Adding function to test if two büchi automata are isomorphic.
And add the corresponding --isomorphic=FILENAME option to autfilt. * src/tgbaalgos/are_isomorphic.cc, src/tgbaalgos/are_isomorphic.hh: New. * src/tgbaalgos/Makefile.am: Add it. * src/bin/autfilt.cc: Add --isomorphic option. * src/tgbatest/isomorph.test: Test it. * src/tgbatest/Makefile.am: Add it.
This commit is contained in:
Thibaud Michaud
Alexandre Duret-Lutz
parent
61edf7f41d
commit
97fdea9d71
6 changed files with 434 additions and 1 deletions
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@ -28,6 +28,7 @@ AM_CXXFLAGS = $(WARNING_CXXFLAGS)
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tgbaalgosdir = $(pkgincludedir)/tgbaalgos
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tgbaalgos_HEADERS = \
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are_isomorphic.hh \
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bfssteps.hh \
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closure.hh \
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complete.hh \
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@ -80,6 +81,7 @@ tgbaalgos_HEADERS = \
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noinst_LTLIBRARIES = libtgbaalgos.la
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libtgbaalgos_la_SOURCES = \
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are_isomorphic.cc \
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bfssteps.cc \
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closure.cc \
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complete.cc \
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215
src/tgbaalgos/are_isomorphic.cc
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215
src/tgbaalgos/are_isomorphic.cc
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@ -0,0 +1,215 @@
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// -*- coding: utf-8 -*-
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// Copyright (C) 2014 Laboratoire de Recherche et
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// Développement de l'Epita (LRDE).
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// Copyright (C) 2004, 2005 Laboratoire d'Informatique de Paris 6 (LIP6),
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// département Systèmes Répartis Coopératifs (SRC), Université Pierre
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// et Marie Curie.
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//
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// This file is part of Spot, a model checking library.
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//
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// Spot is free software; you can redistribute it and/or modify it
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// under the terms of the GNU General Public License as published by
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// the Free Software Foundation; either version 3 of the License, or
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// (at your option) any later version.
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//
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// Spot is distributed in the hope that it will be useful, but WITHOUT
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// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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// or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
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// License for more details.
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//
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// You should have received a copy of the GNU General Public License
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// along with this program. If not, see <http://www.gnu.org/licenses/>.
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#include "tgba/tgbagraph.hh"
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#include "tgbaalgos/are_isomorphic.hh"
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#include <unordered_map>
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#include <vector>
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#include <algorithm>
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#include "misc/hashfunc.hh"
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namespace
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{
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typedef size_t class_t;
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typedef std::vector<unsigned> states_t;
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typedef std::unordered_map<class_t, states_t> class2states_t;
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typedef std::vector<class_t> state2class_t;
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typedef spot::tgba_digraph::graph_t::trans_storage_t trans_storage_t;
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bool
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trans_lessthan(trans_storage_t ts1, trans_storage_t ts2)
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{
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return
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ts1.src != ts2.src ?
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ts1.src < ts2.src :
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ts1.dst != ts2.dst ?
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ts1.dst < ts2.dst :
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ts1.acc != ts2.acc ?
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ts1.acc < ts2.acc :
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ts1.cond.id() < ts2.cond.id();
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}
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std::function<bool(trans_storage_t ts1, trans_storage_t ts2)>
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trans_lessthan_mapped(const std::vector<unsigned>& mapping)
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{
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return [mapping](trans_storage_t ts1,
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trans_storage_t ts2)
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{
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return
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mapping[ts1.src] != mapping[ts2.src] ?
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mapping[ts1.src] < mapping[ts2.src] :
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mapping[ts1.dst] != mapping[ts2.dst] ?
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mapping[ts1.dst] < mapping[ts2.dst] :
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ts1.acc != ts2.acc ?
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ts1.acc < ts2.acc :
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ts1.cond.id() < ts2.cond.id();
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};
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}
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state2class_t
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map_state_class(const spot::const_tgba_digraph_ptr a)
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{
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state2class_t hashin(a->num_states(), 0);
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state2class_t hashout(a->num_states(), 0);
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state2class_t state2class(a->num_states());
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for (auto& t: a->transitions())
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{
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if (!a->is_dead_transition(t))
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{
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hashout[t.src] ^= spot::wang32_hash(t.cond.id());
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hashout[t.src] ^= spot::wang32_hash(t.acc);
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hashin[t.dst] ^= spot::wang32_hash(t.cond.id());
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hashin[t.dst] ^= spot::wang32_hash(t.acc);
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}
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}
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for (unsigned i = 0; i < a->num_states(); ++i)
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// Rehash the ingoing transitions so that the total hash differs for
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// different (in, out) pairs of ingoing and outgoing transitions, even if
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// the union of in and out is the same.
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state2class[i] = spot::wang32_hash(hashin[i]) ^ hashout[i];
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return state2class;
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}
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class2states_t
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map_class_states(const spot::const_tgba_digraph_ptr a)
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{
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unsigned n = a->num_states();
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std::vector<states_t> res;
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class2states_t class2states;
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auto state2class = map_state_class(a);
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for (unsigned s = 0; s < n; ++s)
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{
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class_t c1 = state2class[s];
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(*(class2states.emplace(c1, std::vector<unsigned>()).first)).second.
