Speedup reduccmp.test
This test used to take more than 10min because an instance of valgrind was launched for each separate equivalence check. The list of equivalences to checks are not given in a file, and only two valgrind instances are run. The test takes less than 15sec. * src/ltltest/equalsf.cc: New file. * src/ltltest/Makefile.am (reduccmp, reductaustr): Build using equalsf.cc. * src/ltltest/reduccmp.test: Rewrite. * src/ltltest/uwrm.test: Also rewrite, and use valgrind.
This commit is contained in:
Alexandre Duret-Lutz
parent
b43f75e917
commit
7b9f695265
4 changed files with 597 additions and 354 deletions
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@ -60,13 +60,13 @@ lunabbrev_CPPFLAGS = $(AM_CPPFLAGS) -DLUNABBREV
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nenoform_SOURCES = equals.cc
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nenoform_CPPFLAGS = $(AM_CPPFLAGS) -DNENOFORM
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reduc_SOURCES = reduc.cc
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reduccmp_SOURCES = equals.cc
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reduccmp_SOURCES = equalsf.cc
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reduccmp_CPPFLAGS = $(AM_CPPFLAGS) -DREDUC
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reduceu_SOURCES = equals.cc
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reduceu_CPPFLAGS = $(AM_CPPFLAGS) -DREDUC -DEVENT_UNIV
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reductau_SOURCES = equals.cc
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reductau_CPPFLAGS = $(AM_CPPFLAGS) -DREDUC_TAU
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reductaustr_SOURCES = equals.cc
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reductaustr_SOURCES = equalsf.cc
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reductaustr_CPPFLAGS = $(AM_CPPFLAGS) -DREDUC_TAUSTR
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syntimpl_SOURCES = syntimpl.cc
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tostring_SOURCES = tostring.cc
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251
src/ltltest/equalsf.cc
Normal file
251
src/ltltest/equalsf.cc
Normal file
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@ -0,0 +1,251 @@
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// -*- coding: utf-8 -*-
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// Copyright (C) 2008, 2009, 2010, 2011, 2012, 2014 Laboratoire de
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// Recherche et Développement de l'Epita (LRDE).
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// Copyright (C) 2003, 2004, 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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//
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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 <iostream>
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#include <fstream>
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#include <sstream>
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#include <cassert>
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#include <cstdlib>
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#include <cstring>
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#include "ltlparse/public.hh"
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#include "ltlvisit/lunabbrev.hh"
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#include "ltlvisit/tunabbrev.hh"
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#include "ltlvisit/dump.hh"
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#include "ltlvisit/wmunabbrev.hh"
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#include "ltlvisit/nenoform.hh"
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#include "ltlast/allnodes.hh"
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#include "ltlvisit/simplify.hh"
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#include "ltlvisit/tostring.hh"
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void
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syntax(char* prog)
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{
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std::cerr << prog << " [-E] file" << std::endl;
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exit(2);
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}
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int
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main(int argc, char** argv)
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{
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bool check_first = true;
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if (argc > 1 && !strcmp(argv[1], "-E"))
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{
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check_first = false;
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argv[1] = argv[0];
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++argv;
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--argc;
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}
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if (argc != 2)
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syntax(argv[0]);
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std::ifstream input(argv[1]);
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std::string s;
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unsigned line = 0;
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while (std::getline(input, s))
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{
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++line;
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std::cerr << line << ": " << s << '\n';
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if (s[0] == '#') // Skip comments
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continue;
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std::vector<std::string> formulas;
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{
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std::istringstream ss(s);
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std::string form;
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while (std::getline(ss, form, ','))
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formulas.push_back(form);
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}
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unsigned size = formulas.size();
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if (size == 0) // Skip empty lines
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continue;
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if (size == 1)
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{
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std::cerr << "Not enough formulas on line " << line << '\n';
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return 2;
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}
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spot::ltl::parse_error_list p2;
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const spot::ltl::formula* f2 = spot::ltl::parse(formulas[size - 1], p2);
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if (spot::ltl::format_parse_errors(std::cerr, formulas[size - 1], p2))
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return 2;
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for (unsigned n = 0; n < size - 1; ++n)
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{
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spot::ltl::parse_error_list p1;
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const spot::ltl::formula* f1 = spot::ltl::parse(formulas[n], p1);
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if (check_first &&
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spot::ltl::format_parse_errors(std::cerr, formulas[n], p1))
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return 2;
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int exit_code = 0;
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{
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#if defined LUNABBREV || defined TUNABBREV || defined NENOFORM || defined WM
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const spot::ltl::formula* tmp;
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#endif
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#ifdef LUNABBREV
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tmp = f1;
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f1 = spot::ltl::unabbreviate_logic(f1);
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tmp->destroy();
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spot::ltl::dump(std::cout, f1);
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std::cout << std::endl;
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#endif
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#ifdef TUNABBREV
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tmp = f1;
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f1 = spot::ltl::unabbreviate_ltl(f1);
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tmp->destroy();
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spot::ltl::dump(std::cout, f1);
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std::cout << std::endl;
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#endif
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#ifdef WM
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tmp = f1;
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f1 = spot::ltl::unabbreviate_wm(f1);
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tmp->destroy();
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spot::ltl::dump(std::cout, f1);
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std::cout << std::endl;
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#endif
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#ifdef NENOFORM
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tmp = f1;
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f1 = spot::ltl::negative_normal_form(f1);
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tmp->destroy();
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spot::ltl::dump(std::cout, f1);
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std::cout << std::endl;
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#endif
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#ifdef REDUC
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spot::ltl::ltl_simplifier_options opt(true, true, true,
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false, false);
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# ifdef EVENT_UNIV
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opt.favor_event_univ = true;
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# endif
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spot::ltl::ltl_simplifier simp(opt);
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{
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const spot::ltl::formula* tmp;
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tmp = f1;
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f1 = simp.simplify(f1);
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if (!simp.are_equivalent(f1, tmp))
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{
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std::cerr
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<< "Source and simplified formulae are not equivalent!\n";
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std::cerr
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<< "Simplified: " << spot::ltl::to_string(f1) << '\n';
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exit_code = 1;
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}
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tmp->destroy();
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}
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spot::ltl::dump(std::cout, f1);
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std::cout << std::endl;
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#endif
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#ifdef REDUC_TAU
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spot::ltl::ltl_simplifier_options opt(false, false, false,
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true, false);
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spot::ltl::ltl_simplifier simp(opt);
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{
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const spot::ltl::formula* tmp;
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tmp = f1;
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f1 = simp.simplify(f1);
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if (!simp.are_equivalent(f1, tmp))
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{
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std::cerr
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<< "Source and simplified formulae are not equivalent!\n";
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std::cerr
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<< "Simplified: " << spot::ltl::to_string(f1) << '\n';
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exit_code = 1;
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}
