4815a361de
* spot/twaalgos/translate.cc, spot/twaalgos/translate.hh: Build automata with generic acceptance by doing product of automata for smaller subformulas. * bin/spot-x.cc: Mention ltl-split. * NEWS: Mention the change, and show some results. * tests/core/genltl.test, tests/python/_product_susp.ipynb, tests/python/highlighting.ipynb: Adjust test cases. * doc/org/ltl2tgba.org: Update. * tests/core/gragsa.test: Add another formula to cover more code.
2849 lines
193 KiB
Text
2849 lines
193 KiB
Text
{
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"cells": [
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import spot\n",
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"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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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"a = spot.translate('a U b U c')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The `#` option of `print_dot()` can be used to display the internal number of each transition "
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]
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},
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"cell_type": "code",
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"source": [
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"a.show('.#')"
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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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"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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]
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},
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{
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}
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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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"<g id=\"edge5\" class=\"edge\">\n",
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"<title>2->0</title>\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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"<g id=\"edge2\" class=\"edge\">\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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"<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 0x7f6a1d7ce8a0> >"
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]
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},
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"execution_count": 5,
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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": [
|
|
"a.highlight_edge(6, 2).highlight_states((0, 1), 0)"
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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": [
|
|
"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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|
},
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{
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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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"<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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"<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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"<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",
|
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"<g id=\"edge1\" class=\"edge\">\n",
|
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"<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",
|
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"<!-- 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",
|
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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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"<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",
|
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"<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"
|
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],
|
|
"text/plain": [
|
|
"<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f6a240ef0f0> >"
|
|
]
|
|
},
|
|
"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'))"
|
|
]
|
|
},
|
|
{
|
|
"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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],
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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 0x7f6a1d7ce8d0> >"
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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,
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|
"metadata": {},
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"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"Prefix:\n",
|
|
" 0\n",
|
|
" | 1\n",
|
|
" 1\n",
|
|
" | !a & !b\n",
|
|
"Cycle:\n",
|
|
" 2\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",
|
|
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"metadata": {},
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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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"cell_type": "code",
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"outputs": [
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},
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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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{
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"source": [
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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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"</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 0x7f6a1d7ceb40> >"
