636 lines
17 KiB
C++
636 lines
17 KiB
C++
// Copyright (C) 2003, 2004 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 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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#include "misc/hash.hh"
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#include "misc/bddalloc.hh"
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#include "misc/bddlt.hh"
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#include "misc/minato.hh"
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#include "ltlast/visitor.hh"
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#include "ltlast/allnodes.hh"
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#include "ltlvisit/lunabbrev.hh"
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#include "ltlvisit/nenoform.hh"
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#include "ltlvisit/destroy.hh"
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#include "ltlvisit/tostring.hh"
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#include <cassert>
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#include "tgba/tgbabddconcretefactory.hh"
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#include "ltl2tgba_fm.hh"
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namespace spot
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{
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using namespace ltl;
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namespace
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{
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// Helper dictionary. We represent formulae using BDDs to
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// simplify them, and then translate BDDs back into formulae.
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//
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// The name of the variables are inspired from Couvreur's FM paper.
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// "a" variables are promises (written "a" in the paper)
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// "next" variables are X's operands (the "r_X" variables from the paper)
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// "var" variables are atomic propositions.
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class translate_dict
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{
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public:
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translate_dict(bdd_dict* dict)
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: dict(dict),
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a_set(bddtrue),
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var_set(bddtrue),
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next_set(bddtrue)
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{
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}
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~translate_dict()
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{
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fv_map::iterator i;
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for (i = next_map.begin(); i != next_map.end(); ++i)
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destroy(i->first);
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dict->unregister_all_my_variables(this);
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}
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bdd_dict* dict;
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/// Formula-to-BDD-variable maps.
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typedef Sgi::hash_map<const formula*, int,
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ptr_hash<formula> > fv_map;
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/// BDD-variable-to-formula maps.
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typedef Sgi::hash_map<int, const formula*> vf_map;
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fv_map next_map; ///< Maps "Next" variables to BDD variables
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vf_map next_formula_map; ///< Maps BDD variables to "Next" variables
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bdd a_set;
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bdd var_set;
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bdd next_set;
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int
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register_proposition(const formula* f)
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{
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int num = dict->register_proposition(f, this);
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var_set &= bdd_ithvar(num);
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return num;
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}
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int
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register_a_variable(const formula* f)
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{
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int num = dict->register_acceptance_variable(f, this);
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a_set &= bdd_ithvar(num);
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return num;
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}
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int
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register_next_variable(const formula* f)
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{
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int num;
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// Do not build a Next variable that already exists.
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fv_map::iterator sii = next_map.find(f);
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if (sii != next_map.end())
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{
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num = sii->second;
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}
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else
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{
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f = clone(f);
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num = dict->register_anonymous_variables(1, this);
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next_map[f] = num;
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next_formula_map[num] = f;
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}
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next_set &= bdd_ithvar(num);
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return num;
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}
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std::ostream&
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dump(std::ostream& os) const
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{
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fv_map::const_iterator fi;
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os << "Next Variables:" << std::endl;
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for (fi = next_map.begin(); fi != next_map.end(); ++fi)
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{
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os << " " << fi->second << ": Next[";
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to_string(fi->first, os) << "]" << std::endl;
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}
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os << "Shared Dict:" << std::endl;
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dict->dump(os);
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return os;
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}
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formula*
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var_to_formula(int var) const
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{
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vf_map::const_iterator isi = next_formula_map.find(var);
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if (isi != next_formula_map.end())
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return clone(isi->second);
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isi = dict->acc_formula_map.find(var);
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if (isi != dict->acc_formula_map.end())
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return clone(isi->second);
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isi = dict->var_formula_map.find(var);
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if (isi != dict->var_formula_map.end())
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return clone(isi->second);
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assert(0);
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// Never reached, but some GCC versions complain about
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// a missing return otherwise.
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return 0;
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}
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formula*
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conj_bdd_to_formula(bdd b)
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{
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if (b == bddfalse)
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return constant::false_instance();
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multop::vec* v = new multop::vec;
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while (b != bddtrue)
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{
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int var = bdd_var(b);
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formula* res = var_to_formula(var);
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bdd high = bdd_high(b);
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if (high == bddfalse)
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{
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res = unop::instance(unop::Not, res);
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b = bdd_low(b);
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}
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else
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{
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assert(bdd_low(b) == bddfalse);
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b = high;
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}
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assert(b != bddfalse);
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v->push_back(res);
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}
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return multop::instance(multop::And, v);
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}
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const formula*
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bdd_to_formula(bdd f)
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{
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if (f == bddfalse)
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return constant::false_instance();
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multop::vec* v = new multop::vec;
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minato_isop isop(f);
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bdd cube;
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while ((cube = isop.next()) != bddfalse)
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v->push_back(conj_bdd_to_formula(cube));
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return multop::instance(multop::Or, v);
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}
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void
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conj_bdd_to_acc(tgba_explicit* a, bdd b, tgba_explicit::transition* t)
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{
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assert(b != bddfalse);
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while (b != bddtrue)
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{
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int var = bdd_var(b);
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bdd high = bdd_high(b);
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if (high == bddfalse)
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{
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// Simply ignore negated acceptance variables.
