f5f5daec9a
Fixes #267 * spot/twaalgos/gfguarantee.cc: Fix a typo when comparing automata sizes. * spot/twaalgos/translate.cc, spot/twaalgos/translate.hh: Use ltl-split even for BA/TGBA, but only of conjunctions with GF(..) in those cases. * tests/core/ltl2tgba2.test: Adjust and add the example of #267. * tests/core/degenid.test, tests/core/parity2.test, tests/core/stutter-tgba.test, tests/python/automata.ipynb, tests/python/highlighting.ipynb, tests/python/stutter-inv.ipynb, bin/spot-x.cc: Adjust.
2837 lines
193 KiB
Text
2837 lines
193 KiB
Text
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import spot\n",
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"spot.setup()\n",
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"from IPython.display import display"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"This notebook shows you different ways in which states or transitions can be highlighted in Spot. \n",
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"\n",
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"It should be noted that highlighting works using some special [named properties](https://spot.lrde.epita.fr/concepts.html#named-properties): basically, two maps that are attached to the automaton, and associated state or edge numbers to color numbers. This named properties are fragile: they will be lost if the automaton is transformed into a new automaton, and they can become meaningless of the automaton is modified in place (e.g., if the transitions or states are reordered).\n",
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"\n",
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"Nonetheless, highlighting is OK to use right before displaying or printing the automaton. The `dot` and `hoa` printer both know how to represent highlighted states and transitions.\n",
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"\n",
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"# Manual highlighting"
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]
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},
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"source": [
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"a = spot.translate('a U b U c')"
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]
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},
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"source": [
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"The `#` option of `print_dot()` can be used to display the internal number of each transition "
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"a.show('.#')"
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"source": [
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"Using these numbers you can selectively hightlight some transitions. The second argument is a color number (from a list of predefined colors)."
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"source": [
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"a.highlight_edges([2, 4, 5], 1)"
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]
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},
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"source": [
|
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"Note that these `highlight_` functions work for edges and states, and come with both singular (changing the color of single state or edge) and plural versions.\n",
|
|
"\n",
|
|
"They modify the automaton in place."
|
|
]
|
|
},
|
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{
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"cell_type": "code",
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"</g>\n",
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"<g id=\"edge7\" class=\"edge\">\n",
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"<title>2->2</title>\n",
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"</g>\n",
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"<!-- 2->0 -->\n",
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"<g id=\"edge5\" class=\"edge\">\n",
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"<title>2->0</title>\n",
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"<path fill=\"none\" stroke=\"#ff4da0\" stroke-width=\"2\" d=\"M73.8043,-66.4087C102.797,-73.0076 161.9993,-84.0634 212,-78 224.3248,-76.5054 237.6823,-73.472 249.0644,-70.4443\"/>\n",
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"<g id=\"node4\" class=\"node\">\n",
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"<text text-anchor=\"start\" x=\"189.5\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1</text>\n",
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"</g>\n",
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"<!-- 2->1 -->\n",
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"<g id=\"edge6\" class=\"edge\">\n",
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"<title>2->1</title>\n",
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"<path fill=\"none\" stroke=\"#ff4da0\" stroke-width=\"2\" d=\"M73.1988,-56.5163C97.4739,-48.7764 141.9077,-34.6091 169.5907,-25.7827\"/>\n",
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"<text text-anchor=\"start\" x=\"92\" y=\"-53.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a & b & !c</text>\n",
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"</g>\n",
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"<!-- 0->0 -->\n",
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"<g id=\"edge2\" class=\"edge\">\n",
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"<g id=\"edge3\" class=\"edge\">\n",
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"<title>1->0</title>\n",
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"<text text-anchor=\"start\" x=\"230\" y=\"-43.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">c</text>\n",
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"</g>\n",
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"<!-- 1->1 -->\n",
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"<g id=\"edge4\" class=\"edge\">\n",
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"<title>1->1</title>\n",
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"<path fill=\"none\" stroke=\"#000000\" d=\"M187.2664,-35.0373C185.8922,-44.8579 188.1367,-54 194,-54 198.3975,-54 200.7594,-48.8576 201.0858,-42.1433\"/>\n",
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|
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"<text text-anchor=\"start\" x=\"175.5\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">b & !c</text>\n",
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"</g>\n",
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"</g>\n",
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"</svg>\n"
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],
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"text/plain": [
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"<spot.twa; proxy of <Swig Object of type 'std::shared_ptr< spot::twa > *' at 0x7f7d6b654870> >"
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]
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},
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|
"execution_count": 5,
|
|
"metadata": {},
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"output_type": "execute_result"
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|
}
|
|
],
|
|
"source": [
|
|
"a.highlight_edge(6, 2).highlight_states((0, 1), 0)"
|
|
]
|
|
},
|
|
{
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|
"cell_type": "markdown",
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|
"metadata": {},
|
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"source": [
|
|
"The plural version can take a list or tuple of state numbers (as above) or of Booleans (as below). In the latter case the indices of the True values give the states to highlight."