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]
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},
|
|
"metadata": {},
|
|
"output_type": "display_data"
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|
}
|
|
],
|
|
"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\">2</text>\n",
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"</g>\n",
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"<!-- 1->2 -->\n",
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"<g id=\"edge4\" class=\"edge\">\n",
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"<title>1->2</title>\n",
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"<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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"<!-- 3 -->\n",
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"<g id=\"node5\" class=\"node\">\n",
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"<title>3</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\">3</text>\n",
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"</g>\n",
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"<!-- 1->3 -->\n",
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"<g id=\"edge5\" class=\"edge\">\n",
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"<title>1->3</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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"<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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"<!-- 4 -->\n",
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"</g>\n",
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"<!-- 1->4 -->\n",
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"<g id=\"edge6\" class=\"edge\">\n",
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"<title>1->4</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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|
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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",
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|
"</g>\n",
|
|
"<!-- 2->2 -->\n",
|
|
"<g id=\"edge7\" class=\"edge\">\n",
|
|
"<title>2->2</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",
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|
"</g>\n",
|
|
"<!-- 2->2 -->\n",
|
|
"<g id=\"edge8\" class=\"edge\">\n",
|
|
"<title>2->2</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",
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|
"</g>\n",
|
|
"<!-- 3->3 -->\n",
|
|
"<g id=\"edge9\" class=\"edge\">\n",
|
|
"<title>3->3</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",
|
|
"<!-- 3->3 -->\n",
|
|
"<g id=\"edge10\" class=\"edge\">\n",
|
|
"<title>3->3</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",
|
|
"<!-- 4->2 -->\n",
|
|
"<g id=\"edge11\" class=\"edge\">\n",
|
|
"<title>4->2</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",
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|
"</g>\n",
|
|
"<!-- 4->4 -->\n",
|
|
"<g id=\"edge12\" class=\"edge\">\n",
|
|
"<title>4->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"#000000\" d=\"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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"</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 0x7f6a1d7ced50> >"
|
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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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"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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"source": [
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"spot.randomize(b); b"
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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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"</svg>\n"
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],
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]
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},
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"227.5\" y=\"-90.8\">a & !b</text>\n",
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"238\" y=\"-75.8\">⓿</text>\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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"text/plain": [
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"<IPython.core.display.SVG object>"
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"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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"</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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"<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 class=\"edge\" id=\"edge2\">\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 class=\"node\" id=\"node4\">\n",
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"<title>u1</title>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"205\" y=\"-14.3\">...</text>\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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"<polygon fill=\"#000000\" points=\"191.6896,-18 184.6896,-21.1501 188.1896,-18 184.6896,-18.0001 184.6896,-18.0001 184.6896,-18.0001 188.1896,-18 184.6895,-14.8501 191.6896,-18 191.6896,-18\" stroke=\"#000000\"/>\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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"text/plain": [
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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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}
|
|
],
|
|
"source": [
|
|
"spot.highlight_nondet_edges(b, 4) # let's get those highlighted edges back\n",
