e778965730
This is to workaround differences in minidom's pretty-printing that occurred between Python 3.7 and 3.8. * python/spot/jupyter.py (SVG): New class. * python/spot/__init__.py: Use it. * tests/python/_altscc.ipynb, tests/python/alternation.ipynb, tests/python/automata.ipynb, tests/python/formulas.ipynb, tests/python/gen.ipynb, tests/python/highlighting.ipynb, tests/python/ltsmin-dve.ipynb, tests/python/ltsmin-pml.ipynb, tests/python/product.ipynb, tests/python/randaut.ipynb, tests/python/testingaut.ipynb, tests/python/twagraph-internals.ipynb, tests/python/word.ipynb: Adjust.
3611 lines
236 KiB
Text
3611 lines
236 KiB
Text
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import spot\n",
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"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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{
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"cell_type": "code",
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"execution_count": 3,
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"outputs": [
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"<text text-anchor=\"start\" x=\"175.5\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">b & !c</text>\n",
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"text/plain": [
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"<spot.jupyter.SVG object>"
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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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"a.show('.#')"
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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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"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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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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"data": {
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"<!-- I->2 -->\n",
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"<g id=\"edge1\" class=\"edge\">\n",
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"<text text-anchor=\"start\" x=\"175.5\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">b & !c</text>\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_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f5299f824b0> >"
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]
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},
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"execution_count": 4,
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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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"a.highlight_edges([2, 4, 5], 1)"
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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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"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",
|
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"\n",
|
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"They modify the automaton in place."
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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": 5,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"<!-- Pages: 1 -->\n",
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"<svg width=\"307pt\" height=\"165pt\"\n",
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"</g>\n",
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"</g>\n",
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"</g>\n",
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"<g id=\"edge5\" class=\"edge\">\n",
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"<title>2->0</title>\n",
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"<text text-anchor=\"start\" x=\"190.5\" y=\"-82.8\" font-family=\"Lato\" font-size=\"14.00\">c</text>\n",
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"</g>\n",
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"<g id=\"node4\" class=\"node\">\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=\"M73.4,-56.69C97.4,-48.93 142.19,-34.44 169.63,-25.56\"/>\n",
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"<text text-anchor=\"start\" x=\"92\" y=\"-53.8\" font-family=\"Lato\" font-size=\"14.00\">!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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"<title>0->0</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M269.32,-82.99C268.37,-93.09 270.93,-102 277,-102 281.55,-102 284.13,-96.99 284.74,-90.22\"/>\n",
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"<text text-anchor=\"start\" x=\"272.5\" y=\"-105.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
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"</g>\n",
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"<!-- 1->0 -->\n",
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"<g id=\"edge3\" class=\"edge\">\n",
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"<title>1->0</title>\n",
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"<path fill=\"none\" stroke=\"#ff4da0\" stroke-width=\"2\" d=\"M210.24,-26.28C221.74,-32.52 237.76,-41.23 251.11,-48.48\"/>\n",
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"<text text-anchor=\"start\" x=\"230\" y=\"-43.8\" font-family=\"Lato\" font-size=\"14.00\">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=\"black\" d=\"M187.27,-35.04C185.89,-44.86 188.14,-54 194,-54 198.4,-54 200.76,-48.86 201.09,-42.14\"/>\n",
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"<text text-anchor=\"start\" x=\"175.5\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">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 0x7f5299f82f90> >"
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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": [
|
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"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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"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
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"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
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" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
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"<!-- Generated by graphviz version 2.43.0 (0)\n",
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" -->\n",
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"<!-- Pages: 1 -->\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(1.0 1.0) rotate(0) translate(4 160.8)\">\n",