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b = bdd_low(b);
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}
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else
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{
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formula* ac = var_to_formula(var);
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if (! a->has_acceptance_condition(ac))
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a->declare_acceptance_condition(clone(ac));
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a->add_acceptance_condition(t, ac);
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b = high;
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}
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assert(b != bddfalse);
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}
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}
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};
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// The rewrite rules used here are adapted from Jean-Michel
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// Couvreur's FM paper.
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class ltl_trad_visitor: public const_visitor
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{
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public:
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ltl_trad_visitor(translate_dict& dict)
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: dict_(dict)
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{
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}
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virtual
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~ltl_trad_visitor()
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{
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}
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bdd result() const
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{
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return res_;
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}
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void
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visit(const atomic_prop* node)
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{
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res_ = bdd_ithvar(dict_.register_proposition(node));
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}
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void
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visit(const constant* node)
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{
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switch (node->val())
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{
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case constant::True:
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res_ = bddtrue;
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return;
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case constant::False:
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res_ = bddfalse;
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return;
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}
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/* Unreachable code. */
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assert(0);
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}
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void
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visit(const unop* node)
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{
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switch (node->op())
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{
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case unop::F:
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{
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// r(Fy) = r(y) + a(y)r(XFy)
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const formula* child = node->child();
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bdd y = recurse(child);
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int a = dict_.register_a_variable(child);
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int x = dict_.register_next_variable(node);
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res_ = y | (bdd_ithvar(a) & bdd_ithvar(x));
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return;
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}
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case unop::G:
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{
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// The paper suggests that we optimize GFy
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// as
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// r(GFy) = (r(y) + a(y))r(XGFy)
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// instead of
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// r(GFy) = (r(y) + a(y)r(XFy)).r(XGFy)
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// but this is just a particular case
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// of the "merge all states with the same
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// symbolic rewriting" optimization we do later.
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// (r(Fy).r(GFy) and r(GFy) have the same symbolic
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// rewriting.) Let's keep things simple here.
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// r(Gy) = r(y)r(XGy)
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const formula* child = node->child();
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int x = dict_.register_next_variable(node);
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bdd y = recurse(child);
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res_ = y & bdd_ithvar(x);
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return;
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}
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case unop::Not:
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{
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// r(!y) = !r(y)
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res_ = bdd_not(recurse(node->child()));
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return;
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}
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case unop::X:
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{
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// r(Xy) = Next[y]
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int x = dict_.register_next_variable(node->child());
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res_ = bdd_ithvar(x);
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return;
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}
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}
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/* Unreachable code. */
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assert(0);
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}
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void
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visit(const binop* node)
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{
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bdd f1 = recurse(node->first());
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bdd f2 = recurse(node->second());
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switch (node->op())
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{
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// r(f1 logical-op f2) = r(f1) logical-op r(f2)
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case binop::Xor:
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res_ = bdd_apply(f1, f2, bddop_xor);
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return;
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case binop::Implies:
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res_ = bdd_apply(f1, f2, bddop_imp);
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return;
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case binop::Equiv:
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res_ = bdd_apply(f1, f2, bddop_biimp);
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return;
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case binop::U:
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{
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// r(f1 U f2) = r(f2) + a(f2)r(f1)r(X(f1 U f2))
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int a = dict_.register_a_variable(node->second());
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int x = dict_.register_next_variable(node);
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res_ = f2 | (bdd_ithvar(a) & f1 & bdd_ithvar(x));
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return;
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}
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case binop::R:
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{
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// r(f1 R f2) = r(f1)r(f2) + r(f2)r(X(f1 U f2))
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int x = dict_.register_next_variable(node);
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res_ = (f1 & f2) | (f2 & bdd_ithvar(x));
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return;
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}
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}
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/* Unreachable code. */
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assert(0);
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}
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void
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visit(const multop* node)
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{
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int op = -1;
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switch (node->op())
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{
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case multop::And:
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op = bddop_and;
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res_ = bddtrue;
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break;
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case multop::Or:
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op = bddop_or;
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res_ = bddfalse;
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break;
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}
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assert(op != -1);
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unsigned s = node->size();
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for (unsigned n = 0; n < s; ++n)
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{
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res_ = bdd_apply(res_, recurse(node->nth(n)), op);
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}
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}
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bdd
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recurse(const formula* f)
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{
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ltl_trad_visitor v(dict_);
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f->accept(v);
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return v.result();
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}
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private:
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translate_dict& dict_;
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bdd res_;
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};
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}
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tgba_explicit*
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ltl_to_tgba_fm(const formula* f, bdd_dict* dict,
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bool exprop, bool symb_merge)
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{
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// Normalize the formula. We want all the negations on
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// the atomic propositions. We also suppress logic
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// abbreviations such as <=>, =>, or XOR, since they
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// would involve negations at the BDD level.
