{
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.3"
},
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This example is the left part of Fig.2 in our ATVA'16 paper titled \"*Spot 2.0 \u2014 a framework for LTL and \u03c9-automata manipulation*\"."
]
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"import spot\n",
"spot.setup(show_default='.abr')"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"f = spot.formula('GFa <-> GFb'); f"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$\\mathsf{G} \\mathsf{F} a \\leftrightarrow \\mathsf{G} \\mathsf{F} b$"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 2,
"text": [
"GFa <-> GFb"
]
}
],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"f.translate()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 3,
"svg": [
"\n",
"\n",
"\n",
"\n",
"\n"
],
"text": [
" *' at 0x7f79506d2900> >"
]
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"def implies(f, g):\n",
" f = spot.formula(f)\n",
" g = spot.formula_Not(spot.formula(g))\n",
" return spot.product(f.translate(), g.translate()).is_empty()\n",
"def equiv(f, g):\n",
" return implies(f, g) and implies(g, f)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"equiv('a U (b U a)', 'b U a')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 5,
"text": [
"True"
]
}
],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"equiv('!(a U b)', '!a U !b')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 6,
"text": [
"False"
]
}
],
"prompt_number": 6
}
],
"metadata": {}
}
]
}