|
|
]
|
|
},
|
|
{
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|
"cell_type": "code",
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|
"execution_count": 6,
|
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/svg+xml": [
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"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
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"<svg width=\"307pt\" height=\"165pt\"\n",
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" viewBox=\"0.00 0.00 307.00 164.80\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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"<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 160.8)\">\n",
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"<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-160.8 303,-160.8 303,4 -4,4\"/>\n",
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"<text text-anchor=\"start\" x=\"126.5\" y=\"-126.6\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">[Büchi]</text>\n",
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"<!-- I -->\n",
|
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"<!-- 2 -->\n",
|
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"<g id=\"node2\" class=\"node\">\n",
|
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"<title>2</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"#e31a1c\" stroke-width=\"2\" cx=\"56\" cy=\"-62\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"56\" y=\"-58.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">2</text>\n",
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"</g>\n",
|
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"<!-- I->2 -->\n",
|
|
"<g id=\"edge1\" class=\"edge\">\n",
|
|
"<title>I->2</title>\n",
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"<path fill=\"none\" stroke=\"#000000\" d=\"M1.1233,-62C4.178,-62 17.9448,-62 30.9241,-62\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"37.9807,-62 30.9808,-65.1501 34.4807,-62 30.9807,-62.0001 30.9807,-62.0001 30.9807,-62.0001 34.4807,-62 30.9807,-58.8501 37.9807,-62 37.9807,-62\"/>\n",
|
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"</g>\n",
|
|
"<!-- 2->2 -->\n",
|
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"<g id=\"edge7\" class=\"edge\">\n",
|
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"<title>2->2</title>\n",
|
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"<path fill=\"none\" stroke=\"#ff7f00\" stroke-width=\"2\" d=\"M49.6208,-79.0373C48.3189,-88.8579 50.4453,-98 56,-98 60.166,-98 62.4036,-92.8576 62.7128,-86.1433\"/>\n",
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|
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"<text text-anchor=\"start\" x=\"38\" y=\"-101.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & !c</text>\n",
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"</g>\n",
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"<!-- 0 -->\n",
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"<g id=\"node3\" class=\"node\">\n",
|
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"<title>0</title>\n",
|
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"<ellipse fill=\"#ffffaa\" stroke=\"#1f78b4\" stroke-width=\"2\" cx=\"277\" cy=\"-62\" rx=\"18\" ry=\"18\"/>\n",
|
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"<ellipse fill=\"none\" stroke=\"#1f78b4\" stroke-width=\"2\" cx=\"277\" cy=\"-62\" rx=\"22\" ry=\"22\"/>\n",
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"<text text-anchor=\"middle\" x=\"277\" y=\"-58.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">0</text>\n",
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"</g>\n",
|
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"<!-- 2->0 -->\n",
|
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"<g id=\"edge5\" class=\"edge\">\n",
|
|
"<title>2->0</title>\n",
|
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"<path fill=\"none\" stroke=\"#ff4da0\" stroke-width=\"2\" d=\"M73.8043,-66.4087C102.797,-73.0076 161.9993,-84.0634 212,-78 224.3248,-76.5054 237.6823,-73.472 249.0644,-70.4443\"/>\n",
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"<polygon fill=\"#ff4da0\" stroke=\"#ff4da0\" stroke-width=\"2\" points=\"255.8692,-68.5737 249.9546,-73.4666 252.6269,-69.9836 249.2521,-70.9113 249.1196,-70.4292 248.9871,-69.9471 252.3619,-69.0194 248.2846,-67.3919 255.8692,-68.5737 255.8692,-68.5737\"/>\n",
|
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"<text text-anchor=\"start\" x=\"190.5\" y=\"-82.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">c</text>\n",
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"</g>\n",
|
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"<!-- 1 -->\n",
|
|
"<g id=\"node4\" class=\"node\">\n",
|
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"<title>1</title>\n",
|
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"<ellipse fill=\"#ffffaa\" stroke=\"#e31a1c\" stroke-width=\"2\" cx=\"194\" cy=\"-18\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"start\" x=\"189.5\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1</text>\n",
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"</g>\n",
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"<!-- 2->1 -->\n",
|
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"<g id=\"edge6\" class=\"edge\">\n",
|
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"<title>2->1</title>\n",
|
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"<path fill=\"none\" stroke=\"#ff4da0\" stroke-width=\"2\" d=\"M73.1988,-56.5163C97.4739,-48.7764 141.9077,-34.6091 169.5907,-25.7827\"/>\n",
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"<polygon fill=\"#ff4da0\" stroke=\"#ff4da0\" stroke-width=\"2\" points=\"176.5845,-23.5528 170.8722,-28.6804 173.4018,-25.0924 170.0672,-26.1556 169.9153,-25.6793 169.7634,-25.2029 173.098,-24.1396 168.9584,-22.6781 176.5845,-23.5528 176.5845,-23.5528\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"92\" y=\"-53.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a & b & !c</text>\n",
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|
"</g>\n",
|
|
"<!-- 0->0 -->\n",
|
|
"<g id=\"edge2\" class=\"edge\">\n",
|
|
"<title>0->0</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M269.3173,-82.9908C268.3688,-93.0872 270.9297,-102 277,-102 281.5527,-102 284.1314,-96.9866 284.7361,-90.2204\"/>\n",
|
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"284.6827,-82.9908 287.8844,-89.9673 284.7086,-86.4907 284.7345,-89.9906 284.7345,-89.9906 284.7345,-89.9906 284.7086,-86.4907 281.5846,-90.0139 284.6827,-82.9908 284.6827,-82.9908\"/>\n",
|
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"<text text-anchor=\"start\" x=\"272.5\" y=\"-105.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1->0 -->\n",
|
|
"<g id=\"edge3\" class=\"edge\">\n",
|
|
"<title>1->0</title>\n",
|
|
"<path fill=\"none\" stroke=\"#ff4da0\" stroke-width=\"2\" d=\"M210.0032,-26.4836C221.6622,-32.6643 237.7048,-41.1688 251.1684,-48.3062\"/>\n",
|
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"<polygon fill=\"#ff4da0\" stroke=\"#ff4da0\" stroke-width=\"2\" points=\"257.5402,-51.684 249.8801,-51.1884 254.2136,-50.4864 251.1213,-48.847 251.3555,-48.4053 251.5897,-47.9635 254.682,-49.6028 252.8309,-45.6221 257.5402,-51.684 257.5402,-51.684\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"230\" y=\"-43.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">c</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1->1 -->\n",
|
|
"<g id=\"edge4\" class=\"edge\">\n",
|
|
"<title>1->1</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M187.2664,-35.0373C185.8922,-44.8579 188.1367,-54 194,-54 198.3975,-54 200.7594,-48.8576 201.0858,-42.1433\"/>\n",
|
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"200.7336,-35.0373 204.2263,-41.8728 200.9069,-38.533 201.0802,-42.0287 201.0802,-42.0287 201.0802,-42.0287 200.9069,-38.533 197.934,-42.1847 200.7336,-35.0373 200.7336,-35.0373\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"175.5\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">b & !c</text>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"</svg>\n"