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tmp->destroy();
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}
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spot::ltl::dump(std::cout, f1);
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std::cout << std::endl;
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#endif
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#ifdef REDUC_TAUSTR
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spot::ltl::ltl_simplifier_options opt(false, false, false,
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true, true);
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spot::ltl::ltl_simplifier simp(opt);
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{
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const spot::ltl::formula* tmp;
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tmp = f1;
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f1 = simp.simplify(f1);
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if (!simp.are_equivalent(f1, tmp))
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{
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std::cerr
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<< "Source and simplified formulae are not equivalent!\n";
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std::cerr
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<< "Simplified: " << spot::ltl::to_string(f1) << '\n';
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exit_code = 1;
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}
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tmp->destroy();
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}
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spot::ltl::dump(std::cout, f1);
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std::cout << std::endl;
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#endif
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exit_code |= f1 != f2;
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#if (!defined(REDUC) && !defined(REDUC_TAU) && !defined(REDUC_TAUSTR))
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spot::ltl::ltl_simplifier simp;
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#endif
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if (!simp.are_equivalent(f1, f2))
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{
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#if (!defined(REDUC) && !defined(REDUC_TAU) && !defined(REDUC_TAUSTR))
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std::cerr
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<< "Source and destination formulae are not equivalent!\n";
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#else
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std::cerr
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<< "Simpl. and destination formulae are not equivalent!\n";
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#endif
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exit_code = 1;
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}
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if (exit_code)
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{
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spot::ltl::dump(std::cerr, f1) << std::endl;
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spot::ltl::dump(std::cerr, f2) << std::endl;
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return exit_code;
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}
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}
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f1->destroy();
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}
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f2->destroy();
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}
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spot::ltl::atomic_prop::dump_instances(std::cerr);
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spot::ltl::unop::dump_instances(std::cerr);
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spot::ltl::binop::dump_instances(std::cerr);
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spot::ltl::multop::dump_instances(std::cerr);
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assert(spot::ltl::atomic_prop::instance_count() == 0);
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assert(spot::ltl::unop::instance_count() == 0);
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assert(spot::ltl::binop::instance_count() == 0);
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assert(spot::ltl::multop::instance_count() == 0);
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return 0;
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}
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@ -25,368 +25,373 @@
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# Check LTL reductions
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. ./defs || exit 1
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set -e
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for x in ../reduccmp ../reductaustr; do
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cat >common.txt <<EOF
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# No reduction
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run 0 $x 'a U b' 'a U b'
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run 0 $x 'a R b' 'a R b'
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run 0 $x 'a & b' 'a & b'
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run 0 $x 'a | b' 'a | b'
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run 0 $x 'a & (a U b)' 'a & (a U b)'
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run 0 $x 'a | (a U b)' 'a | (a U b)'
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a U b, a U b
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a R b, a R b
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a & b, a & b
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a | b, a | b
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a & (a U b), a & (a U b)
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a | (a U b), a | (a U b)
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# Syntactic reduction
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run 0 $x 'a & (!b R !a)' 'false'
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run 0 $x '(!b R !a) & a' 'false'
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run 0 $x 'a & (!b R !a) & c' 'false'
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run 0 $x 'c & (!b R !a) & a' 'false'
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a & (!b R !a), false
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(!b R !a) & a, false
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a & (!b R !a) & c, false
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c & (!b R !a) & a, false
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run 0 $x 'a & (!b M !a)' 'false'
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run 0 $x '(!b M !a) & a' 'false'
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run 0 $x 'a & (!b M !a) & c' 'false'
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run 0 $x 'c & (!b M !a) & a' 'false'
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a & (!b M !a), false
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(!b M !a) & a, false
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a & (!b M !a) & c, false
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c & (!b M !a) & a, false
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run 0 $x 'a & (b U a)' 'a'
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run 0 $x '(b U a) & a' 'a'
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run 0 $x 'a | (b U a)' '(b U a)'
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run 0 $x '(b U a) | a' '(b U a)'
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run 0 $x 'a U (b U a)' '(b U a)'
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a & (b U a), a
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(b U a) & a, a
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a | (b U a), (b U a)
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(b U a) | a, (b U a)
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a U (b U a), (b U a)
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run 0 $x 'a & (b W a)' 'a'
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run 0 $x '(b W a) & a' 'a'
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run 0 $x 'a | (b W a)' '(b W a)'
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run 0 $x '(b W a) | a' '(b W a)'
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run 0 $x 'a W (b W a)' '(b W a)'
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a & (b W a), a
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(b W a) & a, a
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a | (b W a), (b W a)
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(b W a) | a, (b W a)
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a W (b W a), (b W a)
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run 0 $x 'a & (b U a) & a' 'a'
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run 0 $x 'a & (b U a) & a' 'a'
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run 0 $x 'a | (b U a) | a' '(b U a)'
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run 0 $x 'a | (b U a) | a' '(b U a)'
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run 0 $x 'a U (b U a)' '(b U a)'
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a & (b U a) & a, a
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a & (b U a) & a, a
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a | (b U a) | a, (b U a)
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a | (b U a) | a, (b U a)
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a U (b U a), (b U a)
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run 0 $x 'a & c & (b W a)' 'a & c'
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run 0 $x 'a & d & c & e & f & g & b & (x W (g & f))' 'a&b&c&d&e&f&g'
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run 0 $x '(F!a & X(!b R a)) | (Ga & X(b U !a))' 'F!a & X(!b R a)'
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run 0 $x 'd & ((!a & d) | (a & d))' '(!a & d) | (a & d)'
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a & c & (b W a), a & c
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a & d & c & e & f & g & b & (x W (g & f)), a&b&c&d&e&f&g
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(F!a & X(!b R a)) | (Ga & X(b U !a)), F!a & X(!b R a)
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d & ((!a & d) | (a & d)), (!a & d) | (a & d)
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run 0 $x 'a <-> !a' '0'
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run 0 $x 'a <-> a' '1'
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run 0 $x 'a ^ a' '0'
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run 0 $x 'a ^ !a' '1'
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a <-> !a, 0
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a <-> a, 1
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a ^ a, 0
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a ^ !a, 1
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run 0 $x 'GFa | FGa' 'GFa'
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run 0 $x 'XXGa | GFa' 'GFa'
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run 0 $x 'GFa & FGa' 'FGa'
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run 0 $x 'XXGa & GFa' 'XXGa'
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GFa | FGa, GFa
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XXGa | GFa, GFa
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GFa & FGa, FGa
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XXGa & GFa, XXGa
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# Basic reductions
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run 0 $x 'X(true)' 'true'
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run 0 $x 'X(false)' 'false'
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run 0 $x 'F(true)' 'true'
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run 0 $x 'F(false)' 'false'
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X(true), true
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X(false), false
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F(true), true
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F(false), false
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run 0 $x 'XGF(f)' 'GF(f)'
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XGF(f), GF(f)
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case $x in
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*tau*);;
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*)
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run 0 $x 'G(true)' 'true'
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run 0 $x 'G(false)' 'false'
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# not reduced
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a R (b W G(c)), a R (b W G(c))
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# not reduced.
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a M ((a&b) R c), a M ((a&b) R c)
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# not reduced.