|
|
"display(b, b.show('.<4'), b.show('.<2'))"
|
|
]
|
|
},
|
|
{
|
|
"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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{
|
|
"cell_type": "code",
|
|
"execution_count": 21,
|
|
"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 0.00 684.90 360.00\" width=\"685pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"455.5\" y=\"-459.8\">⓿</text>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"471.5\" y=\"-459.8\">)</text>\n",
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"</g>\n",
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"<title>cluster_1</title>\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=\"168.5,-101 168.5,-216 498,-216 498,-101 168.5,-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=\"-352.3\">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=\"M64.3119,-290.4883C79.9858,-319.3838 117.0199,-378.0014 168.5,-398 221.8867,-418.7393 288.5224,-388.4401 322.2598,-369.4207\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"176\" y=\"-407.8\">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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"<ellipse cx=\"194.5\" cy=\"-320\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#1f78b4\" stroke-width=\"2\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"194.5\" 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=\"M72.7611,-280.7918C78.793,-283.1633 85.6707,-285.7842 92,-288 118.4422,-297.257 149.162,-306.6732 170.0249,-312.8716\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"176.9701,-314.9243 169.3643,-315.961 173.6137,-313.9322 170.2572,-312.9402 170.2572,-312.9402 170.2572,-312.9402 173.6137,-313.9322 171.1501,-309.9193 176.9701,-314.9243 176.9701,-314.9243\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"108\" y=\"-312.8\">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=\"M56.6779,-255.5966C60.0121,-194.1624 79.6359,0 194.5,0 194.5,0 194.5,0 472,0 495.3255,0 542.9619,-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",
|
|
"<!-- 4 -->\n",
|
|
"<g class=\"node\" id=\"node8\">\n",
|
|
"<title>4</title>\n",
|
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"<ellipse cx=\"194.5\" cy=\"-142\" 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=\"194.5\" y=\"-138.3\">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=\"M69.28,-261.3433C94.1619,-237.6291 147.8378,-186.4722 176.1535,-159.4855\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"181.4625,-154.4257 178.5685,-161.5354 178.9288,-156.8404 176.3952,-159.2551 176.3952,-159.2551 176.3952,-159.2551 178.9288,-156.8404 174.222,-156.9748 181.4625,-154.4257 181.4625,-154.4257\" stroke=\"#000000\"/>\n",
|
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"92\" y=\"-241.8\">!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",
|
|
"<title>5</title>\n",
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"<ellipse cx=\"472\" cy=\"-134\" 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=\"472\" y=\"-130.3\">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=\"M74.1625,-275.0064C114.7106,-276.6504 215.1614,-277.3559 293,-250 357.4634,-227.3447 421.9916,-177.0856 453.0025,-150.7837\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"458.3953,-146.1635 455.1289,-153.11 455.7373,-148.4406 453.0794,-150.7178 453.0794,-150.7178 453.0794,-150.7178 455.7373,-148.4406 451.0299,-148.3257 458.3953,-146.1635 458.3953,-146.1635\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"231\" 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,-370.0417C328.2955,-380.9126 332.1055,-392 344,-392 353.2926,-392 357.6508,-385.2328 357.0745,-377.0885\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"355.4299,-370.0417 360.0885,-376.1426 356.2254,-373.4502 357.0209,-376.8586 357.0209,-376.8586 357.0209,-376.8586 356.2254,-373.4502 353.9534,-377.5745 355.4299,-370.0417 355.4299,-370.0417\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"339.5\" y=\"-410.8\">1</text>\n",
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"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"336\" y=\"-395.8\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2->1 -->\n",
|
|
"<g class=\"edge\" id=\"edge8\">\n",
|
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"<title>2->1</title>\n",
|
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"<path d=\"M212.2367,-324.271C238.8738,-330.6853 289.2919,-342.8261 319.4472,-350.0876\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"246.5\" y=\"-346.8\">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=\"M183.5873,-334.4167C179.7765,-345.166 183.4141,-356 194.5,-356 203.1609,-356 207.2757,-349.3875 206.8443,-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=\"176\" 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=\"186.5\" 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=\"693\" y=\"-232.3\">6</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->6 -->\n",
|
|
"<g class=\"edge\" id=\"edge22\">\n",
|
|
"<title>6->6</title>\n",
|
|
"<path d=\"M688.3583,-253.4099C687.4918,-263.0879 689.0391,-272 693,-272 695.9088,-272 697.5159,-267.1936 697.8213,-260.8073\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"697.6417,-253.4099 700.9607,-260.3314 697.7267,-256.9089 697.8117,-260.4078 697.8117,-260.4078 697.8117,-260.4078 697.7267,-256.9089 694.6626,-260.4843 697.6417,-253.4099 697.6417,-253.4099\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"672.5\" y=\"-290.8\">!b & !c</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"685\" y=\"-275.8\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->6 -->\n",
|
|
"<g class=\"edge\" id=\"edge23\">\n",
|
|
"<title>6->6</title>\n",
|
|
