minimize_wdba() failed to fully minimize some automata.
* src/tgbaalgos/minimize.cc (minimize_wdba): Fix the Löding algorithm to use colors. The previous implementation was an incorrect approximation. * src/tgbatest/wdba2.test: New file showing two equivalent formulas that were minimized in automata with different sizes. * src/tgbatest/Makefile.am: Add it.
This commit is contained in:
Alexandre Duret-Lutz
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commit
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5 changed files with 103 additions and 50 deletions
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@ -531,83 +531,84 @@ namespace spot
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power_map pm;
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det_a = tgba_powerset(a, pm);
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// For each SCC of the deterministic automaton, determine if
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// it is accepting or not.
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// For each SCC of the deterministic automaton, determine if it
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// is accepting or not.
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// This corresponds to the algorithm in Fig. 1 of "Efficient
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// minimization of deterministic weak omega-automata" written by
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// Christof Löding and published in Information Processing
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// Letters 79 (2001) pp 105--109.
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// We also keep track of whether an SCC is useless
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// (i.e., it is not the start of any accepting word).
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scc_map sm(det_a);
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sm.build_map();
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unsigned scc_count = sm.scc_count();
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// SCC that have been marked as accepting.
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std::vector<bool> accepting(scc_count);
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// SCC that have been marked as useless.
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std::vector<bool> useless(scc_count);
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// The "color". Even number correspond to
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// accepting SCCs.
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std::vector<unsigned> d(scc_count);
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// An even number larger than scc_count.
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unsigned k = (scc_count | 1) + 1;
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// SCC are numbered in topological order
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for (unsigned n = 0; n < scc_count; ++n)
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// (but in the reverse order as Löding's)
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for (unsigned m = 0; m < scc_count; ++m)
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{
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bool acc = true;
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bool is_useless = true;
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bool transient = sm.trivial(m);
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const scc_map::succ_type& succ = sm.succ(m);
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if (sm.trivial(n))
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if (transient && succ.empty())
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{
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const scc_map::succ_type& succ = sm.succ(n);
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if (succ.empty())
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{
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// A trivial SCC without successor is useless.
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useless[n] = true;
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accepting[n] = false;
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// Do not add even add it to final or non_final.
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continue;
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}
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// Trivial SCCs are accepting if all their
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// useful successors are accepting.
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// A trivial SCC without successor is useless.
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useless[m] = true;
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d[m] = k - 1;
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continue;
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}
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// This corresponds to the algorithm in Fig. 1 of
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// "Efficient minimization of deterministic weak
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// omega-automata" written by Christof Löding and
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// published in Information Processing Letters 79
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// (2001) pp 105--109. Except we do not keep track
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// of the actual color associated to each SCC.
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// Compute the minimum color l of the successors.
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// Also SCCs are useless if all their successor are
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// useless.
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unsigned l = k;
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for (scc_map::succ_type::const_iterator j = succ.begin();
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j != succ.end(); ++j)
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{
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is_useless &= useless[j->first];
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unsigned dj = d[j->first];
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if (dj < l)
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l = dj;
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}
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// Also they are useless if all their successor are
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// useless.
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for (scc_map::succ_type::const_iterator i = succ.begin();
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i != succ.end(); ++i)
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{
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if (!useless[i->first])
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{
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is_useless = false;
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acc &= accepting[i->first];
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}
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}
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if (transient)
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{
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d[m] = l;
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}
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else
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{
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// Regular SCCs are accepting if any of their loop
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// corresponds to an accepted word in the original
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// automaton.
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acc = wdba_scc_is_accepting(det_a, n, a, sm, pm);
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if (acc)
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if (wdba_scc_is_accepting(det_a, m, a, sm, pm))
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{
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is_useless = false;
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d[m] = (l | 1) - 1; // largest even number inferior or equal
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}
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else
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{
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// Unaccepting SCCs are useless if their successors
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// are all useless.
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const scc_map::succ_type& succ = sm.succ(n);
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for (scc_map::succ_type::const_iterator i = succ.begin();
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i != succ.end(); ++i)
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is_useless &= useless[i->first];
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d[m] = (l - 1) | 1; // largest odd number inferior or equal
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}
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}
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useless[n] = is_useless;
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accepting[n] = acc;
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useless[m] = is_useless;
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if (!is_useless)
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{
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hash_set* dest_set = acc ? final : non_final;
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const std::list<const state*>& l = sm.states_of(n);
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hash_set* dest_set = (d[m]&1) ? non_final : final;
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const std::list<const state*>& l = sm.states_of(m);
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std::list<const state*>::const_iterator il;
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for (il = l.begin(); il != l.end(); ++il)
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dest_set->insert((*il)->clone());
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@ -1,5 +1,5 @@
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## Copyright (C) 2009, 2010, 2011 Laboratoire de Recherche et Développement
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## de l'Epita (LRDE).
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## Copyright (C) 2009, 2010, 2011, 2012 Laboratoire de Recherche et
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## Développement de l'Epita (LRDE).
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## Copyright (C) 2003, 2004, 2005, 2006 Laboratoire d'Informatique de
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## Paris 6 (LIP6), département Systèmes Répartis Coopératifs (SRC),
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## Université Pierre et Marie Curie.
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@ -100,6 +100,7 @@ TESTS = \
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sccsimpl.test \
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obligation.test \
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wdba.test \
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wdba2.test \
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babiak.test \
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randtgba.test \
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emptchk.test \
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38
src/tgbatest/wdba2.test
Executable file
38
src/tgbatest/wdba2.test
Executable file
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@ -0,0 +1,38 @@
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#!/bin/sh
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# Copyright (C) 2012 Laboratoire de Recherche et Développement
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# 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 2 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 Spot; see the file COPYING. If not, write to the Free
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# Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
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# 02111-1307, USA.
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. ./defs
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set -e
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cat >expected <<EOF
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sub trans.: 16
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transitions: 8
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states: 4
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EOF
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# These two equivalent formulae used to produce
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# minimized automata of different sizes...
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run 0 ../ltl2tgba -Rm -kt 'a | X(Gd|Fa)' > out
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run 0 ../ltl2tgba -Rm -kt 'Fa | XGd' > out2
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cmp out expected
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cmp out2 expected
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