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"<polygon fill=\"white\" 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\">[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\">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=\"black\" d=\"M1.15,-62C2.79,-62 17.15,-62 30.63,-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=\"M49.62,-79.04C48.32,-88.86 50.45,-98 56,-98 60.17,-98 62.4,-92.86 62.71,-86.14\"/>\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\">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\">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=\"M73.77,-66.21C102.23,-72.79 161.79,-84.18 212,-78 224.33,-76.48 237.7,-73.38 249.02,-70.3\"/>\n",
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"<polygon fill=\"#ff4da0\" stroke=\"#ff4da0\" stroke-width=\"2\" points=\"255.78,-68.41 249.89,-73.33 252.54,-69.83 249.17,-70.78 249.04,-70.3 248.9,-69.82 252.27,-68.87 248.18,-67.27 255.78,-68.41 255.78,-68.41\"/>\n",
|
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"<text text-anchor=\"start\" x=\"190.5\" y=\"-82.8\" font-family=\"Lato\" font-size=\"14.00\">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\">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=\"M73.4,-56.69C97.4,-48.93 142.19,-34.44 169.63,-25.56\"/>\n",
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|
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"<text text-anchor=\"start\" x=\"92\" y=\"-53.8\" font-family=\"Lato\" font-size=\"14.00\">!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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"<title>0->0</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M269.32,-82.99C268.37,-93.09 270.93,-102 277,-102 281.55,-102 284.13,-96.99 284.74,-90.22\"/>\n",
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"<text text-anchor=\"start\" x=\"272.5\" y=\"-105.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
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"</g>\n",
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"<!-- 1->0 -->\n",
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"<g id=\"edge3\" class=\"edge\">\n",
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"<title>1->0</title>\n",
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"<path fill=\"none\" stroke=\"#ff4da0\" stroke-width=\"2\" d=\"M210.24,-26.28C221.74,-32.52 237.76,-41.23 251.11,-48.48\"/>\n",
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|
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"<text text-anchor=\"start\" x=\"230\" y=\"-43.8\" font-family=\"Lato\" font-size=\"14.00\">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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|
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"<text text-anchor=\"start\" x=\"175.5\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">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": [
|
|
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f5299f824b0> >"
|
|
]
|
|
},
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|
"execution_count": 6,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
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|
}
|
|
],
|
|
"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",
|
|
"metadata": {},
|
|
"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."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 8,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"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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"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
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" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
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"text": [
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"Prefix:\n",
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" 4\n",
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" | 1\n",
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" 0\n",
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" | !a & !b\n",
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"\n"
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}
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"source": [
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"source": [
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"The call of `highlight(5)` on the accepting run `r` modified the original automaton `b`:"
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"source": [
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"# Highlighting an accepting run in an automaton with arbitrary acceptance\n",
|
|
"\n",
|
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"This is not as easy as finding accepting runs in (generalized) Büchi automata, so let's have a few example for testing."
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]
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},
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{
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"cell_type": "code",
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"outputs": [
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"</g>\n",
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"</g>\n",
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"<text text-anchor=\"middle\" x=\"967\" y=\"-280.3\" font-family=\"Lato\" font-size=\"14.00\">7</text>\n",
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"</g>\n",
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"</g>\n",
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"</g>\n",
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"</g>\n",
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"<text text-anchor=\"middle\" x=\"635\" y=\"-33.3\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
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"</g>\n",
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|
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"<g id=\"edge13\" class=\"edge\">\n",
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"<title>3->4</title>\n",
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"<text text-anchor=\"start\" x=\"361\" y=\"-293.8\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
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"<text text-anchor=\"start\" x=\"386\" y=\"-293.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#e31a1c\">❺</text>\n",
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"<text text-anchor=\"start\" x=\"402\" y=\"-293.8\" font-family=\"Lato\" font-size=\"14.00\">) & ((Fin(</text>\n",
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"<text text-anchor=\"start\" x=\"456\" y=\"-293.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"<text text-anchor=\"start\" x=\"472\" y=\"-293.8\" font-family=\"Lato\" font-size=\"14.00\">) & (Inf(</text>\n",