"<path d=\"M686.0017,-252.5959C680.7141,-273.8633 683.0469,-302 693,-302 701.9034,-302 704.7091,-279.4854 701.417,-259.5132\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"699.9983,-252.5959 704.4906,-258.8202 700.7015,-256.0245 701.4048,-259.4531 701.4048,-259.4531 701.4048,-259.4531 700.7015,-256.0245 698.319,-260.0861 699.9983,-252.5959 699.9983,-252.5959\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"674.5\" y=\"-305.8\">b & !c</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7 -->\n",
|
|
"<g class=\"node\" id=\"node6\">\n",
|
|
"<title>7</title>\n",
|
|
"<ellipse cx=\"875\" cy=\"-173\" 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=\"-169.3\">7</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->7 -->\n",
|
|
"<g class=\"edge\" id=\"edge24\">\n",
|
|
"<title>6->7</title>\n",
|
|
"<path d=\"M707.7113,-225.3238C724.2127,-213.9133 752.1888,-196.2241 779,-187 802.161,-179.0318 829.9864,-175.5987 849.7032,-174.1196\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"856.8362,-173.643 850.0619,-177.2528 853.344,-173.8764 849.8518,-174.1098 849.8518,-174.1098 849.8518,-174.1098 853.344,-173.8764 849.6418,-170.9668 856.8362,-173.643 856.8362,-173.643\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"781\" y=\"-205.8\">!b & c</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"791.5\" y=\"-190.8\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->7 -->\n",
|
|
"<g class=\"edge\" id=\"edge25\">\n",
|
|
"<title>6->7</title>\n",
|
|
"<path d=\"M711.0566,-236.2051C736.4385,-235.8609 783.6313,-232.8772 820,-217 833.8054,-210.9731 847.0599,-200.5581 857.0971,-191.3737\" fill=\"none\" stroke=\"#000000\"/>\n",
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"<polygon fill=\"#000000\" points=\"862.3253,-186.4335 859.4008,-193.5307 859.7813,-188.8373 857.2374,-191.2411 857.2374,-191.2411 857.2374,-191.2411 859.7813,-188.8373 855.0739,-188.9515 862.3253,-186.4335 862.3253,-186.4335\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"782.5\" y=\"-232.8\">b & c</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7->6 -->\n",
|
|
"<g class=\"edge\" id=\"edge26\">\n",
|
|
"<title>7->6</title>\n",
|
|
"<path d=\"M868.2515,-189.799C859.937,-207.9458 843.9091,-235.8843 820,-248 786.995,-264.7249 742.9786,-254.5089 716.3806,-245.393\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"709.6876,-242.9955 717.3399,-242.3907 712.9826,-244.1758 716.2776,-245.3561 716.2776,-245.3561 716.2776,-245.3561 712.9826,-244.1758 715.2153,-248.3216 709.6876,-242.9955 709.6876,-242.9955\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"779\" y=\"-259.8\">!b & !c</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7->6 -->\n",
|
|
"<g class=\"edge\" id=\"edge27\">\n",
|
|
"<title>7->6</title>\n",
|
|
"<path d=\"M871.2552,-190.9311C865.1642,-214.9751 850.5771,-256.7486 820,-275 785.5301,-295.575 739.2279,-270.1466 713.1151,-251.7572\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"707.2405,-247.4975 714.7567,-249.0566 710.074,-249.5522 712.9075,-251.6068 712.9075,-251.6068 712.9075,-251.6068 710.074,-249.5522 711.0584,-254.1569 707.2405,-247.4975 707.2405,-247.4975\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"781\" y=\"-300.8\">b & !c</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"791.5\" y=\"-285.8\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7->7 -->\n",
|
|
"<g class=\"edge\" id=\"edge28\">\n",
|
|
"<title>7->7</title>\n",
|
|
"<path d=\"M871.7643,-190.7817C871.2144,-200.3149 872.293,-209 875,-209 876.988,-209 878.0977,-204.3161 878.3292,-198.0521\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"878.2357,-190.7817 881.4756,-197.7406 878.2808,-194.2814 878.3258,-197.7812 878.3258,-197.7812 878.3258,-197.7812 878.2808,-194.2814 875.1761,-197.8217 878.2357,-190.7817 878.2357,-190.7817\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"856.5\" y=\"-212.8\">!b & c</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7->7 -->\n",
|
|
"<g class=\"edge\" id=\"edge29\">\n",
|
|
"<title>7->7</title>\n",
|
|
"<path d=\"M869.6841,-190.4203C866.6538,-207.791 868.4258,-227 875,-227 880.7011,-227 882.7908,-212.5545 881.2691,-197.3894\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"880.3159,-190.4203 884.3856,-196.9288 880.7902,-193.888 881.2646,-197.3557 881.2646,-197.3557 881.2646,-197.3557 880.7902,-193.888 878.1437,-197.7826 880.3159,-190.4203 880.3159,-190.4203\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"858\" y=\"-245.8\">b & c</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"867\" y=\"-230.8\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->6 -->\n",
|
|
"<g class=\"edge\" id=\"edge10\">\n",
|
|
"<title>3->6</title>\n",
|
|
"<path d=\"M599.4245,-105.223C615.085,-117.9544 640.1143,-139.9578 657,-163 668.2272,-178.3206 677.5892,-197.6777 683.9495,-212.6089\" fill=\"none\" stroke=\"#000000\"/>\n",
|
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"<polygon fill=\"#000000\" points=\"686.6565,-219.1274 681.0626,-213.8708 685.3141,-215.895 683.9717,-212.6627 683.9717,-212.6627 683.9717,-212.6627 685.3141,-215.895 686.8809,-211.4545 686.6565,-219.1274 686.6565,-219.1274\" 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=\"M602.5885,-89.8752C646.7134,-80.5871 763.9336,-62.5742 839,-113 851.8806,-121.6525 860.87,-136.6083 866.6445,-149.423\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"869.3748,-155.8843 863.7485,-150.6624 868.0125,-152.6603 866.6501,-149.4363 866.6501,-149.4363 866.6501,-149.4363 868.0125,-152.6603 869.5517,-148.2102 869.3748,-155.8843 869.3748,-155.8843\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"729\" y=\"-86.8\">a & c</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4->6 -->\n",
|
|
"<g class=\"edge\" id=\"edge15\">\n",
|
|
"<title>4->6</title>\n",
|
|