|
|
],
|
|
"text/plain": [
|
|
"<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f7d6b72ef90> >"
|
|
]
|
|
},
|
|
"execution_count": 6,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"a.highlight_states([False, True, True], 5)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# Saving to HOA 1.1\n",
|
|
"\n",
|
|
"When saving to HOA format, the highlighting is only output if version 1.1 of the format is selected, because the headers `spot.highlight.edges` and `spot.highlight.states` contain dots, which are disallowed in version 1. Compare these two outputs:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 7,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"HOA: v1\n",
|
|
"States: 3\n",
|
|
"Start: 2\n",
|
|
"AP: 3 \"a\" \"b\" \"c\"\n",
|
|
"acc-name: Buchi\n",
|
|
"Acceptance: 1 Inf(0)\n",
|
|
"properties: trans-labels explicit-labels state-acc deterministic\n",
|
|
"properties: stutter-invariant terminal\n",
|
|
"--BODY--\n",
|
|
"State: 0 {0}\n",
|
|
"[t] 0\n",
|
|
"State: 1\n",
|
|
"[2] 0\n",
|
|
"[1&!2] 1\n",
|
|
"State: 2\n",
|
|
"[2] 0\n",
|
|
"[!0&1&!2] 1\n",
|
|
"[0&!2] 2\n",
|
|
"--END--\n",
|
|
"\n",
|
|
"HOA: v1.1\n",
|
|
"States: 3\n",
|
|
"Start: 2\n",
|
|
"AP: 3 \"a\" \"b\" \"c\"\n",
|
|
"acc-name: Buchi\n",
|
|
"Acceptance: 1 Inf(0)\n",
|
|
"properties: trans-labels explicit-labels state-acc !complete\n",
|
|
"properties: deterministic stutter-invariant terminal\n",
|
|
"spot.highlight.states: 0 0 1 5 2 5\n",
|
|
"spot.highlight.edges: 2 1 4 1 5 1 6 2\n",
|
|
"--BODY--\n",
|
|
"State: 0 {0}\n",
|
|
"[t] 0\n",
|
|
"State: 1\n",
|
|
"[2] 0\n",
|
|
"[1&!2] 1\n",
|
|
"State: 2\n",
|
|
"[2] 0\n",
|
|
"[!0&1&!2] 1\n",
|
|
"[0&!2] 2\n",
|
|
"--END--\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"print(a.to_str('HOA', '1'))\n",
|
|
"print()\n",
|
|
"print(a.to_str('HOA', '1.1'))"
|
|
]
|
|
},
|
|
{
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|
"cell_type": "markdown",
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"metadata": {},
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"source": [
|
|
"# Highlighting a run\n",
|
|
"\n",
|
|
"One use of this highlighting is to highlight a run in an automaton.\n",
|
|
"\n",
|
|
"The following few command generate an automaton, then an accepting run on this automaton, and highlight that accepting run on the automaton. Note that a run knows the automaton from which it was generated, so calling `highlight()` will directly decorate that automaton."
|
|
]
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},
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{
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"cell_type": "code",
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"</g>\n",
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],
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"text/plain": [
|
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"<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f7d6b6542a0> >"
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]
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},
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"execution_count": 8,
|
|
"metadata": {},
|
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"output_type": "execute_result"
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}
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],
|
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"source": [
|
|
"b = spot.translate('X (F(Ga <-> b) & GF!b)'); b"
|
|
]
|
|
},
|
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{
|
|
"cell_type": "code",
|
|
"execution_count": 9,
|
|
"metadata": {},
|
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"outputs": [
|
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{
|
|
"data": {
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|
"text/plain": [
|
|
"Prefix:\n",
|
|
" 4\n",
|
|
" | 1\n",
|
|
" 0\n",
|
|
" | !a & !b\n",
|
|
"Cycle:\n",
|
|
" 1\n",
|
|
" | !b\t{0}"
|
|
]
|
|
},
|
|
"execution_count": 9,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"r = b.accepting_run(); r"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 10,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"r.highlight(5) # the parameter is a color number"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"The call of `highlight(5)` on the accepting run `r` modified the original automaton `b`:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 11,
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"metadata": {},
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"outputs": [
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"source": [
|
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"# Highlighting from a product\n",
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"\n",
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"Pretty often, accepting runs are found in a product but we want to display them on one of the original automata. This can be done by projecting the runs on those automata before displaying them."
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]
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},
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"left = spot.translate('a U b')\n",
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"display(left, right)"
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" | a\t{0}"
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]
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},
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}
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],
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"run = prod.accepting_run(); run"
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"run.highlight(5)\n",
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"# Note that by default project() needs to know on which side you project, but it cannot \n",
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"# guess it. The left-side is assumed unless you pass True as a second argument.\n",
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"run.project(left).highlight(5)\n",
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"run.project(right, True).highlight(5)"
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]
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},
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]
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{
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"The projection also works for products generated on-the-fly, but the on-the-fly product itself cannot be highlighted (it does not store states or transitions). "
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]
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},
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{
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"cell_type": "code",
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" 1 * 4\n",
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"<text text-anchor=\"middle\" x=\"177.5\" y=\"-25.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1</text>\n",
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"</g>\n",
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"</g>\n",
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"</svg>\n"
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],
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"text/plain": [
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"<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f7d6b654a80> >"
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|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"left2 = spot.translate('!b & FG a')\n",
|
|
"right2 = spot.translate('XXXb')\n",
|
|
"prod2 = spot.otf_product(left2, right2) # Note \"otf_product()\"\n",
|
|
"run2 = prod2.accepting_run()\n",
|
|
"run2.project(left2).highlight(5)\n",
|
|
"run2.project(right2, True).highlight(5)\n",
|
|
"display(run2, prod2, left2, right2)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# Highlighting nondeterminism\n",
|
|
"\n",
|
|