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"<text text-anchor=\"start\" x=\"519\" y=\"-293.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
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"<text text-anchor=\"start\" x=\"535\" y=\"-293.8\" font-family=\"Lato\" font-size=\"14.00\">) | Inf(</text>\n",
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"<text text-anchor=\"start\" x=\"572\" y=\"-293.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#33a02c\">❹</text>\n",
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"<text text-anchor=\"start\" x=\"588\" y=\"-293.8\" font-family=\"Lato\" font-size=\"14.00\">))) | (Fin(</text>\n",
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"<text text-anchor=\"start\" x=\"639\" y=\"-293.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
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"<text text-anchor=\"start\" x=\"655\" y=\"-293.8\" font-family=\"Lato\" font-size=\"14.00\">)|Fin(</text>\n",
|
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"<text text-anchor=\"start\" x=\"687\" y=\"-293.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
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"<text text-anchor=\"start\" x=\"703\" y=\"-293.8\" font-family=\"Lato\" font-size=\"14.00\">)))</text>\n",
|
|
"<!-- I -->\n",
|
|
"<!-- 0 -->\n",
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|
"<g id=\"node2\" class=\"node\">\n",
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"<title>0</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"56\" cy=\"-175\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"56\" y=\"-171.3\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
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|
"</g>\n",
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"<!-- I->0 -->\n",
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"<g id=\"edge1\" class=\"edge\">\n",
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"<title>I->0</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1.15,-175C2.79,-175 17.15,-175 30.63,-175\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"37.94,-175 30.94,-178.15 34.44,-175 30.94,-175 30.94,-175 30.94,-175 34.44,-175 30.94,-171.85 37.94,-175 37.94,-175\"/>\n",
|
|
"</g>\n",
|
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"<!-- 8 -->\n",
|
|
"<g id=\"node3\" class=\"node\">\n",
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|
"<title>8</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"285.5\" cy=\"-104\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"285.5\" y=\"-100.3\" font-family=\"Lato\" font-size=\"14.00\">8</text>\n",
|
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"</g>\n",
|
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"<!-- 0->8 -->\n",
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"<g id=\"edge2\" class=\"edge\">\n",
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"<title>0->8</title>\n",
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"<path fill=\"none\" stroke=\"#e31a1c\" stroke-width=\"2\" d=\"M70.29,-163.74C87,-150.3 117.11,-128.34 147,-118 185.09,-104.82 232.4,-102.91 260.43,-103.15\"/>\n",
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"<polygon fill=\"#e31a1c\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"267.46,-103.26 260.41,-106.3 263.95,-103.71 260.45,-103.65 260.46,-103.15 260.47,-102.65 263.97,-102.71 260.51,-100 267.46,-103.26 267.46,-103.26\"/>\n",
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"<text text-anchor=\"start\" x=\"148\" y=\"-136.8\" font-family=\"Lato\" font-size=\"14.00\">a & b</text>\n",
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"<text text-anchor=\"start\" x=\"157\" y=\"-121.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
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"</g>\n",
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"<!-- 6 -->\n",
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"<g id=\"node4\" class=\"node\">\n",
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"<title>6</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"165\" cy=\"-175\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"165\" y=\"-171.3\" font-family=\"Lato\" font-size=\"14.00\">6</text>\n",
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"</g>\n",
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"<!-- 0->6 -->\n",
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"<g id=\"edge3\" class=\"edge\">\n",
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"<title>0->6</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M74.19,-175C91.9,-175 119.65,-175 139.62,-175\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"146.85,-175 139.85,-178.15 143.35,-175 139.85,-175 139.85,-175 139.85,-175 143.35,-175 139.85,-171.85 146.85,-175 146.85,-175\"/>\n",
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"<text text-anchor=\"start\" x=\"92\" y=\"-193.8\" font-family=\"Lato\" font-size=\"14.00\">a & !b</text>\n",
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"<text text-anchor=\"start\" x=\"102.5\" y=\"-178.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
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"</g>\n",
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"<!-- 3 -->\n",
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"<g id=\"node8\" class=\"node\">\n",
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"<title>3</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"395.5\" cy=\"-67\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"395.5\" y=\"-63.3\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
|
|
"</g>\n",
|
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"<!-- 8->3 -->\n",
|
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"<g id=\"edge17\" class=\"edge\">\n",
|
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"<title>8->3</title>\n",
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"<path fill=\"none\" stroke=\"#e31a1c\" stroke-width=\"2\" d=\"M302.9,-98.38C321.17,-92.12 350.82,-81.96 371.42,-74.91\"/>\n",
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"<polygon fill=\"#e31a1c\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"378.3,-72.55 372.7,-77.8 375.15,-74.16 371.84,-75.29 371.67,-74.82 371.51,-74.35 374.82,-73.21 370.65,-71.84 378.3,-72.55 378.3,-72.55\"/>\n",
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"<text text-anchor=\"start\" x=\"322\" y=\"-107.8\" font-family=\"Lato\" font-size=\"14.00\">a & !b</text>\n",
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"<text text-anchor=\"start\" x=\"324.5\" y=\"-93.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#33a02c\">❹</text>\n",
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"<text text-anchor=\"start\" x=\"340.5\" y=\"-93.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#e31a1c\">❺</text>\n",