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emplace_back(s);
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}
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return class2states;
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}
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bool
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mapping_from_classes(std::vector<unsigned>& mapping,
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class2states_t classes1,
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class2states_t classes2)
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{
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if (classes1.size() != classes2.size())
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return false;
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for (auto& p : classes1)
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{
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if (p.second.size() != classes2[p.first].size())
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return false;
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for (unsigned j = 0; j < p.second.size(); ++j)
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mapping[p.second[j]] = classes2[p.first][j];
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}
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return true;
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}
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bool
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next_class_permutation(class2states_t& classes)
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{
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for (auto& p : classes)
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if (std::next_permutation(p.second.begin(), p.second.end()))
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return true;
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return false;
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}
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bool
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is_isomorphism(const std::vector<unsigned>& mapping,
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const spot::const_tgba_digraph_ptr a1,
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const spot::const_tgba_digraph_ptr a2)
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{
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unsigned n = a1->num_states();
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assert(n == a2->num_states());
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std::vector<trans_storage_t> trans1;
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std::vector<trans_storage_t> trans2;
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for (auto& t: a1->transitions())
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if (!(a1->is_dead_transition(t)))
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trans1.push_back(t);
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for (auto& t: a2->transitions())
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if (!(a2->is_dead_transition(t)))
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trans2.push_back(t);
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// Sort the vectors of transitions so that they can be compared.
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// To use the same metric, the transitions of a1 have to be mapped to
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// a2.
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std::sort(trans1.begin(), trans1.end(), trans_lessthan_mapped(mapping));
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std::sort(trans2.begin(), trans2.end(), trans_lessthan);
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for (unsigned i = 0; i < trans1.size(); ++i)
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{
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auto ts1 = trans1[i];
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auto ts2 = trans2[i];
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if (!(ts2.src == mapping[ts1.src] &&
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ts2.dst == mapping[ts1.dst] &&
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ts1.acc == ts2.acc &&
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ts1.cond.id() == ts2.cond.id()))
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{
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return false;
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}
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}
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return true;
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}
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bool
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are_trivially_different(const spot::const_tgba_digraph_ptr a1,
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const spot::const_tgba_digraph_ptr a2)
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{
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return (a1->num_states() != a2->num_states() ||
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a1->num_transitions() != a2->num_transitions());
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}
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}
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namespace spot
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{
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bool
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are_isomorphic(const const_tgba_digraph_ptr a1,
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const const_tgba_digraph_ptr a2)
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{
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if (are_trivially_different(a1, a2))
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return false;
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unsigned n = a1->num_states();
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assert(n == a2->num_states());
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class2states_t a1_classes = map_class_states(a1);
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class2states_t a2_classes = map_class_states(a2);
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std::vector<unsigned> mapping(n);
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// Get the first possible mapping between a1 and a2, or return false if
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// the number of class or the size of the classes do not match.
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if (!(mapping_from_classes(mapping, a1_classes, a2_classes)))
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return false;
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while (!is_isomorphism(mapping, a1, a2))
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{
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if (!next_class_permutation(a2_classes))
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return false;
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mapping_from_classes(mapping, a1_classes, a2_classes);
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}
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return true;
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}
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}
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41
src/tgbaalgos/are_isomorphic.hh
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41
src/tgbaalgos/are_isomorphic.hh
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@ -0,0 +1,41 @@
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// -*- coding: utf-8 -*-
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// Copyright (C) 2014 Laboratoire de Recherche et
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// Développement de l'Epita (LRDE).
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//
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// This file is part of Spot, a model checking library.
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//
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// Spot is free software; you can redistribute it and/or modify it
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// under the terms of the GNU General Public License as published by
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// the Free Software Foundation; either version 3 of the License, or
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// (at your option) any later version.
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//
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// Spot is distributed in the hope that it will be useful, but WITHOUT
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// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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// or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
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// License for more details.
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//
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// You should have received a copy of the GNU General Public License
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// along with this program. If not, see <http://www.gnu.org/licenses/>.
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#ifndef SPOT_TGBAALGOS_ARE_ISOMORPHIC_HH
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# define SPOT_TGBAALGOS_ARE_ISOMORPHIC_HH
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#include "tgba/tgbagraph.hh"
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namespace spot
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{
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/// \ingroup tgba_misc
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/// \brief Check whether two automata are isomorphic.
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/// Two automata a1 and a2 are said to be isomorphic if there is a bijection
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/// f between the states of a1 and a2 such that for every pair of state (s1,
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/// s2) of a1:
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/// - there is a transition from s1 to s2 iff there is a transition from f(s1)
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/// to f(s2)
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/// - if there is such a transition, then the acceptance set and acceptance
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/// condition are the same on the transition from s1 to s2 and from f(s1) to
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/// f(s2)
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SPOT_API bool are_isomorphic(const const_tgba_digraph_ptr a1,
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const const_tgba_digraph_ptr a2);
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}
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#endif
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