{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This example is the left part of Fig.2 in our ATVA'16 paper titled [\"*Spot 2.0 — a framework for LTL and ω-automata manipulation*\"](https://www.lrde.epita.fr/~adl/dl/adl/duret.16.atva2.pdf), slightly updated to the current version of Spot."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import spot\n",
"spot.setup(show_default='.b')"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\mathsf{G} \\mathsf{F} a \\leftrightarrow \\mathsf{G} \\mathsf{F} b$"
],
"text/plain": [
"spot.formula(\"GFa <-> GFb\")"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f = spot.formula('GFa <-> GFb'); f"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n",
"\n",
"\n"
],
"text/html": [
"\n",
"\n",
"\n",
"\n",
"\n"
],
"text/plain": [
" *' at 0x7f30b04c1d40> >"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f.translate()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"def implies(f, g):\n",
" f = spot.formula(f)\n",
" g = spot.formula.Not(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)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"equiv('a U (b U a)', 'b U a')"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"False"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"equiv('!(a U b)', '!a U !b')"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.12.4"
}
},
"nbformat": 4,
"nbformat_minor": 4
}