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"</g>\n",
|
|
"<!-- 6->8 -->\n",
|
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"<g id=\"edge13\" class=\"edge\">\n",
|
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"<title>6->8</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M176.8,-160.93C183.18,-153.35 191.8,-144.29 201,-138 211.16,-131.05 240.33,-119.81 261.34,-112.18\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"268.11,-109.74 262.59,-115.07 264.81,-110.92 261.52,-112.11 261.52,-112.11 261.52,-112.11 264.81,-110.92 260.45,-109.15 268.11,-109.74 268.11,-109.74\"/>\n",
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"<text text-anchor=\"start\" x=\"206.5\" y=\"-155.8\" font-family=\"Lato\" font-size=\"14.00\">a & !b</text>\n",
|
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"<text text-anchor=\"start\" x=\"201\" y=\"-141.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"<text text-anchor=\"start\" x=\"217\" y=\"-141.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
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"<text text-anchor=\"start\" x=\"233\" y=\"-141.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#e31a1c\">❺</text>\n",
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"</g>\n",
|
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"<!-- 7 -->\n",
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"<g id=\"node10\" class=\"node\">\n",
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"<title>7</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"608\" cy=\"-180\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"608\" y=\"-176.3\" font-family=\"Lato\" font-size=\"14.00\">7</text>\n",
|
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"</g>\n",
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"<!-- 6->7 -->\n",
|
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"<g id=\"edge14\" class=\"edge\">\n",
|
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"<title>6->7</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M183.26,-176.18C206.32,-177.66 248.47,-180 284.5,-180 284.5,-180 284.5,-180 503,-180 530.3,-180 561.62,-180 582.7,-180\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"589.7,-180 582.7,-183.15 586.2,-180 582.7,-180 582.7,-180 582.7,-180 586.2,-180 582.7,-176.85 589.7,-180 589.7,-180\"/>\n",
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"<text text-anchor=\"start\" x=\"377\" y=\"-198.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b</text>\n",
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"<text text-anchor=\"start\" x=\"387.5\" y=\"-183.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
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"</g>\n",
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"<!-- 1 -->\n",
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"<g id=\"node5\" class=\"node\">\n",
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"<title>1</title>\n",
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"</g>\n",
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"<!-- 9 -->\n",
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"<g id=\"node6\" class=\"node\">\n",
|
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"<title>9</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"948.5\" cy=\"-131\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"948.5\" y=\"-127.3\" font-family=\"Lato\" font-size=\"14.00\">9</text>\n",
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"</g>\n",
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"<!-- 1->9 -->\n",
|
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"<g id=\"edge4\" class=\"edge\">\n",
|
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"<title>1->9</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M845.65,-178.83C863.14,-177.07 890.66,-172.71 912,-162 918.69,-158.64 925.13,-153.72 930.65,-148.79\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"935.84,-143.91 932.9,-151 933.29,-146.31 930.74,-148.71 930.74,-148.71 930.74,-148.71 933.29,-146.31 928.58,-146.41 935.84,-143.91 935.84,-143.91\"/>\n",
|
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"<text text-anchor=\"start\" x=\"869.5\" y=\"-193.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b</text>\n",
|
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"<text text-anchor=\"start\" x=\"864\" y=\"-179.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
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"<text text-anchor=\"start\" x=\"880\" y=\"-179.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#33a02c\">❹</text>\n",
|
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"<text text-anchor=\"start\" x=\"896\" y=\"-179.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#e31a1c\">❺</text>\n",
|
|
"</g>\n",
|
|
"<!-- 9->1 -->\n",
|
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"<g id=\"edge19\" class=\"edge\">\n",
|
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"<title>9->1</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M931.05,-125.81C913.39,-121.25 885.04,-116.89 864,-128 852.39,-134.13 843.86,-145.95 838.08,-156.77\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"834.83,-163.32 835.12,-155.65 836.39,-160.19 837.94,-157.05 837.94,-157.05 837.94,-157.05 836.39,-160.19 840.76,-158.45 834.83,-163.32 834.83,-163.32\"/>\n",
|
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"<text text-anchor=\"start\" x=\"871\" y=\"-146.8\" font-family=\"Lato\" font-size=\"14.00\">a & b</text>\n",
|
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|
|
"</g>\n",
|
|
"<!-- 9->3 -->\n",
|
|
"<g id=\"edge18\" class=\"edge\">\n",
|
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"<title>9->3</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M936.18,-117.59C916.61,-96.02 874.17,-56 828.5,-56 501,-56 501,-56 501,-56 473.26,-56 441.6,-59.88 420.47,-63.03\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"413.46,-64.11 419.9,-59.93 416.92,-63.58 420.38,-63.05 420.38,-63.05 420.38,-63.05 416.92,-63.58 420.85,-66.16 413.46,-64.11 413.46,-64.11\"/>\n",
|
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"<text text-anchor=\"start\" x=\"644\" y=\"-73.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"646.5\" y=\"-59.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
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"<text text-anchor=\"start\" x=\"662.5\" y=\"-59.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5 -->\n",
|
|
"<g id=\"node11\" class=\"node\">\n",
|
|
"<title>5</title>\n",
|
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"1058\" cy=\"-203\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"1058\" y=\"-199.3\" font-family=\"Lato\" font-size=\"14.00\">5</text>\n",
|
|
"</g>\n",
|
|
"<!-- 9->5 -->\n",
|
|
"<g id=\"edge20\" class=\"edge\">\n",
