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introduce stutter_invariant_letters()

Browse source 
* spot/twaalgos/stutter.cc,
spot/twaalgos/stutter.hh (stutter_invariant_letters)
(stutter_invariant_states): Get rid of the broken local variant.
* tests/python/stutter-inv.ipynb, NEWS: Document.
* python/spot/impl.i: Bind vector<bdd>.
This commit is contained in:
Alexandre Duret-Lutz 2017-11-03 17:01:05 +01:00
parent f84ca9995c
commit 4711dcd74f
5 changed files with 254 additions and 480 deletions
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602
tests/python/stutter-inv.ipynb
View file

@ -354,7 +354,7 @@
"</svg>\n"
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@ -411,7 +411,7 @@
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"outputs": [],
"prompt_number": 25
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@ -432,7 +432,7 @@
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@ -1066,7 +1066,7 @@
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@ -1271,17 +1271,17 @@
"source": [
"### Third example\n",
"\n",
"These procedures work regardless of the acceptance condition. Here is an example with state-based co-B\u00fcchi acceptance.\n",
"These procedures work regardless of the acceptance condition. Here is an example with co-B\u00fcchi acceptance.\n",
"\n",
"In this case we do not even have a formula to pass as second argument, so the check will perform a costly complementation by determinization."
"In this case we do not even have a formula to pass as second argument, so the check will perform a complementation by determinization."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"aut = spot.automaton('genaut --ks-nca=2 |')\n",
"spot.highlight_stutter_invariant_states(aut, None, 5, True)\n",
"aut = spot.automaton('randaut --seed=30 -Q4 -A\"Fin(0)\" a |')\n",
"spot.highlight_stutter_invariant_states(aut, None, 5)\n",
"display(aut)"
],
"language": "python",
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"## Global vs Local stuttering (experimental)\n",
"## Sutter-invariance at the letter level\n",
"\n",
"Do not build anything on top of what follows, as it is likely to be removed."
"Instead of marking each state as stuttering or not, we can list the letters that we can stutter in each state.\n",
"More precisely, a state $q$ is _stutter-invariant for letter $a$_ if the membership to $L(q)$ of any word starting with $a$ is preserved by the operations that duplicate letters or remove duplicates. \n",
"\n",
"$(\\ell_0\\ldots\\ell_{i-1}\\ell_i\\ell_{i+1}\\ldots\\in L(q) \\land \\ell_0=a) \\iff (\\ell_0\\ldots\\ell_{i-1}\\ell_i\\ell_i\\ell_{i+1}\\ldots\\in L(q)\\land \\ell_0=a)$\n",
"\n",
"Under this definition, we can also say that $q$ is _stutter-invariant_ iff it is _stutter-invariant for any letter_.\n",
"\n",
"For instance consider the following automaton, for which all words that start with $b$ are stutter invariant.\n",
"The initial state may not be declared as stutter-invariant because of words that start with $\\lnot b$."
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"The above result uses a natural definition of \"stutter-invariant state\": a state is stutter-invariant if the language accepted from this state is.\n",
"The `stutter_invariant_letters()` functions returns a vector of BDDs indexed by state numbers. The BDD at index $q$ specifies all letters $\\ell$ for which state $q$ would be stuttering. Note that if $q$ is stutter-invariant or reachable from a stutter-invariant state, the associated BDD will be `bddtrue` (printed as `1` below).\n",
"\n",
"We can also have a \"local\" variant of the stutter invariance check that considers the state as stutter invariant if you can stutter on (or remove duplicates of) the first letter read from that state, but not necessary do the same operations on a different letter that follows. \n",
"In other words, state $q$ is a local stutter-invariant state iff $\\ell_1\\ell_2\\ldots \\in L(q) \\iff \\ell_1\\ell_1\\ell_2\\ldots \\in L(q)$.\n",
"\n",
"Just pass `True` as the last optional parameter, as below."
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"text": [
"<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f1c8045a690> >"
"sil_vec[0] = 1\n",
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{
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"source": [
"Note that an SCC can contain a mix of locally stutter-invariant and local stutter-sensitive states. Here is the deterministic version of the above automaton for example."
]
},
{
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"input": [
"aut = spot.translate(h, 'deterministic')\n",
"spot.highlight_stutter_invariant_states(aut, h, 5, True)\n",
"display(aut.show('.abs'))"
],
"language": "python",
"metadata": {},
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