"Sometimes its is hard to locate non-deterministic states inside a large automaton. Here are two functions that can help for that."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 18,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
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"<text text-anchor=\"middle\" x=\"360\" y=\"-125.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1</text>\n",
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"</g>\n",
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"<!-- 0->1 -->\n",
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"<g id=\"edge3\" class=\"edge\">\n",
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"<title>0->1</title>\n",
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"<path fill=\"none\" stroke=\"#000000\" d=\"M144.8384,-121.309C157.9792,-146.5059 187.0932,-193.9758 228,-213 273.4887,-234.1551 322.045,-181.0667 345.5673,-149.848\"/>\n",
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"<text text-anchor=\"start\" x=\"228\" y=\"-220.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a & !b</text>\n",
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"<g id=\"node5\" class=\"node\">\n",
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"<title>2</title>\n",
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"<text text-anchor=\"middle\" x=\"248.5\" y=\"-101.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">2</text>\n",
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"</g>\n",
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"<!-- 0->2 -->\n",
|
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"<g id=\"edge4\" class=\"edge\">\n",
|
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"<title>0->2</title>\n",
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"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M155.412,-105C173.9217,-105 202.5942,-105 223.2267,-105\"/>\n",
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|
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"<text text-anchor=\"start\" x=\"174.5\" y=\"-108.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & b</text>\n",
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"<!-- 3 -->\n",
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"</g>\n",
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"<!-- 0->3 -->\n",
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"<g id=\"edge5\" class=\"edge\">\n",
|
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"<title>0->3</title>\n",
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"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M151.5767,-93.6263C171.301,-78.236 206.5611,-50.7236 228.6783,-33.4662\"/>\n",
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|
|
"<text text-anchor=\"start\" x=\"173\" y=\"-79.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & !b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1->1 -->\n",
|
|
"<g id=\"edge6\" class=\"edge\">\n",
|
|
"<title>1->1</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M355.1797,-146.4099C354.28,-156.0879 355.8867,-165 360,-165 363.0207,-165 364.6896,-160.1936 365.0067,-153.8073\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"364.8203,-146.4099 368.1457,-153.3283 364.9085,-149.9088 364.9967,-153.4077 364.9967,-153.4077 364.9967,-153.4077 364.9085,-149.9088 361.8477,-153.4871 364.8203,-146.4099 364.8203,-146.4099\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"353.5\" y=\"-183.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"352\" y=\"-168.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1->1 -->\n",
|
|
"<g id=\"edge7\" class=\"edge\">\n",
|
|
"<title>1->1</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M352.7325,-145.5959C347.2416,-166.8633 349.6641,-195 360,-195 369.2458,-195 372.1594,-172.4854 368.7408,-152.5132\"/>\n",
|
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"367.2675,-145.5959 371.8066,-151.7861 367.9966,-149.0191 368.7257,-152.4423 368.7257,-152.4423 368.7257,-152.4423 367.9966,-149.0191 365.6448,-153.0985 367.2675,-145.5959 367.2675,-145.5959\"/>\n",
|
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"<text text-anchor=\"start\" x=\"355.5\" y=\"-198.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2->2 -->\n",
|
|
"<g id=\"edge8\" class=\"edge\">\n",
|
|
"<title>2->2</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M243.5012,-122.4099C242.5681,-132.0879 244.2344,-141 248.5,-141 251.6326,-141 253.3633,-136.1936 253.6921,-129.8073\"/>\n",
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|
|
"<text text-anchor=\"start\" x=\"230\" y=\"-159.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & !b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"240.5\" y=\"-144.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2->2 -->\n",
|
|
"<g id=\"edge9\" class=\"edge\">\n",
|
|
"<title>2->2</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M240.9634,-121.5959C235.269,-142.8633 237.7813,-171 248.5,-171 258.0883,-171 261.1098,-148.4854 257.5645,-128.5132\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"256.0366,-121.5959 260.6223,-127.7517 256.7915,-125.0135 257.5464,-128.4311 257.5464,-128.4311 257.5464,-128.4311 256.7915,-125.0135 254.4706,-129.1106 256.0366,-121.5959 256.0366,-121.5959\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"231.5\" y=\"-174.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->1 -->\n",
|
|
"<g id=\"edge10\" class=\"edge\">\n",
|
|
"<title>3->1</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M261.2905,-30.7331C281.0962,-50.4501 319.2564,-88.4391 341.8888,-110.9701\"/>\n",
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"<polygon fill=\"#000000\" stroke=\"#000000\" points=\"347.0153,-116.0735 339.832,-113.3672 344.5348,-113.6042 342.0544,-111.1348 342.0544,-111.1348 342.0544,-111.1348 344.5348,-113.6042 344.2768,-108.9024 347.0153,-116.0735 347.0153,-116.0735\"/>\n",
|
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"<text text-anchor=\"start\" x=\"287\" y=\"-96.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a & b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->3 -->\n",
|
|
"<g id=\"edge11\" class=\"edge\">\n",
|
|
"<title>3->3</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"M238.9254,-33.5414C236.2303,-43.9087 239.4219,-54 248.5,-54 255.4504,-54 258.9503,-48.0847 258.9995,-40.6591\"/>\n",
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"<text text-anchor=\"start\" x=\"231.5\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & b</text>\n",
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"</g>\n",
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"</g>\n",
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"</svg>\n"
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],
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"text/plain": [
|
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"<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f7d6b654d20> >"
|
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]
|
|
},
|
|
"execution_count": 18,
|
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
|
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"b = spot.translate('X (F(Ga <-> b) & GF!b)')\n",
|
|
"spot.highlight_nondet_states(b, 5)\n",
|
|
"spot.highlight_nondet_edges(b, 4)\n",
|
|
"b"
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|
]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
|
|
"# Disappearing highlights\n",
|
|
"\n",
|
|
"As explained at the top of this notebook, named properties (such as highlights) are fragile, and you should not really on them being preserved across algorithms. In-place algorithm are probably the worst, because they might modify the automaton and ignore the attached named properties. \n",
|
|
"\n",
|
|
"`randomize()` is one such in-place algorithm: it reorder states or transitions of the automaton. By doing so it renumber the states and edges, and that process would completely invalidate the highlights information. Fortunately `randomize()` know about highlights: it will preserve highlighted states, but it will drop all highlighted edges."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 19,
