611 lines
30 KiB
Text
611 lines
30 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()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Let's build a small automaton to use as example."
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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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{
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"data": {
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"<text text-anchor=\"start\" x=\"324.5\" y=\"-5.8\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
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"<title>2->2</title>\n",
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"<!-- 5->4 -->\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_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f14f57d93c0> >"
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]
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},
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"execution_count": 2,
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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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"aut = spot.translate('!a & G(Fa <-> XXb)'); aut"
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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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"Build an accepting 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": 3,
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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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" 0\n",
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" | !a\n",
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" 1\n",
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" | !a\n",
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"Cycle:\n",
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" 2\n",
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" | a & b\t{0}\n",
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" 3\n",
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" | !a & b\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 = aut.accepting_run()\n",
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"print(run)"
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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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"Accessing the contents of the run can be done via the `prefix` and `cycle` lists."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"!a\n",
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"{0}\n"
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]
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}
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],
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"source": [
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"print(spot.bdd_format_formula(aut.get_dict(), run.prefix[0].label))\n",
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"print(run.cycle[0].acc)"
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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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"To convert the run into a word, using `spot.twa_word()`. Note that our runs are labeled by Boolean formulas that are not necessarily a conjunction of all involved litterals. The word is just the projection of the run on its labels."
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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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"name": "stdout",
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"output_type": "stream",
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"text": [
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"!a; !a; cycle{a & b; !a & b}\n"
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]
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},
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{
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"data": {
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"text/latex": [
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"$\\lnot a; \\lnot a; \\mathsf{cycle}\\{a \\land b; \\lnot a \\land b\\}$"
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],
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"text/plain": [
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"<spot.twa_word; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_word > *' at 0x7f14f57d9ed0> >"
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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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"word = spot.twa_word(run)\n",
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"print(word) # print as a string\n",
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"word # LaTeX-style representation in notebooks"
