60f046a574
Several people have asked for a way to check whether a word is accepted by an automaton, including at least Jonah Romero and Scott Buckley. So it's time we have it. * spot/twa/twa.hh, spot/twa/twa.cc, spot/twaalgos/word.hh (intersects): Add the new variant. * spot/twa/fwd.hh: Forward declare twa_word, so that we can use it in twa.hh. * spot/twaalgos/forq_contains.cc: Use the new intersection check. * tests/python/word.ipynb, NEWS: Mention it. * THANKS: Add Scott Buckley.
864 lines
46 KiB
Text
864 lines
46 KiB
Text
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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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"Let's build a small automaton to use as example."
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"<path fill=\"none\" stroke=\"black\" d=\"M152.24,-35.67C167.12,-22.05 193.67,-2 221,-2 221,-2 221,-2 439,-2 467.47,-2 499.76,-7.71 521.14,-12.31\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"528.23,-13.88 520.71,-15.44 524.81,-13.12 521.39,-12.37 521.39,-12.37 521.39,-12.37 524.81,-13.12 522.07,-9.29 528.23,-13.88 528.23,-13.88\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"324.5\" y=\"-5.8\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2->2 -->\n",
|
|
"<g id=\"edge6\" class=\"edge\">\n",
|
|
"<title>2->2</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M214.97,-115.66C213.41,-125.62 215.75,-135 222,-135 226.69,-135 229.18,-129.73 229.47,-122.89\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"229.03,-115.66 232.6,-122.46 229.24,-119.16 229.46,-122.65 229.46,-122.65 229.46,-122.65 229.24,-119.16 226.31,-122.84 229.03,-115.66 229.03,-115.66\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"204\" y=\"-138.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2->3 -->\n",
|
|
"<g id=\"edge7\" class=\"edge\">\n",
|
|
"<title>2->3</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M239.98,-101.62C254.76,-103.19 276.51,-103.75 294,-97 300.58,-94.46 306.78,-90.11 312.08,-85.51\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"317.45,-80.48 314.49,-87.56 314.89,-82.87 312.34,-85.26 312.34,-85.26 312.34,-85.26 314.89,-82.87 310.18,-82.96 317.45,-80.48 317.45,-80.48\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"260\" y=\"-120.8\" font-family=\"Lato\" font-size=\"14.00\">a & b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"268\" y=\"-105.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->2 -->\n",
|
|
"<g id=\"edge8\" class=\"edge\">\n",
|
|
"<title>3->2</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M311.9,-67.8C297.23,-68.92 275.71,-71.59 258,-78 252.96,-79.82 247.84,-82.4 243.14,-85.13\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"237.01,-88.89 241.33,-82.54 240,-87.06 242.98,-85.23 242.98,-85.23 242.98,-85.23 240,-87.06 244.63,-87.91 237.01,-88.89 237.01,-88.89\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"258\" y=\"-81.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->3 -->\n",
|
|
"<g id=\"edge9\" class=\"edge\">\n",
|
|
"<title>3->3</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M320.77,-82.54C318.17,-92.91 321.25,-103 330,-103 336.7,-103 340.08,-97.08 340.12,-89.66\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"339.23,-82.54 343.23,-89.1 339.67,-86.01 340.1,-89.49 340.1,-89.49 340.1,-89.49 339.67,-86.01 336.98,-89.88 339.23,-82.54 339.23,-82.54\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"314\" y=\"-121.8\" font-family=\"Lato\" font-size=\"14.00\">a & b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"322\" y=\"-106.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5 -->\n",
|
|
"<g id=\"node7\" class=\"node\">\n",
|
|
"<title>5</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"438\" cy=\"-57\" rx=\"18\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"438\" y=\"-53.3\" font-family=\"Lato\" font-size=\"14.00\">5</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->5 -->\n",
|
|
"<g id=\"edge10\" class=\"edge\">\n",
|
|
"<title>3->5</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M348.03,-65.39C365.57,-63.74 393.06,-61.15 412.84,-59.28\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"420.01,-58.6 413.34,-62.4 416.53,-58.93 413.04,-59.26 413.04,-59.26 413.04,-59.26 416.53,-58.93 412.75,-56.12 420.01,-58.6 420.01,-58.6\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"366\" y=\"-66.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4->4 -->\n",
|
|
"<g id=\"edge11\" class=\"edge\">\n",
|
|
"<title>4->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M536.77,-33.54C534.17,-43.91 537.25,-54 546,-54 552.7,-54 556.08,-48.08 556.12,-40.66\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"555.23,-33.54 559.23,-40.1 555.67,-37.01 556.1,-40.49 556.1,-40.49 556.1,-40.49 555.67,-37.01 552.98,-40.88 555.23,-33.54 555.23,-33.54\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"526\" y=\"-72.8\" font-family=\"Lato\" font-size=\"14.00\">!a & !b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"538\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->4 -->\n",