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(a&b) W (a U c), (a&b) W (a U c)
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run 0 $x 'a M 1' 'Fa'
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run 0 $x 'a W 0' 'Ga'
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run 0 $x '1 U a' 'Fa'
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run 0 $x '0 R a' 'Ga'
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# Eventuality and universality class reductions
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FFa, Fa
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FGFa, GFa
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b U Fa, Fa
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b U GFa, GFa
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Ga, Ga
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run 0 $x 'G(a R b)' 'G(b)'
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a U XXXFb, XXXFb
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EOF
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run 0 $x 'FX(a)' 'XF(a)'
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run 0 $x 'GX(a)' 'XG(a)'
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cp common.txt nottau.txt
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cat >>nottau.txt<<EOF
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G(true), true
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G(false), false
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run 0 $x '(Xf W 0) | X(f W 0)' 'XGf'
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run 0 $x 'XFa & FXa' 'XFa'
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a M 1, Fa
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a W 0, Ga
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1 U a, Fa
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0 R a, Ga
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run 0 $x 'GF(a | Xb)' 'GF(a | b)'
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run 0 $x 'GF(a | Fb)' 'GF(a | b)'
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run 0 $x 'GF(Xa | Fb)' 'GF(a | b)'
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run 0 $x 'FG(a & Xb)' 'FG(a & b)'
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run 0 $x 'FG(a & Gb)' 'FG(a & b)'
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run 0 $x 'FG(Xa & Gb)' 'FG(a & b)'
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G(a R b), G(b)
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run 0 $x 'X(a) U X(b)' 'X(a U b)'
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run 0 $x 'X(a) R X(b)' 'X(a R b)'
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||||
run 0 $x 'Xa & Xb' 'X(a & b)'
|
||||
run 0 $x 'Xa | Xb' 'X(a | b)'
|
||||
FX(a), XF(a)
|
||||
GX(a), XG(a)
|
||||
|
||||
run 0 $x 'X(a) M X(b)' 'X(a M b)'
|
||||
run 0 $x 'X(a) W X(b)' 'X(a W b)'
|
||||
run 0 $x 'X(a) M b' 'b & X(b U a)'
|
||||
run 0 $x 'X(a) R b' 'b & X(b W a)'
|
||||
run 0 $x 'X(a) U b' 'b | X(b M a)'
|
||||
run 0 $x 'X(a) W b' 'b | X(b R a)'
|
||||
(Xf W 0) | X(f W 0), XGf
|
||||
XFa & FXa, XFa
|
||||
|
||||
run 0 $x '(a U b) & (c U b)' '(a & c) U b'
|
||||
run 0 $x '(a R b) & (a R c)' 'a R (b & c)'
|
||||
run 0 $x '(a U b) | (a U c)' 'a U (b | c)'
|
||||
run 0 $x '(a R b) | (c R b)' '(a | c) R b'
|
||||
GF(a | Xb), GF(a | b)
|
||||
GF(a | Fb), GF(a | b)
|
||||
GF(Xa | Fb), GF(a | b)
|
||||
FG(a & Xb), FG(a & b)
|
||||
FG(a & Gb), FG(a & b)
|
||||
FG(Xa & Gb), FG(a & b)
|
||||
|
||||
run 0 $x 'Xa & FGb' 'X(a & FGb)'
|
||||
run 0 $x 'Xa | FGb' 'X(a | FGb)'
|
||||
run 0 $x 'Xa & GFb' 'X(a & GFb)'
|
||||
run 0 $x 'Xa | GFb' 'X(a | GFb)'
|
||||
X(a) U X(b), X(a U b)
|
||||
X(a) R X(b), X(a R b)
|
||||
Xa & Xb, X(a & b)
|
||||
Xa | Xb, X(a | b)
|
||||
|
||||
X(a) M X(b), X(a M b)
|
||||
X(a) W X(b), X(a W b)
|
||||
X(a) M b, b & X(b U a)
|
||||
X(a) R b, b & X(b W a)
|
||||
X(a) U b, b | X(b M a)
|
||||
X(a) W b, b | X(b R a)
|
||||
|
||||
(a U b) & (c U b), (a & c) U b
|
||||
(a R b) & (a R c), a R (b & c)
|
||||
(a U b) | (a U c), a U (b | c)
|
||||
(a R b) | (c R b), (a | c) R b
|
||||
|
||||
Xa & FGb, X(a & FGb)
|
||||
Xa | FGb, X(a | FGb)
|
||||
Xa & GFb, X(a & GFb)
|
||||
Xa | GFb, X(a | GFb)
|
||||
# The following is not reduced to F(a) & GFb. because
|
||||
# (1) is does not help the translate the formula into a
|
||||
# smaller automaton, and ...
|
||||
run 0 $x 'F(a & GFb)' 'F(a & GFb)'
|
||||
F(a & GFb), F(a & GFb)
|
||||
# (2) ... it would hinder this useful reduction (that helps to
|
||||
# produce a smaller automaton)
|
||||
run 0 $x 'F(f1 & GF(f2)) | F(a & GF(b))' 'F((f1&GFf2)|(a&GFb))'
|
||||
F(f1 & GF(f2)) | F(a & GF(b)), F((f1&GFf2)|(a&GFb))
|
||||
# FIXME: Don't we want the opposite rewriting?
|
||||
# rewriting Fa & GFb as F(a & GFb) seems better, but
|
||||