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"outputs": [
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]
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}
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"source": [
|
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"spot.randomize(b); b"
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]
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},
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{
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"metadata": {},
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"source": [
|
|
"# Highlighting with partial output\n",
|
|
"\n",
|
|
"For simplicity, rendering of partial automata is actually implemented by copying the original automaton and marking some states as \"incomplete\". This also allows the same display code to work with automata generated on-the-fly. However since there is a copy, propagating the highlighting information requires extra work. Let's make sure it has been done:"
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]
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},
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"outputs": [
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"</g>\n",
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"<text text-anchor=\"start\" x=\"231.5\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & b</text>\n",
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"</g>\n",
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"<!-- 4->0 -->\n",
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"<g id=\"edge12\" class=\"edge\">\n",
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"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M153.4522,-112.5252C172.4744,-121.226 203.9159,-135.6073 225.3876,-145.4284\"/>\n",
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"<text text-anchor=\"start\" x=\"174.5\" y=\"-141.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a & b</text>\n",
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"</g>\n",
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"<title>4->1</title>\n",
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"<text text-anchor=\"start\" x=\"228\" y=\"-90.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a & !b</text>\n",
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"</g>\n",
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"</g>\n",
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"<!-- 4->4 -->\n",
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"<g id=\"edge10\" class=\"edge\">\n",
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"<title>4->4</title>\n",
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"<text text-anchor=\"start\" x=\"123.5\" y=\"-144.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a | b</text>\n",
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"</g>\n",
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"</g>\n",
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"</svg>\n"
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],
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]
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},
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"metadata": {},
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{
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"<!-- I->0 -->\n",
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"<!-- 1->1 -->\n",
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"<title>1->1</title>\n",
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"</g>\n",
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"<!-- 1->u1 -->\n",
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"<title>1->u1</title>\n",
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"</g>\n",
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"<title>2</title>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"360\" y=\"-58.3\">1</text>\n",
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"<polygon fill=\"#33a02c\" points=\"233.9495,-29.0204 230.2851,-35.7654 231.4665,-31.5373 228.6808,-33.6562 228.3781,-33.2583 228.0754,-32.8603 230.8611,-30.7414 226.471,-30.7511 233.9495,-29.0204 233.9495,-29.0204\" stroke=\"#33a02c\" stroke-width=\"2\"/>\n",
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"<!-- 2->2 -->\n",
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"<g class=\"edge\" id=\"edge7\">\n",
|
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"<title>2->2</title>\n",
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"<title>2->2</title>\n",
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"</g>\n",
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"<title>3->3</title>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"231.5\" y=\"-57.8\">a & b</text>\n",
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"</g>\n",
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"</svg>"
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],
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},
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{
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"data": {
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"image/svg+xml": [
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"110\" y=\"-90.8\">⓿</text>\n",
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"<!-- I -->\n",
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"<!-- 0 -->\n",
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"<!-- I->0 -->\n",
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"<g class=\"edge\" id=\"edge1\">\n",
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"<title>I->0</title>\n",
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"<path d=\"M1.1233,-18C4.178,-18 17.9448,-18 30.9241,-18\" fill=\"none\" stroke=\"#000000\"/>\n",
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"</g>\n",
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"<!-- 1 -->\n",
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"<!-- 0->1 -->\n",
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"</g>\n",
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"<!-- 1->1 -->\n",
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"<g class=\"edge\" id=\"edge4\">\n",
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"<title>1->1</title>\n",
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"<path d=\"M130.6208,-35.0373C129.3189,-44.8579 131.4453,-54 137,-54 141.166,-54 143.4036,-48.8576 143.7128,-42.1433\" fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"123.5\" y=\"-57.8\">a | b</text>\n",
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"</g>\n",
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"<!-- u1 -->\n",
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"</g>\n",
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"<!-- 1->u1 -->\n",
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"<g class=\"edge\" id=\"edge3\">\n",
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"<title>1->u1</title>\n",
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"<path d=\"M155.2228,-18C164.2871,-18 175.2737,-18 184.6169,-18\" fill=\"none\" stroke=\"#000000\" stroke-dasharray=\"5,2\"/>\n",
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"</g>\n",
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"</g>\n",
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"</svg>"
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],
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"<IPython.core.display.SVG object>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
|
|
"source": [
|
|
"spot.highlight_nondet_edges(b, 4) # let's get those highlighted edges back\n",
|
|
"display(b, b.show('.<4'), b.show('.<2'))"
|
|
]
|
|
},
|
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{
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"cell_type": "markdown",
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"metadata": {},
|
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"source": [
|
|
"# Highlighting languages\n",
|
|