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formula* f1 = unabbreviate_logic(f);
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formula* f2 = negative_normal_form(f1);
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destroy(f1);
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std::set<const formula*> formulae_seen;
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std::set<const formula*> formulae_to_translate;
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// Map a representation of successors to a canonical formula.
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// We do this because many formulae (such as `aR(bRc)' and
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// `aR(bRc).(bRc)') are equivalent, and are trivially identified
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// by looking at the set of successors.
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typedef std::map<bdd, const formula*, bdd_less_than> succ_to_formula;
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succ_to_formula canonical_succ;
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translate_dict d(dict);
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ltl_trad_visitor v(d);
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formulae_seen.insert(f2);
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formulae_to_translate.insert(f2);
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tgba_explicit* a = new tgba_explicit(dict);
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a->set_init_state(to_string(f2));
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while (!formulae_to_translate.empty())
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{
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// Pick one formula.
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const formula* f = *formulae_to_translate.begin();
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formulae_to_translate.erase(formulae_to_translate.begin());
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// Translate it into a BDD to simplify it.
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// FIXME: Currently the same formula can be converted into a
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// BDD twice. Once in the symb_merge block below, and then
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// once here.
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f->accept(v);
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bdd res = v.result();
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succ_to_formula::iterator cs = canonical_succ.find(res);
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if (cs == canonical_succ.end())
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canonical_succ[res] = clone(f);
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std::string now = to_string(f);
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// We used to factor only Next and A variables while computing
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// prime implicants, with
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// minato_isop isop(res, d.next_set & d.a_set);
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// in order to obtain transitions with formulae of atomic
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// proposition directly, but unfortunately this led to strange
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// factorizations. For instance f U g was translated as
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// r(f U g) = g + a(g).r(X(f U g)).(f + g)
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// instead of just
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// r(f U g) = g + a(g).r(X(f U g)).f
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// Of course both formulae are logically equivalent, but the
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// latter is "more deterministic" than the former, so it should
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// be preferred.
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//
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// Therefore we now factor all variables. This may lead to more
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// transitions than necessary (e.g., r(f + g) = f + g will be
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// coded as two transitions), but we later merge all transitions
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// with same source/destination and acceptance conditions. This
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// is the goal of the `dests' hash.
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//
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// Note that this is still not optimal. For instance it is
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// better to encode `f U g' as
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// r(f U g) = g + a(g).r(X(f U g)).f.!g
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// because that leads to a deterministic automaton. In order
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// to handle this, we take the conditions of any transition
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// going to true (it's `g' here), and remove it from the other
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// transitions.
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//
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// In `exprop' mode, considering all possible combinations of
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// outgoing propositions generalizes the above trick.
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typedef std::map<bdd, bdd, bdd_less_than> prom_map;
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typedef Sgi::hash_map<const formula*, prom_map, ptr_hash<formula> >
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dest_map;
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dest_map dests;
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// Compute all outgoing arcs.
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// If EXPROP is set, we will refine the symbolic
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// representation of the successors for all combinations of
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// the atomic properties involved in the formula.
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// VAR_SET is the set of these properties.
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bdd var_set = bdd_existcomp(bdd_support(res), d.var_set);
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// ALL_PROPS is the combinations we have yet to consider.
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// We used to start with `all_props = bddtrue', but it is
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// more efficient to start with the set of all satisfiable
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// variables combinations.
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bdd all_props = bdd_existcomp(res, d.var_set);
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while (all_props != bddfalse)
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{
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bdd one_prop_set =
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exprop ? bdd_satoneset(all_props, var_set, bddtrue) : bddtrue;
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all_props -= one_prop_set;
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minato_isop isop(res & one_prop_set);
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bdd cube;
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while ((cube = isop.next()) != bddfalse)
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{
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const formula* dest =
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d.conj_bdd_to_formula(bdd_existcomp(cube, d.next_set));
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// If we already know a state with the same successors,
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// use it in lieu of the current one. (See the comments
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// for canonical_succ.) We need to do this only for new
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// destinations.