|
|
"<g id=\"edge12\" class=\"edge\">\n",
|
|
"<title>5->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M455.1,-51.08C472.92,-44.52 501.79,-33.9 522,-26.46\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"528.75,-23.98 523.27,-29.35 525.46,-25.19 522.18,-26.4 522.18,-26.4 522.18,-26.4 525.46,-25.19 521.09,-23.44 528.75,-23.98 528.75,-23.98\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"474\" y=\"-46.8\" 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 0x7f1f80568c60> >"
|
|
]
|
|
},
|
|
"execution_count": 2,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"aut = spot.translate('!a & G(Fa <-> XXb)'); aut"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Build an accepting run:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 3,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Prefix:\n",
|
|
" 0\n",
|
|
" | !a\n",
|
|
" 1\n",
|
|
" | !a\n",
|
|
"Cycle:\n",
|
|
" 2\n",
|
|
" | a & b\t{0}\n",
|
|
" 3\n",
|
|
" | !a & b\n",
|
|
"\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"run = aut.accepting_run()\n",
|
|
"print(run)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Accessing the contents of the run can be done via the `prefix` and `cycle` lists."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 4,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"!a\n",
|
|
"{0}\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"print(spot.bdd_format_formula(aut.get_dict(), run.prefix[0].label))\n",
|
|
"print(run.cycle[0].acc)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"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 literals. The word is just the projection of the run on its labels."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 5,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"!a; !a; cycle{a & b; !a & b}\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"text/latex": [
|
|
"$\\lnot a; \\lnot a; \\mathsf{cycle}\\{a \\land b; \\lnot a \\land b\\}$"
|
|
],
|
|
"text/plain": [
|
|
"<spot.twa_word; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_word > *' at 0x7f1f805686f0> >"
|
|
]
|
|
},
|
|
"execution_count": 5,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"word = spot.twa_word(run)\n",
|
|
"print(word) # print as a string\n",
|
|
"word # LaTeX-style representation in notebooks"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"A word can be represented as a collection of signals (one for each atomic proposition). The cycle part is shown twice."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 6,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/html": [
|
|
"\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=\"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 0x7f1f8060d770> >"
|
|
]
|
|
},
|
|
"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 0x7f1f8060df80> >"
|
|
]
|
|
},
|
|
"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": {
|
|
"text/html": [
|
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"Words can be easily converted to automata"
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"source": [
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"w.as_automaton()"
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]
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},
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"metadata": {},
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"source": [
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"To check if a word is accepted by an automaton, you can use `intersects`. The name `intersects` actually makes more sense than `accepts` or `accepted`, because a word actually describes a set of words because of the don't care atomic propositions."
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]
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},
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"False\n",
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"False\n",
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"True\n",
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"True\n"
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]
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}
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],
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"source": [
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"print(w.intersects(aut))\n",
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"print(aut.intersects(w))\n",
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"print(word.intersects(aut))\n",
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"print(aut.intersects(word))"
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]
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},
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