"\n",
|
|
"For deterministic automata, the function `spot.highlight_languages()` can be used to highlight states that recognize the same language. This can be a great help in reading automata. States with a colored border share their language, and states with a black border all have a language different from all other states."
|
|
]
|
|
},
|
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{
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"cell_type": "code",
|
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"execution_count": 21,
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|
"metadata": {},
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"outputs": [
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{
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"data": {
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"image/svg+xml": [
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"<svg height=\"360pt\" viewBox=\"0.00 0.00 664.23 360.00\" width=\"664pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"471.5\" y=\"-474.8\">)</text>\n",
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"</g>\n",
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"</g>\n",
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"<g class=\"cluster\" id=\"clust3\">\n",
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"<title>cluster_2</title>\n",
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"</g>\n",
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"<g class=\"cluster\" id=\"clust4\">\n",
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"<title>cluster_3</title>\n",
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"</g>\n",
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"<g class=\"cluster\" id=\"clust5\">\n",
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"<title>cluster_4</title>\n",
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"<polygon fill=\"none\" points=\"164.5,-101 164.5,-216 498,-216 498,-101 164.5,-101\" stroke=\"#00ff00\"/>\n",
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"</g>\n",
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"<g class=\"cluster\" id=\"clust6\">\n",
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"<title>cluster_5</title>\n",
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"<polygon fill=\"none\" points=\"30,-248 30,-300 82,-300 82,-248 30,-248\" stroke=\"#000000\"/>\n",
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"</g>\n",
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"<!-- I -->\n",
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"<!-- 0 -->\n",
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"<g class=\"node\" id=\"node2\">\n",
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"<title>0</title>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"56\" y=\"-270.3\">0</text>\n",
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"</g>\n",
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"<!-- I->0 -->\n",
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"<g class=\"edge\" id=\"edge1\">\n",
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"<title>I->0</title>\n",
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"</g>\n",
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"<!-- 1 -->\n",
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"<g class=\"node\" id=\"node3\">\n",
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"<title>1</title>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"344\" y=\"-367.3\">1</text>\n",
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"</g>\n",
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"<!-- 0->1 -->\n",
|
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"<g class=\"edge\" id=\"edge2\">\n",
|
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"<title>0->1</title>\n",
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"<path d=\"M63.8824,-290.3811C78.7868,-319.1066 114.1788,-377.4637 164.5,-398 217.5667,-419.6567 285.8315,-396.9135 320.9146,-381.9272\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"172\" y=\"-409.8\">a & !b</text>\n",
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"</g>\n",
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"<!-- 2 -->\n",
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"<g class=\"node\" id=\"node4\">\n",
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"<title>2</title>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"190.5\" y=\"-316.3\">2</text>\n",
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"</g>\n",
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"<!-- 0->2 -->\n",
|
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"<g class=\"edge\" id=\"edge3\">\n",
|
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"<title>0->2</title>\n",
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"<path d=\"M72.7754,-280.7513C78.8086,-283.1189 85.6835,-285.7478 92,-288 117.039,-296.9278 146.0092,-306.2165 166.019,-312.4716\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"106\" y=\"-311.8\">a & b</text>\n",
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"</g>\n",
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"<!-- 3 -->\n",
|
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"<g class=\"node\" id=\"node7\">\n",
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|
"<title>3</title>\n",
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"<ellipse cx=\"585\" cy=\"-94\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"585\" y=\"-90.3\">3</text>\n",
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"</g>\n",
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"<!-- 0->3 -->\n",
|
|
"<g class=\"edge\" id=\"edge4\">\n",
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"<title>0->3</title>\n",
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"<path d=\"M60.5211,-256.4433C76.6018,-195.9686 133.1366,0 190.5,0 190.5,0 190.5,0 472,0 495.3255,0 542.9619,-47.9358 568.2929,-75.3444\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"323.5\" y=\"-3.8\">!a & !b</text>\n",
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"</g>\n",
|
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"<!-- 4 -->\n",
|
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"<g class=\"node\" id=\"node8\">\n",
|
|
"<title>4</title>\n",
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"<ellipse cx=\"190.5\" cy=\"-135\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#ff4da0\" stroke-width=\"2\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"190.5\" y=\"-131.3\">4</text>\n",
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"</g>\n",
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"<!-- 0->4 -->\n",
|
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"<g class=\"edge\" id=\"edge5\">\n",
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"<title>0->4</title>\n",
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"<path d=\"M68.6534,-260.9232C92.6859,-236.0867 144.9938,-182.0287 172.605,-153.4938\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"177.7822,-148.1433 175.1783,-155.3643 175.3484,-150.6586 172.9145,-153.1738 172.9145,-153.1738 172.9145,-153.1738 175.3484,-150.6586 170.6508,-150.9834 177.7822,-148.1433 177.7822,-148.1433\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"92\" y=\"-239.8\">!a & b & c</text>\n",
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"</g>\n",
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"<!-- 5 -->\n",
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"<g class=\"node\" id=\"node9\">\n",
|
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"<title>5</title>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"472\" y=\"-143.3\">5</text>\n",
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"</g>\n",
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"<!-- 0->5 -->\n",
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"<g class=\"edge\" id=\"edge6\">\n",
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"<title>0->5</title>\n",