|
|
"<title>9->5</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M964,-140.71C982.78,-153.29 1015.61,-175.28 1036.82,-189.48\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"1042.73,-193.44 1035.16,-192.17 1039.82,-191.5 1036.92,-189.55 1036.92,-189.55 1036.92,-189.55 1039.82,-191.5 1038.67,-186.93 1042.73,-193.44 1042.73,-193.44\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"985\" y=\"-195.8\" font-family=\"Lato\" font-size=\"14.00\">a & !b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"995.5\" y=\"-180.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2 -->\n",
|
|
"<g id=\"node7\" class=\"node\">\n",
|
|
"<title>2</title>\n",
|
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"717.5\" cy=\"-180\" rx=\"18\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"717.5\" y=\"-176.3\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2->1 -->\n",
|
|
"<g id=\"edge5\" class=\"edge\">\n",
|
|
"<title>2->1</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M735.85,-180C753.8,-180 781.98,-180 802.15,-180\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"809.19,-180 802.19,-183.15 805.69,-180 802.19,-180 802.19,-180 802.19,-180 805.69,-180 802.19,-176.85 809.19,-180 809.19,-180\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"754\" y=\"-183.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->3 -->\n",
|
|
"<g id=\"edge6\" class=\"edge\">\n",
|
|
"<title>3->3</title>\n",
|
|
"<path fill=\"none\" stroke=\"#e31a1c\" stroke-width=\"2\" d=\"M386.52,-82.92C384.18,-93.15 387.17,-103 395.5,-103 401.88,-103 405.13,-97.23 405.25,-89.93\"/>\n",
|
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"<polygon fill=\"#e31a1c\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"404.48,-82.92 408.37,-89.53 405.36,-86.34 405.74,-89.82 405.24,-89.87 404.74,-89.93 404.36,-86.45 402.11,-90.22 404.48,-82.92 404.48,-82.92\"/>\n",
|
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"<text text-anchor=\"start\" x=\"377\" y=\"-121.8\" font-family=\"Lato\" font-size=\"14.00\">a & !b</text>\n",
|
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"<text text-anchor=\"start\" x=\"387.5\" y=\"-106.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4 -->\n",
|
|
"<g id=\"node9\" class=\"node\">\n",
|
|
"<title>4</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"502\" cy=\"-123\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"502\" y=\"-119.3\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->4 -->\n",
|
|
"<g id=\"edge7\" class=\"edge\">\n",
|
|
"<title>3->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M411.92,-75.26C429.85,-84.87 459.55,-100.79 479.68,-111.58\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"485.86,-114.89 478.2,-114.36 482.77,-113.23 479.69,-111.58 479.69,-111.58 479.69,-111.58 482.77,-113.23 481.18,-108.8 485.86,-114.89 485.86,-114.89\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"432\" y=\"-120.8\" font-family=\"Lato\" font-size=\"14.00\">a & b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"433\" y=\"-106.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
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"</g>\n",
|
|
"<!-- 4->0 -->\n",
|
|
"<g id=\"edge10\" class=\"edge\">\n",
|
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"<title>4->0</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M494.79,-139.97C481.86,-171.96 448.84,-238 396.5,-238 164,-238 164,-238 164,-238 129.5,-238 120.91,-227.82 92,-209 85.4,-204.7 78.97,-199.04 73.47,-193.57\"/>\n",
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|
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"<text text-anchor=\"start\" x=\"267\" y=\"-255.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b</text>\n",
|
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"<text text-anchor=\"start\" x=\"269.5\" y=\"-241.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
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|
|
"</g>\n",
|
|
"<!-- 4->9 -->\n",
|
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"<g id=\"edge9\" class=\"edge\">\n",
|
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"<title>4->9</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M520.08,-121.87C525.78,-121.53 532.16,-121.2 538,-121 682.81,-115.98 719.1,-117.89 864,-117 885.33,-116.87 891.04,-113.02 912,-117 916.44,-117.84 921.04,-119.23 925.39,-120.82\"/>\n",
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|
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"<text text-anchor=\"start\" x=\"699\" y=\"-135.8\" font-family=\"Lato\" font-size=\"14.00\">a & !b</text>\n",
|
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"<text text-anchor=\"start\" x=\"709.5\" y=\"-120.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
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"</g>\n",
|
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"<!-- 4->7 -->\n",
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]
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}
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],
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"source": [
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"def show_accrun(string):\n",
|
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" aut = spot.automaton(string)\n",
|
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" run = aut.accepting_run()\n",
|
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" run.highlight(5)\n",
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" display(aut)\n",
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"\n",
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"show_accrun(\"\"\"\n",
|
|
"HOA: v1 States: 10 Start: 0 AP: 2 \"a\" \"b\" Acceptance: 5 (Inf(1) | (Fin(0)\n",
|
|
"& Inf(4)) | Fin(2)) & Fin(3) properties: trans-labels explicit-labels\n",
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"trans-acc --BODY-- State: 0 [0&1] 9 {3} [!0&!1] 0 {3} [0&!1] 5 {0 1} State:\n",
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"1 [0&!1] 9 {4} [0&1] 8 {3} State: 2 [!0&!1] 8 {0} [!0&1] 6 {2 4} [0&1]\n",
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"2 {3} [!0&1] 7 State: 3 [0&!1] 2 {0 4} [!0&!1] 3 {1 3} [!0&1] 4 {0} State: 4\n",
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"[0&!1] 5 {2} [0&1] 0 [!0&1] 1 {0} State: 5 [!0&!1] 0 {3} [!0&!1] 6 {3} State: 6\n",
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"[0&1] 3 {2} [!0&1] 1 [0&1] 2 {0 1 3 4} State: 7 [0&1] 1 [!0&1] 7 {0 2}\n",
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"State: 8 [!0&1] 7 [!0&!1] 9 {0} State: 9 [0&1] 8 {3} [0&!1] 5 [0&!1]\n",
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"1 --END--\n",
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"\"\"\")\n",
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"show_accrun(\"\"\"\n",