# it not clear how that scales to Fa & Fb & GFc...
|
||||
run 0 $x 'Fa & GFb' 'Fa & GFb'
|
||||
run 0 $x 'G(a | GFb)' 'Ga | GFb'
|
||||
Fa & GFb, Fa & GFb
|
||||
G(a | GFb), Ga | GFb
|
||||
# The following is not reduced to F(a & c) & GF(b) for the same
|
||||
# reason as above.
|
||||
run 0 $x 'F(a & GFb & c)' 'F(a & GFb & c)'
|
||||
run 0 $x 'G(a | GFb | c)' 'G(a | c) | GFb'
|
||||
F(a & GFb & c), F(a & GFb & c)
|
||||
G(a | GFb | c), G(a | c) | GFb
|
||||
|
||||
run 0 $x 'GFa <=> GFb' 'G(Fa&Fb)|FG(!a&!b)'
|
||||
GFa <=> GFb, G(Fa&Fb)|FG(!a&!b)
|
||||
|
||||
run 0 $x 'Gb W a' 'Gb|a'
|
||||
run 0 $x 'Fb M Fa' 'Fa & Fb'
|
||||
Gb W a, Gb|a
|
||||
Fb M Fa, Fa & Fb
|
||||
|
||||
run 0 $x 'a U (b | G(a) | c)' 'a W (b | c)'
|
||||
run 0 $x 'a U (G(a))' 'Ga'
|
||||
run 0 $x '(a U b) | (a W c)' 'a W (b | c)'
|
||||
run 0 $x '(a U b) | Ga' 'a W b'
|
||||
a U (b | G(a) | c), a W (b | c)
|
||||
a U (G(a)), Ga
|
||||
(a U b) | (a W c), a W (b | c)
|
||||
(a U b) | Ga, a W b
|
||||
|
||||
run 0 $x 'a R (b & F(a) & c)' 'a M (b & c)'
|
||||
run 0 $x 'a R (F(a))' 'Fa'
|
||||
run 0 $x '(a R b) & (a M c)' 'a M (b & c)'
|
||||
run 0 $x '(a R b) & Fa' 'a M b'
|
||||
a R (b & F(a) & c), a M (b & c)
|
||||
a R (F(a)), Fa
|
||||
(a R b) & (a M c), a M (b & c)
|
||||
(a R b) & Fa, a M b
|
||||
|
||||
run 0 $x '(a U b) & (c W b)' '(a & c) U b'
|
||||
run 0 $x '(a W b) & (c W b)' '(a & c) W b'
|
||||
run 0 $x '(a R b) | (c M b)' '(a | c) R b'
|
||||
run 0 $x '(a M b) | (c M b)' '(a | c) M b'
|
||||
(a U b) & (c W b), (a & c) U b
|
||||
(a W b) & (c W b), (a & c) W b
|
||||
(a R b) | (c M b), (a | c) R b
|
||||
(a M b) | (c M b), (a | c) M b
|
||||
|
||||
run 0 $x '(a R b) | Gb' 'a R b'
|
||||
run 0 $x '(a M b) | Gb' 'a R b'
|
||||
run 0 $x '(a U b) & Fb' 'a U b'
|
||||
run 0 $x '(a W b) & Fb' 'a U b'
|
||||
run 0 $x '(a M b) | Gb | (c M b)' '(a | c) R b'
|
||||
(a R b) | Gb, a R b
|
||||
(a M b) | Gb, a R b
|
||||
(a U b) & Fb, a U b
|
||||
(a W b) & Fb, a U b
|
||||
(a M b) | Gb | (c M b), (a | c) R b
|
||||
|
||||
run 0 $x 'GFGa' 'FGa'
|
||||
run 0 $x 'b R Ga' 'Ga'
|
||||
run 0 $x 'b R FGa' 'FGa'
|
||||
GFGa, FGa
|
||||
b R Ga, Ga
|
||||
b R FGa, FGa
|
||||
|
||||
run 0 $x 'G(!a M a) M 1' '0'
|
||||
run 0 $x 'G(!a M a) U 1' '1'
|
||||
run 0 $x 'a R (!a M a)' '0'
|
||||
run 0 $x 'a W (!a M a)' 'Ga'
|
||||
G(!a M a) M 1, 0
|
||||
G(!a M a) U 1, 1
|
||||
a R (!a M a), 0
|
||||
a W (!a M a), Ga
|
||||
|
||||
run 0 $x 'F(a U b)' 'Fb'
|
||||
run 0 $x 'F(a M b)' 'F(a & b)'
|
||||
run 0 $x 'G(a R b)' 'Gb'
|
||||
run 0 $x 'G(a W b)' 'G(a | b)'
|
||||
F(a U b), Fb
|
||||
F(a M b), F(a & b)
|
||||
G(a R b), Gb
|
||||
G(a W b), G(a | b)
|
||||
|
||||
run 0 $x 'Fa W Fb' 'F(GFa | b)'
|
||||
run 0 $x 'Ga M Gb' 'FGa & Gb'
|
||||
Fa W Fb, F(GFa | b)
|
||||
Ga M Gb, FGa & Gb
|
||||
|
||||
run 0 $x 'a & XGa' 'Ga'
|
||||
run 0 $x 'a & XG(a&b)' '(XGb)&(Ga)'
|
||||
run 0 $x 'a & b & XG(a&b)' 'G(a&b)'
|
||||
run 0 $x 'a & b & X(Ga&Gb)' 'G(a&b)'
|
||||
run 0 $x 'a & b & XGa &XG(b)' 'G(a&b)'
|
||||
run 0 $x 'a & b & XGa & XGc' 'b & Ga & XGc'
|
||||
run 0 $x 'a & b & X(G(a&d) & b) & X(Gc)' 'b & Ga & X(b & G(c&d))'
|
||||
run 0 $x 'a|b|c|X(F(a|b)|F(c)|Gd)' 'F(a|b|c)|XGd'
|
||||
run 0 $x 'b|c|X(F(a|b)|F(c)|Gd)' 'b|c|X(F(a|b|c)|Gd)'
|
||||
a & XGa, Ga
|
||||
a & XG(a&b), (XGb)&(Ga)
|
||||
a & b & XG(a&b), G(a&b)
|
||||
a & b & X(Ga&Gb), G(a&b)
|
||||
a & b & XGa &XG(b), G(a&b)
|
||||
a & b & XGa & XGc, b & Ga & XGc
|
||||
a & b & X(G(a&d) & b) & X(Gc), b & Ga & X(b & G(c&d))
|
||||
a|b|c|X(F(a|b)|F(c)|Gd), F(a|b|c)|XGd
|
||||
b|c|X(F(a|b)|F(c)|Gd), b|c|X(F(a|b|c)|Gd)
|
||||
|
||||
run 0 $x 'a | (Xa R b) | c' '(b W a) | c'
|
||||
run 0 $x 'a | (Xa M b) | c' '(b U a) | c'
|
||||
run 0 $x 'a | (Xa M b) | (Xa R c)' '(b U a) | (c W a)'
|
||||
run 0 $x 'a | (Xa M b) | XF(a)' 'Fa'
|
||||
run 0 $x 'a | (Xa R b) | XF(a)' '(b W a) | Fa' # Gb | Fa ?
|
||||
run 0 $x 'a & (Xa W b) & c' '(b R a) & c'
|
||||
run 0 $x 'a & (Xa U b) & c' '(b M a) & c'
|
||||
run 0 $x 'a & (Xa W b) & (Xa U c)' '(b R a) & (c M a)'
|
||||
run 0 $x 'a & (Xa W b) & XGa' 'Ga'
|
||||
run 0 $x 'a & (Xa U b) & XGa' '(b M a) & Ga' # Fb & Ga ?
|
||||
run 0 $x 'a|(c&b&X((b&c) U a))|d' '((b&c) U a)|d'
|
||||
run 0 $x 'a|(c&X((b&c) W a)&b)|d' '((b&c) W a)|d'
|
||||
run 0 $x 'a&(c|b|X((b|c) M a))&d' '((b|c) M a)&d'
|
||||
run 0 $x 'a&(c|X((b|c) R a)|b)&d' '((b|c) R a)&d'
|
||||
run 0 $x 'g R (f|g|h)' '(f|h) W g'
|
||||
run 0 $x 'g M (f|g|h)' '(f|h) U g'
|
||||
run 0 $x 'g U (f&g&h)' '(f&h) M g'
|
||||
run 0 $x 'g W (f&g&h)' '(f&h) R g'
|
||||
a | (Xa R b) | c, (b W a) | c
|
||||
a | (Xa M b) | c, (b U a) | c
|
||||
a | (Xa M b) | (Xa R c), (b U a) | (c W a)
|
||||
a | (Xa M b) | XF(a), Fa
|
||||
# Gb | Fa ?
|
||||
a | (Xa R b) | XF(a), (b W a) | Fa
|
||||
a & (Xa W b) & c, (b R a) & c
|
||||
a & (Xa U b) & c, (b M a) & c
|
||||
a & (Xa W b) & (Xa U c), (b R a) & (c M a)