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"<path d=\"M74.0581,-274.6959C114.3952,-275.7124 214.4468,-275.2309 293,-250 355.4054,-229.9557 419.964,-186.0138 451.7765,-162.527\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"457.6921,-158.1156 453.9637,-164.8254 454.8863,-160.2079 452.0806,-162.3003 452.0806,-162.3003 452.0806,-162.3003 454.8863,-160.2079 450.1975,-159.7751 457.6921,-158.1156 457.6921,-158.1156\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"227\" y=\"-268.8\">!a & b & !c</text>\n",
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"</g>\n",
|
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"<!-- 1->1 -->\n",
|
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"<g class=\"edge\" id=\"edge7\">\n",
|
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"<title>1->1</title>\n",
|
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"<path d=\"M332.5701,-385.0417C328.2955,-395.9126 332.1055,-407 344,-407 353.2926,-407 357.6508,-400.2328 357.0745,-392.0885\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"339.5\" y=\"-425.8\">1</text>\n",
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"336\" y=\"-410.8\">⓿</text>\n",
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"</g>\n",
|
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"<!-- 2->1 -->\n",
|
|
"<g class=\"edge\" id=\"edge8\">\n",
|
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"<title>2->1</title>\n",
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"<path d=\"M207.81,-325.7512C235.218,-334.8574 288.6836,-352.6213 319.8499,-362.9762\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"326.5177,-365.1916 318.8816,-365.9737 323.1963,-364.088 319.8748,-362.9844 319.8748,-362.9844 319.8748,-362.9844 323.1963,-364.088 320.868,-359.9951 326.5177,-365.1916 326.5177,-365.1916\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"244.5\" y=\"-356.8\">a | !b</text>\n",
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"</g>\n",
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"<!-- 2->2 -->\n",
|
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"<g class=\"edge\" id=\"edge9\">\n",
|
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"<title>2->2</title>\n",
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"<path d=\"M179.5873,-334.4167C175.7765,-345.166 179.4141,-356 190.5,-356 199.1609,-356 203.2757,-349.3875 202.8443,-341.3688\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"172\" y=\"-374.8\">!a & b</text>\n",
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"182.5\" y=\"-359.8\">⓿</text>\n",
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"</g>\n",
|
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"<!-- 6 -->\n",
|
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"<g class=\"node\" id=\"node5\">\n",
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"<title>6</title>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"689\" y=\"-232.3\">6</text>\n",
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"</g>\n",
|
|
"<!-- 6->6 -->\n",
|
|
"<g class=\"edge\" id=\"edge22\">\n",
|
|
"<title>6->6</title>\n",
|
|
"<path d=\"M684.3583,-253.4099C683.4918,-263.0879 685.0391,-272 689,-272 691.9088,-272 693.5159,-267.1936 693.8213,-260.8073\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"693.6417,-253.4099 696.9607,-260.3314 693.7267,-256.9089 693.8117,-260.4078 693.8117,-260.4078 693.8117,-260.4078 693.7267,-256.9089 690.6626,-260.4843 693.6417,-253.4099 693.6417,-253.4099\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"670.5\" y=\"-275.8\">!b & c</text>\n",
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|
"</g>\n",
|
|
"<!-- 6->6 -->\n",
|
|
"<g class=\"edge\" id=\"edge23\">\n",
|
|
"<title>6->6</title>\n",
|
|
"<path d=\"M681.5375,-252.5858C676.8641,-270.1697 679.3516,-290 689,-290 697.367,-290 700.3489,-275.0873 697.9456,-259.659\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"696.4625,-252.5858 700.982,-258.7903 697.1808,-256.0113 697.8991,-259.4368 697.8991,-259.4368 697.8991,-259.4368 697.1808,-256.0113 694.8161,-260.0833 696.4625,-252.5858 696.4625,-252.5858\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"672\" y=\"-308.8\">b & c</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"681\" y=\"-293.8\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7 -->\n",
|
|
"<g class=\"node\" id=\"node6\">\n",
|
|
"<title>7</title>\n",
|
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"<ellipse cx=\"875\" cy=\"-186\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#ff7f00\" stroke-width=\"2\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"875\" y=\"-182.3\">7</text>\n",
|
|
"</g>\n",
|
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"<!-- 6->7 -->\n",
|
|
"<g class=\"edge\" id=\"edge24\">\n",
|
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"<title>6->7</title>\n",
|
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"<path d=\"M705.5151,-228.0187C723.2665,-219.7696 752.5101,-207.1224 779,-200 802.5091,-193.6791 830.0733,-190.033 849.6199,-188.0562\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"856.6936,-187.3782 850.0261,-191.1818 853.2096,-187.7122 849.7256,-188.0461 849.7256,-188.0461 849.7256,-188.0461 853.2096,-187.7122 849.425,-184.9105 856.6936,-187.3782 856.6936,-187.3782\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"779\" y=\"-203.8\">!b & !c</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->7 -->\n",
|
|
"<g class=\"edge\" id=\"edge25\">\n",
|
|
"<title>6->7</title>\n",
|
|
"<path d=\"M707.2418,-234.9539C732.9675,-233.0613 781.1089,-227.9784 820,-215 831.5915,-211.1318 843.6862,-205.014 853.5725,-199.3924\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"859.7228,-195.7986 855.2682,-202.05 856.7009,-197.5644 853.679,-199.3303 853.679,-199.3303 853.679,-199.3303 856.7009,-197.5644 852.0897,-196.6105 859.7228,-195.7986 859.7228,-195.7986\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"781\" y=\"-243.8\">b & !c</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"791.5\" y=\"-228.8\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7->6 -->\n",
|
|
"<g class=\"edge\" id=\"edge26\">\n",
|
|
"<title>7->6</title>\n",
|
|
"<path d=\"M867.9738,-202.6857C859.5061,-220.3681 843.431,-247.3165 820,-259 784.7574,-276.5731 738.3315,-260.524 711.2642,-247.8515\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"704.8184,-244.7249 712.4913,-244.9457 707.9675,-246.2524 711.1166,-247.7799 711.1166,-247.7799 711.1166,-247.7799 707.9675,-246.2524 709.7418,-250.6141 704.8184,-244.7249 704.8184,-244.7249\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"781\" y=\"-284.8\">!b & c</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"791.5\" y=\"-269.8\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7->6 -->\n",
|
|
"<g class=\"edge\" id=\"edge27\">\n",
|
|
"<title>7->6</title>\n",
|
|
"<path d=\"M872.2777,-204.1752C867.2316,-230.6201 853.6853,-278.8509 820,-300 781.1735,-324.3769 731.7148,-282.2264 706.1025,-255.4817\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"701.0115,-250.038 708.0935,-252.999 703.4022,-252.5943 705.7929,-255.1506 705.7929,-255.1506 705.7929,-255.1506 703.4022,-252.5943 703.4922,-257.3022 701.0115,-250.038 701.0115,-250.038\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"782.5\" y=\"-310.8\">b & c</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7->7 -->\n",
|
|
"<g class=\"edge\" id=\"edge28\">\n",
|
|
"<title>7->7</title>\n",
|
|
"<path d=\"M871.7643,-203.7817C871.2144,-213.3149 872.293,-222 875,-222 876.988,-222 878.0977,-217.3161 878.3292,-211.0521\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"878.2357,-203.7817 881.4756,-210.7406 878.2808,-207.2814 878.3258,-210.7812 878.3258,-210.7812 878.3258,-210.7812 878.2808,-207.2814 875.1761,-210.8217 878.2357,-203.7817 878.2357,-203.7817\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"854.5\" y=\"-240.8\">!b & !c</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"867\" y=\"-225.8\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7->7 -->\n",
|
|
"<g class=\"edge\" id=\"edge29\">\n",
|
|
"<title>7->7</title>\n",
|
|