|
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"HOA: v1 States: 10 Start: 0 AP: 2 \"a\" \"b\" Acceptance: 6 Fin(5) &\n",
|
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"((Fin(1) & (Inf(3) | Inf(4))) | Fin(0) | Fin(2)) properties: trans-labels\n",
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"explicit-labels trans-acc --BODY-- State: 0 [0&1] 8 {0} [0&!1] 6 {2}\n",
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"State: 1 [!0&1] 9 {0 4 5} State: 2 [!0&1] 1 State: 3 [0&!1] 3 {2}\n",
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"[0&1] 4 {3 5} State: 4 [0&1] 7 {5} [0&!1] 9 {2} [!0&1] 0 {0 2} State:\n",
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"5 [!0&1] 1 [!0&1] 3 {2 3} State: 6 [0&!1] 8 {1 2 5} [!0&1] 7 {3} State:\n",
|
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"7 [0&1] 2 {0} [!0&1] 5 State: 8 [0&!1] 3 {4 5} State: 9 [!0&1] 3 {1 2}\n",
|
|
"[0&1] 1 {4} [0&!1] 5 {2} --END--\"\"\")\n",
|
|
"show_accrun(\"\"\"\n",
|
|
"HOA: v1 States: 4 properties: implicit-labels trans-labels no-univ-branch\n",
|
|
"deterministic complete tool: \"ltl2dstar\" \"0.5.4\" name: \"i G F a G F b\"\n",
|
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"comment: \"Union{Safra[NBA=2],Safra[NBA=2]}\" acc-name: Rabin 2 Acceptance:\n",
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"4 (Fin(0)&Inf(1))|(Fin(2)&Inf(3)) Start: 0 AP: 2 \"a\" \"b\" --BODY-- State:\n",
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"0 {0} 1 0 3 2 State: 1 {1} 1 0 3 2 State: 2 {0 3} 1 0 3 2 State: 3 {1 3}\n",
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"1 0 3 2 --END--\n",
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"\"\"\")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
|
|
"# Highlighting from a product\n",
|
|
"\n",
|
|
"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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{
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"source": [
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"left = spot.translate('a U b')\n",
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"right = spot.translate('GFa')\n",
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"display(left, right)"
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]
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},
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]
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},
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"execution_count": 14,
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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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"prod = spot.product(left, right); prod"
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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": 15,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
|
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"Prefix:\n",
|
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" 1,0\n",
|
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" | !a & b\n",
|
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"Cycle:\n",
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" 0,0\n",
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" | a\t{0}\n",
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"\n"
|
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]
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}
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],
|
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"source": [
|
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"run = prod.accepting_run(); print(run)"
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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": 16,
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"metadata": {},
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"outputs": [],
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"source": [
|
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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",
|
|
"# guess it. The left-side is assumed unless you pass True as a second argument.\n",
|
|
"run.project(left).highlight(5)\n",
|
|
"run.project(right, True).highlight(5)"
|
|
]
|
|
},
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{
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"cell_type": "code",
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"execution_count": 17,
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"metadata": {},
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"outputs": [
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{
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"text/plain": [
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"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f5299f82b40> >"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"display(prod, left, right)"
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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 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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"execution_count": 18,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"Prefix:\n",
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" 0 * 3\n",
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" | a & !b\n",
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" 1 * 2\n",
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" | a\t{0}\n",
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" 1 * 1\n",
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|
" | a\t{0}\n",
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|
" 1 * 0\n",
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|
" | a & b\t{0}\n",
|
|
"Cycle:\n",
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|
" 1 * 4\n",
|
|
" | a\t{0,1}\n",
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"\n"
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]
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},
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"</svg>\n"
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],
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"text/plain": [
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"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f5299fa0480> >"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
|
|
"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",
|
|
"print(run2)\n",
|
|
"display(prod2, left2, right2)"
|
|
]
|
|
},
|
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{
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"cell_type": "markdown",
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"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."