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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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"A word can be represented as a collection of signals (one for each atomic proposition). The cycle part is shown twice."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"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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"<line x1=\"100\" y1=\"0\" x2=\"100\" y2=\"100\"\n",
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" stroke=\"white\" stroke-width=\"4\"/>\n",
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" stroke=\"white\" stroke-width=\"4\"/>\n",
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"<line x1=\"0\" y1=\"0\" x2=\"300\" y2=\"0\" stroke=\"white\" stroke-width=\"4\"/><text x=\"3\" y=\"30\" text-anchor=\"start\" font-size=\"20\">a</text><line x1=\"50\" y1=\"0\" x2=\"50\" y2=\"50\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"0\" y1=\"45\" x2=\"50\" y2=\"45\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"100\" y1=\"0\" x2=\"100\" y2=\"50\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"50\" y1=\"45\" x2=\"100\" y2=\"45\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"150\" y1=\"0\" x2=\"150\" y2=\"50\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"100\" y1=\"5\" x2=\"100\" y2=\"45\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"100\" y1=\"5\" x2=\"150\" y2=\"5\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"200\" y1=\"0\" x2=\"200\" y2=\"50\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"150\" y1=\"5\" x2=\"150\" y2=\"45\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"150\" y1=\"45\" x2=\"200\" y2=\"45\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"250\" y1=\"0\" x2=\"250\" y2=\"50\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"200\" y1=\"5\" x2=\"200\" y2=\"45\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"200\" y1=\"5\" x2=\"250\" y2=\"5\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"300\" y1=\"0\" x2=\"300\" y2=\"50\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"250\" y1=\"5\" x2=\"250\" y2=\"45\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"250\" y1=\"45\" x2=\"300\" y2=\"45\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"0\" y1=\"50\" x2=\"300\" y2=\"50\" stroke=\"white\" stroke-width=\"4\"/><text x=\"3\" y=\"80\" text-anchor=\"start\" font-size=\"20\">b</text><line x1=\"50\" y1=\"50\" x2=\"50\" y2=\"100\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"100\" y1=\"50\" x2=\"100\" y2=\"100\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"150\" y1=\"50\" x2=\"150\" y2=\"100\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"100\" y1=\"55\" x2=\"150\" y2=\"55\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"200\" y1=\"50\" x2=\"200\" y2=\"100\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"150\" y1=\"55\" x2=\"200\" y2=\"55\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"250\" y1=\"50\" x2=\"250\" y2=\"100\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"200\" y1=\"55\" x2=\"250\" y2=\"55\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"300\" y1=\"50\" x2=\"300\" y2=\"100\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"250\" y1=\"55\" x2=\"300\" y2=\"55\" stroke=\"#ff0000\" stroke-width=\"2\"/><text x=\"0\" y=\"110\" text-anchor=\"start\" font-size=\"10\">prefix</text><text x=\"100\" y=\"110\" text-anchor=\"start\" font-size=\"10\">cycle</text>\n",
|
|
"<text x=\"200\" y=\"110\" text-anchor=\"start\" font-size=\"10\">cycle</text></svg>"
|
|
],
|
|
"text/plain": [
|
|
"<spot.jupyter.SVG object>"
|
|
]
|
|
},
|
|
"execution_count": 6,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"word.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Accessing the different formulas (stored as BDDs) can be done again via the `prefix` and `cycle` lists."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 7,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"!a\n",
|
|
"!a\n",
|
|
"a & b\n",
|
|
"!a & b\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"print(spot.bdd_format_formula(aut.get_dict(), word.prefix[0]))\n",
|
|
"print(spot.bdd_format_formula(aut.get_dict(), word.prefix[1]))\n",
|
|
"print(spot.bdd_format_formula(aut.get_dict(), word.cycle[0]))\n",
|
|
"print(spot.bdd_format_formula(aut.get_dict(), word.cycle[1]))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Calling `simplify()` will produce a shorter word that is compatible with the original word. For instance, in the above word the second `a` is compatible with `!a & b`, so the prefix can be shortened by rotating the cycle."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 8,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"!a; cycle{!a & b; a & b}\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"word.simplify()\n",
|
|
"print(word)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Such a simplified word can be created directly from the automaton:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 9,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/latex": [
|
|
"$\\lnot a; \\mathsf{cycle}\\{\\lnot a \\land b; a \\land b\\}$"
|
|
],
|
|
"text/plain": [
|
|
"<spot.twa_word; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_word > *' at 0x7f14f57d9660> >"