|
||||
a & (Xa W b) & XGa, Ga
|
||||
# Fb & Ga ?
|
||||
a & (Xa U b) & XGa, (b M a) & Ga
|
||||
a|(c&b&X((b&c) U a))|d, ((b&c) U a)|d
|
||||
a|(c&X((b&c) W a)&b)|d, ((b&c) W a)|d
|
||||
a&(c|b|X((b|c) M a))&d, ((b|c) M a)&d
|
||||
a&(c|X((b|c) R a)|b)&d, ((b|c) R a)&d
|
||||
g R (f|g|h), (f|h) W g
|
||||
g M (f|g|h), (f|h) U g
|
||||
g U (f&g&h), (f&h) M g
|
||||
g W (f&g&h), (f&h) R g
|
||||
|
||||
# Syntactic implication
|
||||
run 0 $x '(a & b) R (a R c)' '(a & b)R c'
|
||||
run 0 $x 'a R ((a & b) R c)' '(a & b)R c'
|
||||
run 0 $x 'a R ((a & b) M c)' '(a & b)M c'
|
||||
run 0 $x 'a M ((a & b) M c)' '(a & b)M c'
|
||||
run 0 $x '(a & b) M (a R c)' '(a & b)M c'
|
||||
run 0 $x '(a & b) M (a M c)' '(a & b)M c'
|
||||
(a & b) R (a R c), (a & b)R c
|
||||
a R ((a & b) R c), (a & b)R c
|
||||
a R ((a & b) M c), (a & b)M c
|
||||
a M ((a & b) M c), (a & b)M c
|
||||
(a & b) M (a R c), (a & b)M c
|
||||
(a & b) M (a M c), (a & b)M c
|
||||
|
||||
run 0 $x 'a U ((a & b) U c)' 'a U c'
|
||||
run 0 $x '(a&c) U (b R (c U d))' 'b R (c U d)'
|
||||
run 0 $x '(a&c) U (b R (c W d))' 'b R (c W d)'
|
||||
run 0 $x '(a&c) U (b M (c U d))' 'b M (c U d)'
|
||||
run 0 $x '(a&c) U (b M (c W d))' 'b M (c W d)'
|
||||
a U ((a & b) U c), a U c
|
||||
(a&c) U (b R (c U d)), b R (c U d)
|
||||
(a&c) U (b R (c W d)), b R (c W d)
|
||||
(a&c) U (b M (c U d)), b M (c U d)
|
||||
(a&c) U (b M (c W d)), b M (c W d)
|
||||
|
||||
run 0 $x '(a R c) R (b & a)' 'c R (b & a)'
|
||||
run 0 $x '(a M c) R (b & a)' 'c R (b & a)'
|
||||
(a R c) R (b & a), c R (b & a)
|
||||
(a M c) R (b & a), c R (b & a)
|
||||
|
||||
run 0 $x 'a W ((a&b) U c)' 'a W c'
|
||||
run 0 $x 'a W ((a&b) W c)' 'a W c'
|
||||
a W ((a&b) U c), a W c
|
||||
a W ((a&b) W c), a W c
|
||||
|
||||
run 0 $x '(a M c) M (b&a)' 'c M (b&a)'
|
||||
(a M c) M (b&a), c M (b&a)
|
||||
|
||||
run 0 $x '((a&c) U b) U c' 'b U c'
|
||||
run 0 $x '((a&c) W b) U c' 'b U c'
|
||||
run 0 $x '((a&c) U b) W c' 'b W c'
|
||||
run 0 $x '((a&c) W b) W c' 'b W c'
|
||||
run 0 $x '(a R b) R (c&a)' 'b R (c&a)'
|
||||
run 0 $x '(a M b) R (c&a)' 'b R (c&a)'
|
||||
run 0 $x '(a R b) M (c&a)' 'b M (c&a)'
|
||||
run 0 $x '(a M b) M (c&a)' 'b M (c&a)'
|
||||
|
||||
run 0 $x '(a R (b&c)) R (c)' '(a&b&c) R c'
|
||||
run 0 $x '(a M (b&c)) R (c)' '(a&b&c) R c'
|
||||
run 0 $x '(a R (b&c)) M (c)' '(a R (b&c)) M (c)' # not reduced
|
||||
run 0 $x '(a M (b&c)) M (c)' '(a&b&c) M c'
|
||||
run 0 $x '(a W (c&b)) W b' '(a W (c&b)) | b'
|
||||
run 0 $x '(a U (c&b)) W b' '(a U (c&b)) | b'
|
||||
run 0 $x '(a U (c&b)) U b' '(a U (c&b)) | b'
|
||||
run 0 $x '(a W (c&b)) U b' '(a W (c&b)) U b' # not reduced
|
||||
((a&c) U b) U c, b U c
|
||||
((a&c) W b) U c, b U c
|
||||
((a&c) U b) W c, b W c
|
||||
((a&c) W b) W c, b W c
|
||||
(a R b) R (c&a), b R (c&a)
|
||||
(a M b) R (c&a), b R (c&a)
|
||||
(a R b) M (c&a), b M (c&a)
|
||||
(a M b) M (c&a), b M (c&a)
|
||||
|
||||
(a R (b&c)) R (c), (a&b&c) R c
|
||||
(a M (b&c)) R (c), (a&b&c) R c
|
||||
# not reduced
|
||||
(a R (b&c)) M (c), (a R (b&c)) M (c)
|
||||
(a M (b&c)) M (c), (a&b&c) M c
|
||||
(a W (c&b)) W b, (a W (c&b)) | b
|
||||
(a U (c&b)) W b, (a U (c&b)) | b
|
||||
(a U (c&b)) U b, (a U (c&b)) | b
|
||||
# not reduced
|
||||
(a W (c&b)) U b, (a W (c&b)) U b
|
||||
|
||||
# Eventuality and universality class reductions
|
||||
run 0 $x 'Fa M b' 'Fa & b'
|
||||
run 0 $x 'GFa M b' 'GFa & b'
|
||||
Fa M b, Fa & b
|
||||
GFa M b, GFa & b
|
||||
|
||||
run 0 $x 'Fa|Xb|GFc' 'Fa | X(b|GFc)'
|
||||
run 0 $x 'Fa|GFc' 'F(a|GFc)'
|
||||
run 0 $x 'FGa|GFc' 'F(Ga|GFc)'
|
||||
run 0 $x 'Ga&Xb&FGc' 'Ga & X(b&FGc)'
|
||||
run 0 $x 'Ga&Xb&GFc' 'Ga & X(b&GFc)'
|
||||
run 0 $x 'Ga&GFc' 'G(a&Fc)'
|
||||
run 0 $x 'G(a|b|GFc|GFd|FGe|FGf)' 'G(a|b)|GF(c|d)|F(Ge|Gf)'
|
||||
run 0 $x 'G(a|b)|GFc|GFd|FGe|FGf' 'G(a|b)|GF(c|d)|F(Ge|Gf)'
|
||||
run 0 $x 'X(a|b)|GFc|GFd|FGe|FGf' 'X(a|b|GF(c|d)|F(Ge|Gf))'
|
||||
run 0 $x 'Xa&Xb&GFc&GFd&Ge' 'X(a&b&G(Fc&Fd))&Ge'
|
||||
Fa|Xb|GFc, Fa | X(b|GFc)
|
||||
Fa|GFc, F(a|GFc)
|
||||
FGa|GFc, F(Ga|GFc)
|
||||
Ga&Xb&FGc, Ga & X(b&FGc)
|
||||
Ga&Xb&GFc, Ga & X(b&GFc)
|
||||
Ga&GFc, G(a&Fc)
|
||||
G(a|b|GFc|GFd|FGe|FGf), G(a|b)|GF(c|d)|F(Ge|Gf)
|
||||
G(a|b)|GFc|GFd|FGe|FGf, G(a|b)|GF(c|d)|F(Ge|Gf)
|
||||
X(a|b)|GFc|GFd|FGe|FGf, X(a|b|GF(c|d)|F(Ge|Gf))
|
||||
Xa&Xb&GFc&GFd&Ge, X(a&b&G(Fc&Fd))&Ge
|
||||
|
||||
# F comes in front when possible...
|
||||
run 0 $x 'GFc|GFd|FGe|FGf' 'F(GF(c|d)|Ge|Gf)'
|
||||
run 0 $x 'G(GFc|GFd|FGe|FGf)' 'F(GF(c|d)|Ge|Gf)'
|
||||
GFc|GFd|FGe|FGf, F(GF(c|d)|Ge|Gf)
|
||||
G(GFc|GFd|FGe|FGf), F(GF(c|d)|Ge|Gf)