|
|
]
|
|
},
|
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{
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"cell_type": "code",
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"execution_count": 19,
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"metadata": {},
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"outputs": [
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{
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" viewBox=\"0.00 0.00 386.00 276.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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"<text text-anchor=\"start\" x=\"190\" y=\"-253.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
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"</g>\n",
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"<!-- I->4 -->\n",
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"<title>I->4</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1.15,-105C2.79,-105 17.15,-105 30.63,-105\"/>\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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"<title>0->0</title>\n",
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"b = spot.translate('X (F(Ga <-> b) & GF!b)')\n",
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"b"
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"# Disappearing highlights\n",
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"\n",
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"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",
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|
"\n",
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"`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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"<g id=\"edge10\" class=\"edge\">\n",
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"<title>4->4</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M129.97,-121.66C128.41,-131.62 130.75,-141 137,-141 141.69,-141 144.18,-135.73 144.47,-128.89\"/>\n",
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"<text text-anchor=\"start\" x=\"123.5\" y=\"-144.8\" font-family=\"Lato\" font-size=\"14.00\">a | b</text>\n",
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"</svg>\n"
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"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f5299fa0930> >"
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]
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},
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"execution_count": 20,
|
|
"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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"spot.randomize(b); 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": [
|
|
"# 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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"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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"</g>\n",
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"<!-- 0->0 -->\n",
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"<title>0->0</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M240.96,-172.6C235.27,-193.86 237.78,-222 248.5,-222 258.09,-222 261.11,-199.49 257.56,-179.51\"/>\n",
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"<title>1->1</title>\n",
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"</g>\n",
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"<!-- 1->1 -->\n",
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"<g id=\"edge5\" class=\"edge\">\n",
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"<title>1->1</title>\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=\"black\" d=\"M265.66,-24.49C284.36,-32.01 315.3,-44.44 336.39,-52.91\"/>\n",
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"<text text-anchor=\"start\" x=\"287\" y=\"-50.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b</text>\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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"<!-- 4->0 -->\n",
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"<g id=\"edge12\" class=\"edge\">\n",
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"<title>4->0</title>\n",
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"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M153.69,-112.31C172.47,-121.06 204.05,-135.76 225.33,-145.67\"/>\n",
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"</g>\n",
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"<!-- 4->1 -->\n",
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"<g id=\"edge9\" class=\"edge\">\n",
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"<title>4->1</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M154.88,-101.72C169.47,-98.88 191.13,-94.67 210,-91 254.12,-82.42 305.58,-72.4 335.02,-66.67\"/>\n",
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"</g>\n",
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"<!-- 4->2 -->\n",
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"<g id=\"edge11\" class=\"edge\">\n",
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"<title>4->2</title>\n",
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"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M151.22,-93.89C157.74,-88.45 165.74,-81.83 173,-76 191.5,-61.14 212.91,-44.54 228.01,-32.91\"/>\n",
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"<g id=\"edge10\" class=\"edge\">\n",
|
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"<title>4->4</title>\n",
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"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M129.97,-121.66C128.41,-131.62 130.75,-141 137,-141 141.69,-141 144.18,-135.73 144.47,-128.89\"/>\n",
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"</svg>\n"
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],
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"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f5299fa0930> >"
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]
|
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},
|
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"metadata": {},
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"output_type": "display_data"
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{
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}
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],
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"source": [
|
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"spot.highlight_nondet_edges(b, 4) # let's get those highlighted edges back\n",
|
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"display(b, b.show('.<4'), b.show('.<2'))"
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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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"# Highlighting languages\n",
|
|
"\n",
|
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"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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},
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{
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"cell_type": "code",
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"execution_count": 22,
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"metadata": {},
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"outputs": [
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"<text text-anchor=\"start\" x=\"107\" y=\"-98.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
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"</g>\n",
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"<!-- 4 -->\n",
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"<g id=\"node3\" class=\"node\">\n",
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"<title>4</title>\n",
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"<text text-anchor=\"middle\" x=\"496\" y=\"-233.3\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
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"</g>\n",
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"<!-- 6 -->\n",
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"<g id=\"node4\" class=\"node\">\n",
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"<title>6</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"#ff4da0\" stroke-width=\"2\" cx=\"584\" cy=\"-231\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"584\" y=\"-227.3\" font-family=\"Lato\" font-size=\"14.00\">6</text>\n",
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"</g>\n",
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"<!-- 4->6 -->\n",
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"<g id=\"edge11\" class=\"edge\">\n",
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"<title>4->6</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M511.72,-227.46C517.75,-224.08 524.96,-220.7 532,-219 541.35,-216.74 551.67,-218.39 560.58,-221.11\"/>\n",
