,-15.3493 401.747,-12.2917 377,-24.0072 367.6034,-28.4557 359.7823,-36.6744 353.8572,-44.7442\" fill=\"none\" stroke=\"#000000\"/>\n",
"<polygon fill=\"#000000\" points=\"349.7011,-50.8213 351.0526,-43.265 351.6769,-47.9323 353.6527,-45.0433 353.6527,-45.0433 353.6527,-45.0433 351.6769,-47.9323 356.2528,-46.8215 349.7011,-50.8213 349.7011,-50.8213\" stroke=\"#000000\"/>\n",
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"377\" y=\"-42.8072\">!p0 &amp; !p1</text>\n",
"<text fill=\"#33a02c\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"398.5\" y=\"-27.8072\">❹</text>\n",
"</g>\n",
"</g>\n",
"</svg>"
],
"text/plain": [
"<IPython.core.display.SVG object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"aut_min_odd4_colored_bis = spot.colorize_parity(aut_min_odd4, True)\n",
"display(aut_min_odd4_colored_bis.show(\".a\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Remark: colorizing a parity min won't change the **style** of the acceptance."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
Reference in a new issue View git blame Copy permalink