|
||||
|
||||
# Because reduccmp will translate the formula,
|
||||
# this also check for an old bug in ltl2tgba_fm.
|
||||
run 0 $x '{(c&!c)[->0..1]}!' '0'
|
||||
{(c&!c)[->0..1]}!, 0
|
||||
|
||||
# Tricky case that used to break the translator,
|
||||
# because it was translating closer on-the-fly
|
||||
# without pruning the rational automaton.
|
||||
run 0 $x '{(c&!c)[=2]}' '0'
|
||||
{(c&!c)[=2]}, 0
|
||||
|
||||
run 0 $x '{a && b && c*} <>-> d' 'a&b&c&d'
|
||||
run 0 $x '{a && b && c[*1..3]} <>-> d' 'a&b&c&d'
|
||||
run 0 $x '{a && b && c[->0..2]} <>-> d' 'a&b&c&d'
|
||||
run 0 $x '{a && b && c[+]} <>-> d' 'a&b&c&d'
|
||||
run 0 $x '{a && b && c[=1]} <>-> d' 'a&b&c&d'
|
||||
run 0 $x '{a && b && d[=2]} <>-> d' '0'
|
||||
run 0 $x '{a && b && d[*2..]} <>-> d' '0'
|
||||
run 0 $x '{a && b && d[->2..4]} <>-> d' '0'
|
||||
run 0 $x '{a && { c* : b* : (g|h)*}} <>-> d' 'a & c & b & (g | h) & d'
|
||||
run 0 $x '{a && {b;c}} <>-> d' '0'
|
||||
run 0 $x '{a && {(b;c):e}} <>-> d' '0'
|
||||
run 0 $x '{a && {b*;c*}} <>-> d' '{a && {b*|c*}} <>-> d' # until better
|
||||
run 0 $x '{a && {(b*;c*):e}} <>-> d' '{a && {b*|c*} && e} <>-> d' # idem
|
||||
run 0 $x '{a && {b*;c}} <>-> d' 'a & c & d'
|
||||
run 0 $x '{a && {(b*;c):e}} <>-> d' 'a & c & d & e'
|
||||
run 0 $x '{a && {b;c*}} <>-> d' 'a & b & d'
|
||||
run 0 $x '{a && {(b;c*):e}} <>-> d' 'a & b & d & e'
|
||||
run 0 $x '{{{b1;r1*}&&{b2;r2*}};c}' 'b1&b2&X{{r1*&&r2*};c}'
|
||||
run 0 $x '{{b1:r1*}&&{b2:r2*}}' '{{b1&&b2}:{r1*&&r2*}}'
|
||||
run 0 $x '{{r1*;b1}&&{r2*;b2}}' '{{r1*&&r2*};{b1&&b2}}'
|
||||
run 0 $x '{{r1*:b1}&&{r2*:b2}}' '{{r1*&&r2*}:{b1&&b2}}'
|
||||
run 0 $x '{{a;b*;c}&&{d;e*}&&{f*;g}&&{h*}}' \
|
||||
'{{f*;g}&&{h*}&&{{a&&d};{e* && {b*;c}}}}'
|
||||
run 0 $x '{{{b1;r1*}&{b2;r2*}};c}' 'b1&b2&X{{r1*&r2*};c}'
|
||||
run 0 $x '{{b1:(r1;x1*)}&{b2:(r2;x2*)}}' '{{b1&&b2}:{{r1&&r2};{x1*&x2*}}}'
|
||||
run 0 $x '{{b1:r1*}&{b2:r2*}}' '{{b1:r1*}&{b2:r2*}}' # Not reduced
|
||||
run 0 $x '{{r1*;b1}&{r2*;b2}}' '{{r1*;b1}&{r2*;b2}}' # Not reduced
|
||||
run 0 $x '{{r1*:b1}&{r2*:b2}}' '{{r1*:b1}&{r2*:b2}}' # Not reduced
|
||||
run 0 $x '{{a;b*;c}&{d;e*}&{f*;g}&{h*}}' \
|
||||
'{{f*;g}&{h*}&{{a&&d};{e* & {b*;c}}}}'
|
||||
run 0 $x '{a;(b*;c*;([*0]+{d;e}))*}!' '{a;{b|c|{d;e}}*}!'
|
||||
run 0 $x '{a&b&c*}|->!Xb' '(X!b | !(a & b)) & (!(a & b) | !c | X(!c R !b))'
|
||||
run 0 $x '{[*]}[]->b' 'Gb'
|
||||
run 0 $x '{a;[*]}[]->b' 'Gb | !a'
|
||||
run 0 $x '{[*];a}[]->b' 'G(b | !a)'
|
||||
run 0 $x '{a;b;[*]}[]->c' '!a | X(!b | Gc)'
|
||||
run 0 $x '{a;a;[*]}[]->c' '!a | X(!a | Gc)'
|
||||
run 0 $x '{s[*]}[]->b' 'b W !s'
|
||||
run 0 $x '{s[+]}[]->b' 'b W !s'
|
||||
run 0 $x '{s[*2..]}[]->b' '!s | X(b W !s)'
|
||||
run 0 $x '{a;b*;c;d*}[]->e' '!a | X(!b R ((e & X(e W !d)) | !c))'
|
||||
run 0 $x '{a:b*:c:d*}[]->e' '!a | ((!c | (e W !d)) W !b)'
|
||||
run 0 $x '{a|b*|c|d*}[]->e' '(e | !(a | c)) & (e W !b) & (e W !d)'
|
||||
run 0 $x '{{[*0] | a};b;{[*0] | a};c;e[*]} []-> f' \
|
||||
'{{[*0] | a};b;{[*0] | a}} []-> X((f & X(f W !e)) | !c)'
|
||||
|
||||
run 0 $x '{a&b&c*}<>->!Xb' '(a & b & X!b) | (a & b & c & X(c U !b))'
|
||||
run 0 $x '{[*]}<>->b' 'Fb'
|
||||
run 0 $x '{a;[*]}<>->b' 'Fb & a'
|
||||
run 0 $x '{[*];a}<>->b' 'F(a & b)'
|
||||
run 0 $x '{a;b;[*]}<>->c' 'a & X(b & Fc)'
|
||||
run 0 $x '{a;a;[*]}<>->c' 'a & X(a & Fc)'
|
||||
run 0 $x '{s[*]}<>->b' 'b M s'
|
||||
run 0 $x '{s[+]}<>->b' 'b M s'
|
||||
run 0 $x '{s[*2..]}<>->b' 's & X(b M s)'
|
||||
run 0 $x '{1:a*}!' 'a'
|
||||
run 0 $x '{(1;1):a*}!' 'Xa'
|
||||
run 0 $x '{a;b*;c;d*}<>->e' 'a & X(b U (c & (e | X(e M d))))'
|
||||
run 0 $x '{a:b*:c:d*}<>->e' 'a & ((c & (e M d)) M b)'
|
||||
run 0 $x '{a|b*|c|d*}<>->e' '((a | c) & e) | (e M b) | (e M d)'
|
||||
run 0 $x '{{[*0] | a};b;{[*0] | a};c;e[*]} <>-> f' \
|
||||
'{{[*0] | a};b;{[*0] | a}} <>-> X(c & (f | X(f M e)))'
|
||||
run 0 $x '{a;b[*];c[*];e;f*}' 'a & X(b W (c W e))'
|
||||
run 0 $x '{a;b*;(a* && (b;c));c*}' 'a & X(b W {a[*] && {b;c}})'
|
||||
run 0 $x '{a;a;b[*2..];b}' 'a & X(a & X(b & X(b & Xb)))'
|
||||