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"<text text-anchor=\"start\" x=\"534.5\" y=\"-222.8\" font-family=\"Lato\" font-size=\"14.00\">!c</text>\n",
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"</g>\n",
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"<!-- 7 -->\n",
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"<g id=\"node5\" class=\"node\">\n",
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"<title>7</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"#ff4da0\" stroke-width=\"2\" cx=\"697\" cy=\"-236\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"697\" y=\"-232.3\" font-family=\"Lato\" font-size=\"14.00\">7</text>\n",
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"</g>\n",
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"<!-- 4->7 -->\n",
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"<g id=\"edge12\" class=\"edge\">\n",
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"<title>4->7</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M509.43,-224.76C522.34,-212.99 543.72,-195.99 566,-189 605.86,-176.5 651.61,-202.72 676.82,-220.79\"/>\n",
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"<text text-anchor=\"start\" x=\"580.5\" y=\"-192.8\" font-family=\"Lato\" font-size=\"14.00\">c</text>\n",
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"</g>\n",
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"<!-- 6->4 -->\n",
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"<g id=\"edge16\" class=\"edge\">\n",
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"<title>6->4</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M565.92,-232.56C560.22,-233.05 553.84,-233.58 548,-234 539.24,-234.63 529.63,-235.22 521.14,-235.71\"/>\n",
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"<text text-anchor=\"start\" x=\"533.5\" y=\"-253.8\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
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"<text text-anchor=\"start\" x=\"532\" y=\"-238.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
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"</g>\n",
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"<!-- 6->6 -->\n",
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"<g id=\"edge17\" class=\"edge\">\n",
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"<title>6->6</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M576.33,-247.29C574.48,-257.39 577.04,-267 584,-267 589.22,-267 591.96,-261.59 592.23,-254.63\"/>\n",
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"<text text-anchor=\"start\" x=\"565.5\" y=\"-270.8\" font-family=\"Lato\" font-size=\"14.00\">b & !c</text>\n",
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"</g>\n",
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"<!-- 6->7 -->\n",
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"<g id=\"edge18\" class=\"edge\">\n",
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"<title>6->7</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M600.69,-223.82C606.61,-221.47 613.49,-219.17 620,-218 637.93,-214.78 643.29,-213.71 661,-218 665.73,-219.14 670.54,-221.05 675.01,-223.19\"/>\n",
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"</g>\n",
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"<!-- 7->4 -->\n",
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"<g id=\"edge19\" class=\"edge\">\n",
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"<title>7->4</title>\n",
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"</g>\n",
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"<!-- 7->6 -->\n",
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"<g id=\"edge20\" class=\"edge\">\n",
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"<title>7->6</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M678.79,-235.41C663.39,-234.86 640.18,-233.97 620,-233 616.53,-232.83 612.88,-232.64 609.29,-232.44\"/>\n",
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"</g>\n",
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"<!-- 7->7 -->\n",
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"<g id=\"edge21\" class=\"edge\">\n",
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"<title>7->7</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M687.43,-251.54C684.73,-261.91 687.92,-272 697,-272 703.95,-272 707.45,-266.08 707.5,-258.66\"/>\n",
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"</g>\n",
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"<!-- 1->4 -->\n",
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"<g id=\"edge5\" class=\"edge\">\n",
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"<title>1->4</title>\n",
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"</g>\n",
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"<!-- 2->4 -->\n",
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"<g id=\"edge8\" class=\"edge\">\n",
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"<title>2->4</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M171.13,-224.14C176.26,-237.91 185.64,-256.33 201,-265 290.95,-315.78 421.39,-269.3 472.9,-247.19\"/>\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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"</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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"</g>\n",
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"<!-- 5 -->\n",
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"<g id=\"node8\" class=\"node\">\n",
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"<title>5</title>\n",
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"</g>\n",
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"<!-- 2->5 -->\n",
|
|
"<g id=\"edge9\" class=\"edge\">\n",
|
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"<title>2->5</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M182.87,-204.5C202.53,-202.19 235.81,-200.17 263,-208 269.12,-209.76 275.23,-212.81 280.69,-216.13\"/>\n",
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"</g>\n",
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"<!-- 5->4 -->\n",
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"<g id=\"edge15\" class=\"edge\">\n",
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"<title>5->4</title>\n",
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|
"<path fill=\"none\" stroke=\"black\" d=\"M319.58,-231.53C353.83,-232.6 430.98,-235 470.56,-236.24\"/>\n",
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"</g>\n",
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"<!-- 5->1 -->\n",
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"<g id=\"edge13\" class=\"edge\">\n",
|
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"<title>5->1</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M316.77,-221.44C323.63,-217.05 332.07,-211.96 340,-208 357.28,-199.37 377.68,-191.44 392.99,-185.9\"/>\n",
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"<text text-anchor=\"start\" x=\"340\" y=\"-211.8\" font-family=\"Lato\" font-size=\"14.00\">!a & !b</text>\n",
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|
"</g>\n",
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|
"<!-- 5->2 -->\n",
|
|
"<g id=\"edge14\" class=\"edge\">\n",
|
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"<title>5->2</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M283.3,-231.41C263.22,-231.48 229.18,-230.33 201,-223 196.59,-221.85 192.04,-220.18 187.74,-218.34\"/>\n",
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"</g>\n",
|
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"<!-- 3->3 -->\n",
|
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"<g id=\"edge10\" class=\"edge\">\n",
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"<title>3->3</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M155.77,-49.54C153.17,-59.91 156.25,-70 165,-70 171.7,-70 175.08,-64.08 175.12,-56.66\"/>\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.jupyter.SVG object>"
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]
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},
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"execution_count": 22,
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"metadata": {},
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"output_type": "execute_result"
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}
|
|
],
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|
"source": [
|
|
"aut = spot.translate('(b W Xa) & GF(c <-> Xb) | a', 'generic', 'det')\n",
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"spot.highlight_languages(aut)\n",
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"aut.show('.bas')"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.5"
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}
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},
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"nbformat_minor": 2
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