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if (symb_merge
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&& formulae_seen.find(dest) == formulae_seen.end())
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{
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dest->accept(v);
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bdd succbdd = v.result();
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succ_to_formula::iterator cs =
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canonical_succ.find(succbdd);
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if (cs != canonical_succ.end())
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{
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destroy(dest);
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dest = clone(cs->second);
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}
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else
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{
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canonical_succ[succbdd] = clone(dest);
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}
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}
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bdd promises = bdd_existcomp(cube, d.a_set);
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bdd conds =
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exprop ? one_prop_set : bdd_existcomp(cube, var_set);
|
|
|
|
dest_map::iterator i = dests.find(dest);
|
|
if (i == dests.end())
|
|
{
|
|
dests[dest][promises] = conds;
|
|
}
|
|
else
|
|
{
|
|
i->second[promises] |= conds;
|
|
destroy(dest);
|
|
}
|
|
}
|
|
}
|
|
|
|
// Check for an arc going to 1 (True). Register it first, that
|
|
// way it will be explored before the other during the model
|
|
// checking.
|
|
dest_map::const_iterator i = dests.find(constant::true_instance());
|
|
// COND_FOR_TRUE is the conditions of the True arc, so when
|
|
// can remove them from all other arcs. It might sounds that
|
|
// this is not needed when exprop is used, but in fact it is
|
|
// complementary.
|
|
//
|
|
// Consider
|
|
// f = r(X(1) R p) = p.(1 + r(X(1) R p))
|
|
// with exprop the two outgoing arcs would be
|
|
// p p
|
|
// f ----> 1 f ----------> 1
|
|
//
|
|
// where in fact we could output
|
|
// p
|
|
// f ----> 1
|
|
//
|
|
// because there is no point in looping on f if we can go to 1.
|
|
bdd cond_for_true = bddfalse;
|
|
if (i != dests.end())
|
|
{
|
|
// Transitions going to 1 (true) are not expected to make
|
|
// any promises.
|
|
assert(i->second.size() == 1);
|
|
prom_map::const_iterator j = i->second.find(bddtrue);
|
|
assert(j != i->second.end());
|
|
|
|
cond_for_true = j->second;
|
|
tgba_explicit::transition* t =
|
|
a->create_transition(now, constant::true_instance()->val_name());
|
|
a->add_condition(t, d.bdd_to_formula(cond_for_true));
|
|
}
|
|
// Register other transitions.
|
|
for (i = dests.begin(); i != dests.end(); ++i)
|
|
{
|
|
const formula* dest = i->first;
|
|
// The cond_for_true optimization can cause some
|
|
// transitions to be removed. So we have to remember
|
|
// whether a formula is actually reachable.
|
|
bool reachable = false;
|
|
|
|
if (dest != constant::true_instance())
|
|
{
|
|
std::string next = to_string(dest);
|
|
for (prom_map::const_iterator j = i->second.begin();
|
|
j != i->second.end(); ++j)
|
|
{
|
|
bdd cond = j->second - cond_for_true;
|
|
if (cond == bddfalse) // Skip false transitions.
|
|
continue;
|
|
tgba_explicit::transition* t =
|
|
a->create_transition(now, next);
|
|
a->add_condition(t, d.bdd_to_formula(cond));
|
|
d.conj_bdd_to_acc(a, j->first, t);
|
|
reachable = true;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
// "1" is reachable.
|
|
reachable = true;
|
|
}
|
|
if (reachable
|
|
&& formulae_seen.find(dest) == formulae_seen.end())
|
|
{
|
|
formulae_seen.insert(dest);
|
|
formulae_to_translate.insert(dest);
|
|
}
|
|
else
|
|
{
|
|
destroy(dest);
|
|
}
|
|
}
|
|
}
|
|
|
|
// Free all formulae.
|
|
for (std::set<const formula*>::iterator i = formulae_seen.begin();
|
|
i != formulae_seen.end(); ++i)
|
|
destroy(*i);
|
|
for (succ_to_formula::iterator i = canonical_succ.begin();
|
|
i != canonical_succ.end(); ++i)
|
|
destroy(i->second);
|
|
|
|
// Turn all promises into real acceptance conditions.
|
|
a->complement_all_acceptance_conditions();
|
|
return a;
|
|
}
|
|
|
|
}
|