"<path d=\"M869.9906,-203.5771C866.5451,-224.718 868.2148,-252 875,-252 881.043,-252 883.0285,-230.3596 880.9564,-210.6907\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"880.0094,-203.5771 884.0556,-210.1002 880.4713,-207.0465 880.9332,-210.5159 880.9332,-210.5159 880.9332,-210.5159 880.4713,-207.0465 877.8107,-210.9316 880.0094,-203.5771 880.0094,-203.5771\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"856.5\" y=\"-255.8\">b & !c</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->6 -->\n",
|
|
"<g class=\"edge\" id=\"edge10\">\n",
|
|
"<title>3->6</title>\n",
|
|
"<path d=\"M598.8412,-105.6195C613.6039,-118.5256 637.0155,-140.521 653,-163 663.9361,-178.3795 673.2592,-197.5791 679.6759,-212.4277\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"682.4151,-218.9146 676.7901,-213.6912 681.0535,-215.6902 679.692,-212.4659 679.692,-212.4659 679.692,-212.4659 681.0535,-215.6902 682.5939,-211.2405 682.4151,-218.9146 682.4151,-218.9146\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"621\" y=\"-166.8\">a & c</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->7 -->\n",
|
|
"<g class=\"edge\" id=\"edge11\">\n",
|
|
"<title>3->7</title>\n",
|
|
"<path d=\"M602.945,-91.0507C647.3899,-84.7604 764.372,-74.5063 839,-126 851.5701,-134.6734 860.4762,-149.2981 866.2855,-161.9371\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"869.1978,-168.7041 863.5371,-163.5196 867.8142,-165.4892 866.4305,-162.2743 866.4305,-162.2743 866.4305,-162.2743 867.8142,-165.4892 869.3239,-161.029 869.1978,-168.7041 869.1978,-168.7041\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"725\" y=\"-96.8\">a & !c</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4->6 -->\n",
|
|
"<g class=\"edge\" id=\"edge15\">\n",
|
|
"<title>4->6</title>\n",
|
|
"<path d=\"M201.897,-149.4708C225.2917,-177.3982 281.7937,-236 344,-236 344,-236 344,-236 585,-236 611.9726,-236 642.8801,-236 663.9454,-236\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"670.9634,-236 663.9635,-239.1501 667.4634,-236 663.9634,-236.0001 663.9634,-236.0001 663.9634,-236.0001 667.4634,-236 663.9634,-232.8501 670.9634,-236 670.9634,-236\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"456\" y=\"-239.8\">a & c</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4->7 -->\n",
|
|
"<g class=\"edge\" id=\"edge16\">\n",
|
|
"<title>4->7</title>\n",
|
|
"<path d=\"M202.5433,-121.4251C226.6527,-95.8337 283.7257,-43 344,-43 344,-43 344,-43 799.5,-43 852.2032,-43 868.2105,-119.8983 873,-160.9136\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"873.7469,-167.889 869.8695,-161.2642 873.3742,-164.4088 873.0016,-160.9287 873.0016,-160.9287 873.0016,-160.9287 873.3742,-164.4088 876.1336,-160.5933 873.7469,-167.889 873.7469,-167.889\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"567\" y=\"-46.8\">a & !c</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4->3 -->\n",
|
|
"<g class=\"edge\" id=\"edge12\">\n",
|
|
"<title>4->3</title>\n",
|
|
"<path d=\"M208.3429,-132.1959C256.5239,-124.7569 393.3563,-104.5101 508,-96 525.3054,-94.7154 544.8514,-94.2192 559.92,-94.0423\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"566.9282,-93.979 559.957,-97.1922 563.4283,-94.0106 559.9285,-94.0423 559.9285,-94.0423 559.9285,-94.0423 563.4283,-94.0106 559.9,-90.8924 566.9282,-93.979 566.9282,-93.979\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"395\" y=\"-109.8\">!a & !b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4->4 -->\n",
|
|
"<g class=\"edge\" id=\"edge13\">\n",
|
|
"<title>4->4</title>\n",
|
|
"<path d=\"M179.5873,-149.4167C175.7765,-160.166 179.4141,-171 190.5,-171 199.1609,-171 203.2757,-164.3875 202.8443,-156.3688\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"201.4127,-149.4167 205.9099,-155.6375 202.1187,-152.8447 202.8246,-156.2728 202.8246,-156.2728 202.8246,-156.2728 202.1187,-152.8447 199.7394,-156.9082 201.4127,-149.4167 201.4127,-149.4167\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"159.5\" y=\"-189.8\">!a & b & c</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"182.5\" y=\"-174.8\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4->5 -->\n",
|
|
"<g class=\"edge\" id=\"edge14\">\n",
|
|
"<title>4->5</title>\n",
|
|
"<path d=\"M208.5111,-135.3944C241.7985,-136.1645 315.1953,-138.0548 377,-141 400.6079,-142.125 427.4875,-143.8656 446.6154,-145.1829\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"453.7971,-145.6826 446.5953,-148.339 450.3056,-145.4396 446.814,-145.1966 446.814,-145.1966 446.814,-145.1966 450.3056,-145.4396 447.0327,-142.0542 453.7971,-145.6826 453.7971,-145.6826\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"311\" y=\"-159.8\">!a & b & !c</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"336\" y=\"-144.8\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->6 -->\n",
|
|
"<g class=\"edge\" id=\"edge20\">\n",
|
|
"<title>5->6</title>\n",
|
|
"<path d=\"M488.6673,-153.8359C527.0087,-169.5612 621.5487,-208.3356 665.6477,-226.4223\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"672.2759,-229.1408 664.6041,-229.3989 669.0377,-227.8127 665.7994,-226.4845 665.7994,-226.4845 665.7994,-226.4845 669.0377,-227.8127 666.9948,-223.5701 672.2759,-229.1408 672.2759,-229.1408\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"569\" y=\"-206.8\">a & c</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->7 -->\n",
|
|
"<g class=\"edge\" id=\"edge21\">\n",
|
|
"<title>5->7</title>\n",
|
|
"<path d=\"M490.099,-148.7515C554.8067,-155.0136 774.8091,-176.3041 849.7547,-183.5569\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"856.9509,-184.2533 849.68,-186.7143 853.4672,-183.9161 849.9834,-183.579 849.9834,-183.579 849.9834,-183.579 853.4672,-183.9161 850.2869,-180.4436 856.9509,-184.2533 856.9509,-184.2533\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"671\" y=\"-172.8\">a & !c</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->3 -->\n",
|
|
"<g class=\"edge\" id=\"edge17\">\n",
|
|
"<title>5->3</title>\n",
|
|
"<path d=\"M484.2148,-133.5487C490.7151,-127.1095 499.1767,-119.7796 508,-115 524.1242,-106.2656 544.1557,-100.9496 559.7453,-97.852\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"567.005,-96.5042 560.6976,-100.8791 563.5638,-97.1431 560.1226,-97.782 560.1226,-97.782 560.1226,-97.782 563.5638,-97.1431 559.5476,-94.6849 567.005,-96.5042 567.005,-96.5042\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"508\" y=\"-118.8\">!a & !b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->4 -->\n",
|
|
"<g class=\"edge\" id=\"edge18\">\n",
|
|
"<title>5->4</title>\n",
|
|
"<path d=\"M454.7373,-152.737C435.8867,-158.6757 404.6852,-167.557 377,-171 347.8909,-174.6201 340.0248,-175.243 311,-171 276.3928,-165.9409 237.9146,-153.1176 213.96,-144.2276\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"207.3083,-141.7212 214.9695,-141.2418 210.5835,-142.9553 213.8587,-144.1895 213.8587,-144.1895 213.8587,-144.1895 210.5835,-142.9553 212.748,-147.1372 207.3083,-141.7212 207.3083,-141.7212\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"313\" y=\"-176.8\">!a & b & c</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->5 -->\n",
|
|
"<g class=\"edge\" id=\"edge19\">\n",
|
|
"<title>5->5</title>\n",
|
|
"<path d=\"M462.4254,-162.5414C459.7303,-172.9087 462.9219,-183 472,-183 478.9504,-183 482.4503,-177.0847 482.4995,-169.6591\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"481.5746,-162.5414 485.6004,-169.0771 482.0256,-166.0123 482.4767,-169.4831 482.4767,-169.4831 482.4767,-169.4831 482.0256,-166.0123 479.353,-169.889 481.5746,-162.5414 481.5746,-162.5414\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"439\" y=\"-186.8\">!a & b & !c</text>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"</svg>"
|
|
],
|
|
"text/plain": [
|
|
"<IPython.core.display.SVG object>"
|
|
]
|
|
},
|
|
"execution_count": 21,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"aut = spot.translate('(b W Xa) & GF(c <-> Xb) | a', 'generic', 'det')\n",
|
|
"spot.highlight_languages(aut)\n",
|
|
"aut.show('.bas')"
|
|
]
|
|
}
|
|
],
|
|
"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": "3.6.6"
|
|
}
|
|
},
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"nbformat": 4,
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"nbformat_minor": 2
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}
|