{
"metadata": {
"name": "",
"signature": "sha256:e975b9a64657f38248c434a89f29b28f0bf90f9c40b7e8afdd7459734cbdcd38"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"import spot\n",
"spot.setup()"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's build a small automaton to use as example."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"aut = spot.translate('G(Fa <-> Xb)'); aut"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 2,
"svg": [
"\n",
"\n",
"\n",
"\n",
"\n"
],
"text": [
" *' at 0x7f4f0c2e0810> >"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The call to `couvreur99()` just instanciate the emptiness check, but does not run the check. Calling `check()` will return `None` if no accepting run was found. Otherwise the presence of the accepting run is established, but an accepting run hasn't necessarily been calculated: calling `accepting_run()` on the result will cause this computation to happen.\n",
"\n",
"\n",
"In the example below, we do not check the result of `check()` because we know that the input formula is satisfiable, so the automaton has an accepting run."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"run = spot.couvreur99(aut).check().accepting_run(); run"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 3,
"text": [
"Prefix:\n",
" 0\n",
" | !a\n",
"Cycle:\n",
" 1\n",
" | a & b\t{0}\n",
" 2\n",
" | !a & b"
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Accessing the contents of the run can be done via the `prefix` and `cycle` lists."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print(spot.bdd_format_formula(aut.get_dict(), run.prefix[0].label))\n",
"print(run.cycle[0].acc)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"!a\n",
"{0}\n"
]
}
],
"prompt_number": 4
},
{
"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 litterals. The word is just the projection of the run on its labels."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"word = spot.twa_word(run); word"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 5,
"text": [
"!a; cycle{a & b; !a & b}"
]
}
],
"prompt_number": 5
},
{
"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",
"collapsed": false,
"input": [
"print(spot.bdd_format_formula(aut.get_dict(), word.prefix[0]))\n",
"print(spot.bdd_format_formula(aut.get_dict(), word.cycle[0]))\n",
"print(spot.bdd_format_formula(aut.get_dict(), word.cycle[1]))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"!a\n",
"a & b\n",
"!a & b\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Calling `simplifify()` will produce a shorter word that is compatible with the original word. For instance in the above word, the initial `!a` is compatible with both `a & b` and `!a & b`. The word obtained by restricting `!a` to `!a & b` is therefore still accepted, but it allows removing the prefix by rotating the cycle:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"word.simplify()\n",
"word"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 7,
"text": [
"cycle{!a & b; a & b}"
]
}
],
"prompt_number": 7
}
],
"metadata": {}
}
]
}