|
|
]
|
|
},
|
|
"execution_count": 9,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"aut.accepting_word()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Words can be created using the `parse_word` function:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 10,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"a; b; cycle{a & b}\n",
|
|
"cycle{(a & bb) | (aaa & bac) | (bac & bbb)}\n",
|
|
"a; b; b; qiwuei; \"a;b&c;a\"; cycle{a}\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"print(spot.parse_word('a; b; cycle{a&b}'))\n",
|
|
"print(spot.parse_word('cycle{a&bb|bac&(aaa|bbb)}'))\n",
|
|
"print(spot.parse_word('a; b;b; qiwuei;\"a;b&c;a\" ;cycle{a}'))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 11,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/latex": [
|
|
"$a; a \\land b; \\mathsf{cycle}\\{\\lnot a \\land \\lnot b; \\lnot a \\land b\\}$"
|
|
],
|
|
"text/plain": [
|
|
"<spot.twa_word; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_word > *' at 0x7f14f5799ea0> >"
|
|
]
|
|
},
|
|
"execution_count": 11,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"# make sure that we can parse a word back after it has been printed\n",
|
|
"w = spot.parse_word(str(spot.parse_word('a;b&a;cycle{!a&!b;!a&b}'))); w"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 12,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/svg+xml": [
|
|
"\n",
|
|
"<svg height=\"112\" width=\"300\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n",
|
|
"<rect x=\"0\" y=\"0\" width=\"300\" height=\"100\" fill=\"#f4f4f4\"/>\n",
|
|
"<line x1=\"100\" y1=\"0\" x2=\"100\" y2=\"100\"\n",
|
|
" stroke=\"white\" stroke-width=\"4\"/>\n",
|
|
"<line x1=\"200\" y1=\"0\" x2=\"200\" y2=\"100\"\n",
|
|
" stroke=\"white\" stroke-width=\"4\"/>\n",
|
|
"<line x1=\"0\" y1=\"0\" x2=\"300\" y2=\"0\" stroke=\"white\" stroke-width=\"4\"/><text x=\"3\" y=\"30\" text-anchor=\"start\" font-size=\"20\">a</text><line x1=\"50\" y1=\"0\" x2=\"50\" y2=\"50\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"0\" y1=\"5\" x2=\"50\" y2=\"5\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"100\" y1=\"0\" x2=\"100\" y2=\"50\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"50\" y1=\"5\" x2=\"100\" y2=\"5\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"150\" y1=\"0\" x2=\"150\" y2=\"50\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"100\" y1=\"5\" x2=\"100\" y2=\"45\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"100\" y1=\"45\" x2=\"150\" y2=\"45\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"200\" y1=\"0\" x2=\"200\" y2=\"50\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"150\" y1=\"45\" x2=\"200\" y2=\"45\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"250\" y1=\"0\" x2=\"250\" y2=\"50\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"200\" y1=\"45\" x2=\"250\" y2=\"45\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"300\" y1=\"0\" x2=\"300\" y2=\"50\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"250\" y1=\"45\" x2=\"300\" y2=\"45\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"0\" y1=\"50\" x2=\"300\" y2=\"50\" stroke=\"white\" stroke-width=\"4\"/><text x=\"3\" y=\"80\" text-anchor=\"start\" font-size=\"20\">b</text><line x1=\"50\" y1=\"50\" x2=\"50\" y2=\"100\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"100\" y1=\"50\" x2=\"100\" y2=\"100\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"50\" y1=\"55\" x2=\"100\" y2=\"55\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"150\" y1=\"50\" x2=\"150\" y2=\"100\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"100\" y1=\"55\" x2=\"100\" y2=\"95\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"100\" y1=\"95\" x2=\"150\" y2=\"95\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"200\" y1=\"50\" x2=\"200\" y2=\"100\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"150\" y1=\"55\" x2=\"150\" y2=\"95\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"150\" y1=\"55\" x2=\"200\" y2=\"55\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"250\" y1=\"50\" x2=\"250\" y2=\"100\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"200\" y1=\"55\" x2=\"200\" y2=\"95\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"200\" y1=\"95\" x2=\"250\" y2=\"95\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"300\" y1=\"50\" x2=\"300\" y2=\"100\" stroke=\"white\" stroke-width=\"1\"/><line x1=\"250\" y1=\"55\" x2=\"250\" y2=\"95\" stroke=\"#ff0000\" stroke-width=\"2\"/><line x1=\"250\" y1=\"55\" x2=\"300\" y2=\"55\" stroke=\"#ff0000\" stroke-width=\"2\"/><text x=\"0\" y=\"110\" text-anchor=\"start\" font-size=\"10\">prefix</text><text x=\"100\" y=\"110\" text-anchor=\"start\" font-size=\"10\">cycle</text>\n",
|
|
"<text x=\"200\" y=\"110\" text-anchor=\"start\" font-size=\"10\">cycle</text></svg>"
|
|
],
|
|
"text/plain": [
|
|
"<spot.jupyter.SVG object>"
|
|
]
|
|
},
|
|
"execution_count": 12,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"w.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Words can be easily converted to automata"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 13,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/svg+xml": [