run 0 $x '!{a;a;b[*2..];b}' '!a | X(!a | X(!b | X(!b | X!b)))'
|
||||
run 0 $x '!{a;b[*];c[*];e;f*}' '!a | X(!b M (!c M !e))'
|
||||
run 0 $x '!{a;b*;(a* && (b;c));c*}' '!a | X(!b M !{a[*] && {b;c}})'
|
||||
run 0 $x '{(a;c*;d)|(b;c)}' '(a & X(c W d)) | (b & Xc)'
|
||||
run 0 $x '!{(a;c*;d)|(b;c)}' '(X(!c M !d) | !a) & (X!c | !b)'
|
||||
run 0 $x '(Xc R b) & (Xc W 0)' 'b & XGc'
|
||||
run 0 $x '{{c*|1}[*0..1]}<>-> v' '{{c[+]|1}[*0..1]}<>-> v'
|
||||
run 0 $x '{{b*;c*}[*3..5]}<>-> v' '{{b*;c*}[*0..5]} <>-> v'
|
||||
run 0 $x '{{b*&c*}[*3..5]}<>-> v' '{{b[+]|c[+]}[*0..5]} <>-> v'
|
||||
{a && b && c*} <>-> d, a&b&c&d
|
||||
{a && b && c[*1..3]} <>-> d, a&b&c&d
|
||||
{a && b && c[->0..2]} <>-> d, a&b&c&d
|
||||
{a && b && c[+]} <>-> d, a&b&c&d
|
||||
{a && b && c[=1]} <>-> d, a&b&c&d
|
||||
{a && b && d[=2]} <>-> d, 0
|
||||
{a && b && d[*2..]} <>-> d, 0
|
||||
{a && b && d[->2..4]} <>-> d, 0
|
||||
{a && { c* : b* : (g|h)*}} <>-> d, a & c & b & (g | h) & d
|
||||
{a && {b;c}} <>-> d, 0
|
||||
{a && {(b;c):e}} <>-> d, 0
|
||||
# until better
|
||||
{a && {b*;c*}} <>-> d, {a && {b*|c*}} <>-> d
|
||||
# until better
|
||||
{a && {(b*;c*):e}} <>-> d, {a && {b*|c*} && e} <>-> d
|
||||
{a && {b*;c}} <>-> d, a & c & d
|
||||
{a && {(b*;c):e}} <>-> d, a & c & d & e
|
||||
{a && {b;c*}} <>-> d, a & b & d
|
||||
{a && {(b;c*):e}} <>-> d, a & b & d & e
|
||||
{{{b1;r1*}&&{b2;r2*}};c}, b1&b2&X{{r1*&&r2*};c}
|
||||
{{b1:r1*}&&{b2:r2*}}, {{b1&&b2}:{r1*&&r2*}}
|
||||
{{r1*;b1}&&{r2*;b2}}, {{r1*&&r2*};{b1&&b2}}
|
||||
{{r1*:b1}&&{r2*:b2}}, {{r1*&&r2*}:{b1&&b2}}
|
||||
{{a;b*;c}&&{d;e*}&&{f*;g}&&{h*}}, {{f*;g}&&{h*}&&{{a&&d};{e* && {b*;c}}}}
|
||||
{{{b1;r1*}&{b2;r2*}};c}, b1&b2&X{{r1*&r2*};c}
|
||||
{{b1:(r1;x1*)}&{b2:(r2;x2*)}}, {{b1&&b2}:{{r1&&r2};{x1*&x2*}}}
|
||||
# Not reduced
|
||||
{{b1:r1*}&{b2:r2*}}, {{b1:r1*}&{b2:r2*}}
|
||||
# Not reduced
|
||||
{{r1*;b1}&{r2*;b2}}, {{r1*;b1}&{r2*;b2}}
|
||||
# Not reduced
|
||||
{{r1*:b1}&{r2*:b2}}, {{r1*:b1}&{r2*:b2}}
|
||||
{{a;b*;c}&{d;e*}&{f*;g}&{h*}}, {{f*;g}&{h*}&{{a&&d};{e* & {b*;c}}}}
|
||||
{a;(b*;c*;([*0]+{d;e}))*}!, {a;{b|c|{d;e}}*}!
|
||||
{a&b&c*}|->!Xb, (X!b | !(a & b)) & (!(a & b) | !c | X(!c R !b))
|
||||
{[*]}[]->b, Gb
|
||||
{a;[*]}[]->b, Gb | !a
|
||||
{[*];a}[]->b, G(b | !a)
|
||||
{a;b;[*]}[]->c, !a | X(!b | Gc)
|
||||
{a;a;[*]}[]->c, !a | X(!a | Gc)
|
||||
{s[*]}[]->b, b W !s
|
||||
{s[+]}[]->b, b W !s
|
||||
{s[*2..]}[]->b, !s | X(b W !s)
|
||||
{a;b*;c;d*}[]->e, !a | X(!b R ((e & X(e W !d)) | !c))
|
||||
{a:b*:c:d*}[]->e, !a | ((!c | (e W !d)) W !b)
|
||||
{a|b*|c|d*}[]->e, (e | !(a | c)) & (e W !b) & (e W !d)
|
||||
{{[*0]|a};b;{[*0]|a};c;e[*]}[]->f,{{[*0]|a};b;{[*0]|a}}[]->X((f&X(f W !e))|!c)
|
||||
|
||||
{a&b&c*}<>->!Xb, (a & b & X!b) | (a & b & c & X(c U !b))
|
||||
{[*]}<>->b, Fb
|
||||
{a;[*]}<>->b, Fb & a
|
||||
{[*];a}<>->b, F(a & b)
|
||||
{a;b;[*]}<>->c, a & X(b & Fc)
|
||||
{a;a;[*]}<>->c, a & X(a & Fc)
|
||||
{s[*]}<>->b, b M s
|
||||
{s[+]}<>->b, b M s
|
||||
{s[*2..]}<>->b, s & X(b M s)
|
||||
{1:a*}!, a
|
||||
{(1;1):a*}!, Xa
|
||||
{a;b*;c;d*}<>->e, a & X(b U (c & (e | X(e M d))))
|
||||
{a:b*:c:d*}<>->e, a & ((c & (e M d)) M b)
|
||||
{a|b*|c|d*}<>->e, ((a | c) & e) | (e M b) | (e M d)
|
||||
{{[*0]|a};b;{[*0]|a};c;e[*]}<>->f, {{[*0]|a};b;{[*0]|a}}<>->X(c&(f|X(f M e)))
|
||||
{a;b[*];c[*];e;f*}, a & X(b W (c W e))
|
||||
{a;b*;(a* && (b;c));c*}, a & X(b W {a[*] && {b;c}})
|
||||
{a;a;b[*2..];b}, a & X(a & X(b & X(b & Xb)))
|
||||
!{a;a;b[*2..];b}, !a | X(!a | X(!b | X(!b | X!b)))
|
||||
!{a;b[*];c[*];e;f*}, !a | X(!b M (!c M !e))
|
||||
!{a;b*;(a* && (b;c));c*}, !a | X(!b M !{a[*] && {b;c}})
|
||||
{(a;c*;d)|(b;c)}, (a & X(c W d)) | (b & Xc)
|
||||
!{(a;c*;d)|(b;c)}, (X(!c M !d) | !a) & (X!c | !b)
|
||||
(Xc R b) & (Xc W 0), b & XGc
|
||||
{{c*|1}[*0..1]}<>-> v, {{c[+]|1}[*0..1]}<>-> v
|
||||
{{b*;c*}[*3..5]}<>-> v, {{b*;c*}[*0..5]} <>-> v
|
||||
{{b*&c*}[*3..5]}<>-> v, {{b[+]|c[+]}[*0..5]} <>-> v
|
||||
# not reduced
|
||||
run 0 $x '{a;(b[*2..4];c*;([*0]+{d;e}))*}!' \
|
||||
'{a;(b[*2..4];c*;([*0]+{d;e}))*}!'