"<path d=\"M206.0931,-155.87C229.3352,-182.0177 284.5214,-236 344,-236 344,-236 344,-236 585,-236 613.1777,-236 645.4908,-236 667.3737,-236\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"674.655,-236 667.6551,-239.1501 671.155,-236 667.655,-236.0001 667.655,-236.0001 667.655,-236.0001 671.155,-236 667.655,-232.8501 674.655,-236 674.655,-236\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"454\" 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=\"M205.9324,-127.3922C228.8929,-99.8537 283.6082,-43 344,-43 344,-43 344,-43 799.5,-43 847.458,-43 865.4676,-109.9758 871.8132,-147.7805\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"872.9322,-154.9241 868.7367,-148.4959 872.3905,-151.4662 871.8488,-148.0084 871.8488,-148.0084 871.8488,-148.0084 872.3905,-151.4662 874.9608,-147.5209 872.9322,-154.9241 872.9322,-154.9241\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"569\" 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=\"M212.2864,-138.3794C218.2247,-137.2266 224.886,-135.9938 231,-135 353.5956,-115.0729 384.3247,-109.4533 508,-98 525.2965,-96.3982 544.8427,-95.3925 559.9135,-94.7902\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"566.923,-94.5261 560.0466,-97.9375 563.4255,-94.6579 559.9279,-94.7897 559.9279,-94.7897 559.9279,-94.7897 563.4255,-94.6579 559.8093,-91.642 566.923,-94.5261 566.923,-94.5261\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"395\" y=\"-112.8\">!a & !b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4->4 -->\n",
|
|
"<g class=\"edge\" id=\"edge13\">\n",
|
|
"<title>4->4</title>\n",
|
|
"<path d=\"M183.5873,-156.4167C179.7765,-167.166 183.4141,-178 194.5,-178 203.1609,-178 207.2757,-171.3875 206.8443,-163.3688\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"205.4127,-156.4167 209.9099,-162.6375 206.1187,-159.8447 206.8246,-163.2728 206.8246,-163.2728 206.8246,-163.2728 206.1187,-159.8447 203.7394,-163.9082 205.4127,-156.4167 205.4127,-156.4167\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"161.5\" y=\"-181.8\">!a & b & !c</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4->5 -->\n",
|
|
"<g class=\"edge\" id=\"edge14\">\n",
|
|
"<title>4->5</title>\n",
|
|
"<path d=\"M212.7076,-141.4751C260.7301,-140.0907 390.9341,-136.337 446.4098,-134.7377\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"453.7254,-134.5268 446.8191,-137.8773 450.2269,-134.6277 446.7283,-134.7286 446.7283,-134.7286 446.7283,-134.7286 450.2269,-134.6277 446.6375,-131.58 453.7254,-134.5268 453.7254,-134.5268\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"313\" y=\"-141.8\">!a & b & c</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->6 -->\n",
|
|
"<g class=\"edge\" id=\"edge20\">\n",
|
|
"<title>5->6</title>\n",
|
|
"<path d=\"M486.6714,-144.6952C493.0532,-149.1042 500.7232,-154.0858 508,-158 537.4417,-173.8366 626.6308,-209.7338 669.4995,-226.7372\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"676.2101,-229.3945 668.542,-229.7459 672.9559,-228.1059 669.7018,-226.8172 669.7018,-226.8172 669.7018,-226.8172 672.9559,-228.1059 670.8616,-223.8885 676.2101,-229.3945 676.2101,-229.3945\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"567\" y=\"-205.8\">a & !c</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->7 -->\n",
|
|
"<g class=\"edge\" id=\"edge21\">\n",
|
|
"<title>5->7</title>\n",
|
|
"<path d=\"M490.099,-135.7515C554.8067,-142.0136 774.8091,-163.3041 849.7547,-170.5569\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"856.9509,-171.2533 849.68,-173.7143 853.4672,-170.9161 849.9834,-170.579 849.9834,-170.579 849.9834,-170.579 853.4672,-170.9161 850.2869,-167.4436 856.9509,-171.2533 856.9509,-171.2533\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"677\" y=\"-160.8\">a & c</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->3 -->\n",
|
|
"<g class=\"edge\" id=\"edge17\">\n",
|
|
"<title>5->3</title>\n",
|
|
"<path d=\"M487.7728,-124.7133C493.9403,-121.3401 501.1635,-117.6984 508,-115 524.9465,-108.311 544.7975,-102.9534 560.099,-99.3241\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"567.2125,-97.6829 561.0998,-102.326 563.8021,-98.4698 560.3917,-99.2566 560.3917,-99.2566 560.3917,-99.2566 563.8021,-98.4698 559.6835,-96.1872 567.2125,-97.6829 567.2125,-97.6829\" 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=\"M454.6985,-139.2604C435.8147,-144.7055 404.5849,-152.8477 377,-156 320.7026,-162.4335 254.2876,-153.112 219.1642,-146.8623\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"212.1591,-145.5821 219.6114,-143.742 215.6021,-146.2114 219.0451,-146.8406 219.0451,-146.8406 219.0451,-146.8406 215.6021,-146.2114 218.4787,-149.9393 212.1591,-145.5821 212.1591,-145.5821\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"311\" y=\"-176.8\">!a & b & !c</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"336\" y=\"-161.8\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->5 -->\n",
|
|
"<g class=\"edge\" id=\"edge19\">\n",
|
|
"<title>5->5</title>\n",
|
|
"<path d=\"M462.4254,-149.5414C459.7303,-159.9087 462.9219,-170 472,-170 478.9504,-170 482.4503,-164.0847 482.4995,-156.6591\" fill=\"none\" stroke=\"#000000\"/>\n",
|
|
"<polygon fill=\"#000000\" points=\"481.5746,-149.5414 485.6004,-156.0771 482.0256,-153.0123 482.4767,-156.4831 482.4767,-156.4831 482.4767,-156.4831 482.0256,-153.0123 479.353,-156.889 481.5746,-149.5414 481.5746,-149.5414\" stroke=\"#000000\"/>\n",
|
|
"<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"441\" y=\"-188.8\">!a & b & c</text>\n",
|
|
"<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"464\" y=\"-173.8\">⓿</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')"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"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": "3.6.5+"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|