|
|
"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
|
|
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
|
|
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
|
|
"<!-- Generated by graphviz version 2.43.0 (0)\n",
|
|
" -->\n",
|
|
"<!-- Pages: 1 -->\n",
|
|
"<svg width=\"377pt\" height=\"86pt\"\n",
|
|
" viewBox=\"0.00 0.00 377.00 86.28\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
|
|
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1.0 1.0) rotate(0) translate(4 82.28)\">\n",
|
|
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-82.28 373,-82.28 373,4 -4,4\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"181.5\" y=\"-63.08\" font-family=\"Lato\" font-size=\"14.00\">t</text>\n",
|
|
"<text text-anchor=\"start\" x=\"173.5\" y=\"-48.08\" font-family=\"Lato\" font-size=\"14.00\">[all]</text>\n",
|
|
"<!-- I -->\n",
|
|
"<!-- 0 -->\n",
|
|
"<g id=\"node2\" class=\"node\">\n",
|
|
"<title>0</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"56\" cy=\"-22.28\" rx=\"18\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"56\" y=\"-18.58\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
|
|
"</g>\n",
|
|
"<!-- I->0 -->\n",
|
|
"<g id=\"edge1\" class=\"edge\">\n",
|
|
"<title>I->0</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M1.15,-22.28C2.79,-22.28 17.15,-22.28 30.63,-22.28\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"37.94,-22.28 30.94,-25.43 34.44,-22.28 30.94,-22.28 30.94,-22.28 30.94,-22.28 34.44,-22.28 30.94,-19.13 37.94,-22.28 37.94,-22.28\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 1 -->\n",
|
|
"<g id=\"node3\" class=\"node\">\n",
|
|
"<title>1</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"135\" cy=\"-22.28\" rx=\"18\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"135\" y=\"-18.58\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
|
|
"</g>\n",
|
|
"<!-- 0->1 -->\n",
|
|
"<g id=\"edge2\" class=\"edge\">\n",
|
|
"<title>0->1</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M74.09,-22.28C84.56,-22.28 98.12,-22.28 109.69,-22.28\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"116.96,-22.28 109.96,-25.43 113.46,-22.28 109.96,-22.28 109.96,-22.28 109.96,-22.28 113.46,-22.28 109.96,-19.13 116.96,-22.28 116.96,-22.28\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"92\" y=\"-26.08\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2 -->\n",
|
|
"<g id=\"node4\" class=\"node\">\n",
|
|
"<title>2</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"239\" cy=\"-22.28\" rx=\"18\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"239\" y=\"-18.58\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1->2 -->\n",
|
|
"<g id=\"edge3\" class=\"edge\">\n",
|
|
"<title>1->2</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M153.3,-22.28C169.96,-22.28 195.3,-22.28 213.93,-22.28\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"220.95,-22.28 213.95,-25.43 217.45,-22.28 213.95,-22.28 213.95,-22.28 213.95,-22.28 217.45,-22.28 213.95,-19.13 220.95,-22.28 220.95,-22.28\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"171\" y=\"-26.08\" font-family=\"Lato\" font-size=\"14.00\">a & b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3 -->\n",
|
|
"<g id=\"node5\" class=\"node\">\n",
|
|
"<title>3</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"351\" cy=\"-22.28\" rx=\"18\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"351\" y=\"-18.58\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2->3 -->\n",
|
|
"<g id=\"edge4\" class=\"edge\">\n",
|
|
"<title>2->3</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M257.19,-22.28C275.59,-22.28 304.95,-22.28 325.71,-22.28\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"332.93,-22.28 325.93,-25.43 329.43,-22.28 325.93,-22.28 325.93,-22.28 325.93,-22.28 329.43,-22.28 325.93,-19.13 332.93,-22.28 332.93,-22.28\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"275\" y=\"-26.08\" font-family=\"Lato\" font-size=\"14.00\">!a & !b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->2 -->\n",
|
|
"<g id=\"edge5\" class=\"edge\">\n",
|
|
"<title>3->2</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M335.69,-12.42C329.6,-8.79 322.24,-5.12 315,-3.28 297.77,1.09 292.23,1.09 275,-3.28 270.14,-4.52 265.22,-6.58 260.67,-8.9\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"254.31,-12.42 258.91,-6.27 257.37,-10.72 260.44,-9.03 260.44,-9.03 260.44,-9.03 257.37,-10.72 261.96,-11.78 254.31,-12.42 254.31,-12.42\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"277\" y=\"-7.08\" font-family=\"Lato\" font-size=\"14.00\">!a & b</text>\n",
|
|
"</g>\n",
|
|
"</g>\n",
|
|
"</svg>\n"
|
|
],
|
|
"text/plain": [
|
|
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f14f5799ed0> >"
|
|
]
|
|
},
|
|
"execution_count": 13,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"w.as_automaton()"
|
|
]
|
|
}
|
|
],
|
|
"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",
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|
"pygments_lexer": "ipython3",
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|
"version": "3.9.2"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|