|
||||
run 0 $x '{((a*;b)+[*0])[*4..6]}!' '{((a*;b))[*0..6]}!'
|
||||
run 0 $x '{c[*];e[*]}[]-> a' '{c[*];e[*]}[]-> a'
|
||||
;;
|
||||
esac
|
||||
{a;(b[*2..4];c*;([*0]+{d;e}))*}!, {a;(b[*2..4];c*;([*0]+{d;e}))*}!
|
||||
{((a*;b)+[*0])[*4..6]}!, {((a*;b))[*0..6]}!
|
||||
{c[*];e[*]}[]-> a, {c[*];e[*]}[]-> a
|
||||
EOF
|
||||
|
||||
run 0 $x 'a R (b W G(c))' 'a R (b W G(c))' #not reduced
|
||||
|
||||
run 0 $x 'a M ((a&b) R c)' 'a M ((a&b) R c)' #not reduced.
|
||||
run 0 $x '(a&b) W (a U c)' '(a&b) W (a U c)' #not reduced.
|
||||
|
||||
# Eventuality and universality class reductions
|
||||
run 0 $x 'FFa' 'Fa'
|
||||
run 0 $x 'FGFa' 'GFa'
|
||||
run 0 $x 'b U Fa' 'Fa'
|
||||
run 0 $x 'b U GFa' 'GFa'
|
||||
run 0 $x 'Ga' 'Ga'
|
||||
|
||||
run 0 $x 'a U XXXFb' 'XXXFb'
|
||||
done
|
||||
run 0 ../reduccmp nottau.txt
|
||||
run 0 ../reductaustr common.txt
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
#! /bin/sh
|
||||
# Copyright (C) 2012 Laboratoire de Recherche et Developpement
|
||||
# Copyright (C) 2012, 2014 Laboratoire de Recherche et Developpement
|
||||
# de l'Epita (LRDE).
|
||||
#
|
||||
# This file is part of Spot, a model checking library.
|
||||
|
|
@ -22,52 +22,39 @@
|
|||
# These formulas comes from an appendix of tl/tl.tex
|
||||
|
||||
. ./defs || exit 1
|
||||
|
||||
set -e
|
||||
|
||||
equiv()
|
||||
{
|
||||
dst=$1
|
||||
shift
|
||||
for src in "$@"; do
|
||||
../reduccmp "$src" "$dst"
|
||||
done
|
||||
}
|
||||
|
||||
cat >input.txt<<EOF
|
||||
# Equivalences with U
|
||||
|
||||
equiv Ff '1 U f'
|
||||
equiv Gf '!F!f' '!(1 U!f)'
|
||||
equiv 'f W g' '(f U g) | (G f)' '(f U g) | !(1 U ! f)' \
|
||||
'f U (g | G f)' 'f U (g | !(1 U ! f ))'
|
||||
equiv 'f M g' 'g U (f & g)'
|
||||
equiv 'f R g' 'g W (f & g)' '(g U (f & g)) | !(1 U ! g)' \
|
||||
'g U ((f & g) | !(1 U ! g))'
|
||||
1 U f, Ff
|
||||
!F!f, !(1 U!f), Gf
|
||||
(f U g)|(G f), (f U g) | !(1 U ! f), f U (g | G f), f U (g | !(1 U !f)), f W g
|
||||
g U (f & g), f M g
|
||||
g W (f & g), (g U (f & g)) | !(1 U ! g), g U ((f & g) | !(1 U ! g)), f R g
|
||||
|
||||
# Equivalences with W
|
||||
|
||||
equiv Ff '!G!f' '!((! f) W 0)'
|
||||
equiv Gf '0 R f' 'f W 0'
|
||||
equiv 'f U g' '(f W g) & (F g)' '(f W g) & !((! g) W 0)'
|
||||
equiv 'f M g' '(g W (f & g)) & (F f)' '(g W (f & g)) & !((!f) W 0)'
|
||||
equiv 'f R g' 'g W (f & g)'
|
||||
!G!f, !((! f) W 0), Ff
|
||||
0 R f, f W 0, Gf
|
||||
(f W g) & (F g), (f W g) & !((! g) W 0), f U g
|
||||
(g W (f & g)) & (F f), (g W (f & g)) & !((!f) W 0), f M g
|
||||
g W (f & g), f R g
|
||||
|
||||
# Equivalences with R
|
||||
!G!f, !(0 R !f), Ff
|
||||
0 R f, Gf
|
||||
# (((X g) R f) & F g) | g, (((X g) R f ) & (!(0 R ! g))) | g, f U g
|
||||
((X g) R f) | g, g R (f | g), f W g
|
||||
(f R g) & F f, (f R g) & !(0 R !f), f R (g & F f), f R (g & !(0 R !f)), f M g
|
||||
|
||||
equiv Ff '!G!f' '!(0 R !f)'
|
||||
equiv Gf '0 R f'
|
||||
#equiv 'f U g' '(((X g) R f) & F g) | g' '(((X g) R f ) & (!(0 R ! g))) | g'
|
||||
equiv 'f W g' '((X g) R f) | g' 'g R (f | g)'
|
||||
equiv 'f M g' '( f R g) & F f' '(f R g) & ! (0 R ! f)' \
|
||||
'f R (g & F f)' 'f R (g & !(0 R !f))'
|
||||
# Equivalences with M
|
||||
|
||||
equiv Ff 'f M 1'
|
||||
equiv Gf '!F!f' '!((!f) M 1)'
|
||||
equiv 'f U g' '((X g) M f) | g' 'g M (f | g)'
|
||||
equiv 'f W g' '(f U g) | G f' '((X g) M f) | g | !((! f ) M 1)'
|
||||
equiv 'f R g' '(f M g) | G g' '(f M g) | !((! g) M 1)'
|
||||
f M 1, Ff
|
||||
!F!f, !((!f) M 1), Gf
|
||||
((X g) M f) | g, g M (f | g), f U g
|
||||
(f U g) | G f, ((X g) M f) | g | !((! f ) M 1), f W g
|
||||
(f M g) | G g, (f M g) | !((! g) M 1), f R g
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# Example from tl.tex
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#(((f U (Xg & f))|!(1 U !f))&(1 U Xg)) | g, f U g
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EOF
|
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# equiv 'f U g' '(((f U (Xg & f))|!(1 U !f))&(1 U Xg)) | g'
|
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run 0 ../reduccmp input.txt
|
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|
|
|
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Loading…
Add table
Add a link
Reference in a new issue