60296317c7
* NEWS: Mention the change. * python/spot/__init__.py: Add _repr_latex_ for twa_word, and remove __repr__ and __str__ for atomic_prop_set. * python/spot/impl.i: Implement __repr__ and __str__ for atomic_prop_set. Fix __repr__ for trival, acc_code, acc_cond, mark_t. Remove __repr__ for twa_run and twa_word. * tests/python/acc_cond.ipynb, tests/python/accparse.ipynb, tests/python/atva16-fig2a.ipynb, tests/python/automata.ipynb, tests/python/bdditer.py, tests/python/contains.ipynb, tests/python/gen.ipynb, tests/python/highlighting.ipynb, tests/python/ltlsimple.py, tests/python/ltsmin-dve.ipynb, tests/python/product.ipynb, tests/python/relabel.py, tests/python/satmin.ipynb tests/python/stutter-inv.ipynb, tests/python/word.ipynb: Adjust test cases. * tests/python/formulas.ipynb: Add test for atomic_prop_set.
513 lines
16 KiB
Text
513 lines
16 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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"from spot.jupyter import display_inline\n",
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"spot.setup(show_default='.a')"
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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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"# Containement checks\n",
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"\n",
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"The `spot.contains()` function checks whether the language of its right argument is included in the language of its left argument. The arguments may mix automata and formulas; the latter can be given as strings."
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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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"source": [
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"f = spot.formula('GFa'); aut_f = f.translate()\n",
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"g = spot.formula('FGa'); aut_g = g.translate()"
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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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"data": {
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"text/plain": [
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"(True, False)"
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]
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},
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"execution_count": 3,
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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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"spot.contains(f, g), spot.contains(g, f)"
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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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"data": {
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"text/plain": [
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"(True, False)"
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]
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},
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"execution_count": 4,
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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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"spot.contains(aut_f, aut_g), spot.contains(aut_g, aut_f)"
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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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"data": {
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"text/plain": [
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"(True, False)"
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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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"spot.contains(aut_f, g), spot.contains(aut_g, f)"
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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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"text/plain": [
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"(True, False)"
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]
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},
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"execution_count": 6,
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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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"spot.contains(f, aut_g), spot.contains(g, aut_f)"
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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": 7,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(True, False)"
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]
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},
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"execution_count": 7,
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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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"spot.contains(\"GFa\", aut_g), spot.contains(\"FGa\", aut_f)"
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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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"Those functions are also usable as methods:"
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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": 8,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(True, False)"
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]
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},
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"execution_count": 8,
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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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"f.contains(aut_g), g.contains(aut_f)"
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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": 9,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(True, False)"
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]
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},
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"execution_count": 9,
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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_f.contains(\"FGa\"), aut_g.contains(\"GFa\")"
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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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"# Equivalence checks\n",
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"\n",
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"The `spot.are_equivalent()` tests the equivalence of the languages of its two arguments. Note that the corresponding method is called `equivalent_to()`."
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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": 10,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(False, False)"
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]
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},
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"execution_count": 10,
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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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"spot.are_equivalent(f, g), spot.are_equivalent(aut_f, aut_g)"
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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": 11,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(False, False)"
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]
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},
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"execution_count": 11,
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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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"f.equivalent_to(aut_g), aut_f.equivalent_to(g)"
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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": 12,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"True"
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]
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},
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"execution_count": 12,
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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_f.equivalent_to('XXXGFa')"
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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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"# Containement checks between formulas with cache\n",
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"\n",
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"In the case of containement checks between formulas, `language_containement_checker` instances provide similar services, but they cache automata representing the formulas checked. This should be prefered when performing several containement checks using the same formulas."
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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": 13,
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"metadata": {},
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"outputs": [],
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"source": [
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"lcc = spot.language_containment_checker()"
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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": 14,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(True, False)"
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]
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},
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"execution_count": 14,
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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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"lcc.contains(f, g), lcc.contains(g, f)"
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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": 15,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"False"
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]
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},
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"execution_count": 15,
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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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"lcc.are_equivalent(f, g)"
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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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"# Help for distinguishing languages\n",
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"\n",
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"Assume you have computed two automata, that `are_equivalent(a1, a2)` returns `False`, and you want to know why. (This often occur when debugging some algorithm that produce an automaton that is not equivalent to which it should.) The automaton class has a method called `a1.exclusive_run(a2)` that can help with this task: it returns a run that recognizes a word is is accepted by one of the two automata but not by both. The method `a1.exclusive_run(a2)` will return just a word.\n",
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"\n",
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"For instance let's find a word that is exclusive between `aut_f` and `aut_g`. (The adjective *exlusive* is a reference to the *exclusive or* operator: the word belongs to L(aut_f) \"xor\" it belongs to L(aut_g).)"
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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": 16,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\mathsf{cycle}\\{a; \\lnot a\\}$"
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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 0x7faa9424d9c0> >"
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]
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},
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"execution_count": 16,
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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_f.exclusive_word(aut_g)"
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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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"We can even write a small function that highlights one difference between two automata. Note that the `run` returned will belong to either `left` or `right`, so calling the `highlight()` method will colorize one of those two automata."
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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": 17,
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"metadata": {},
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"outputs": [],
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"source": [
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"def show_one_difference(left, right):\n",
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" run = left.exclusive_run(right)\n",
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" if not run:\n",
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" print(\"The two automata are equivalent.\")\n",
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" else:\n",
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" print(\"The following word is only accepted by one automaton:\", spot.make_twa_word(run))\n",
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" run.highlight(5)\n",
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" display_inline(left, right)"
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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": 18,
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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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"The following word is only accepted by one automaton: cycle{!a; a; !a}\n"
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]
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},
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