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Speedup reduccmp.test

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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 2014-08-17 11:22:00 +02:00
parent b43f75e917
commit 7b9f695265
4 changed files with 597 additions and 354 deletions
Download patch file Download diff file Expand all files Collapse all files

4
src/ltltest/Makefile.am
View file

@ -60,13 +60,13 @@ lunabbrev_CPPFLAGS = $(AM_CPPFLAGS) -DLUNABBREV
nenoform_SOURCES = equals.cc nenoform_SOURCES = equals.cc
nenoform_CPPFLAGS = $(AM_CPPFLAGS) -DNENOFORM nenoform_CPPFLAGS = $(AM_CPPFLAGS) -DNENOFORM
reduc_SOURCES = reduc.cc reduc_SOURCES = reduc.cc
reduccmp_SOURCES = equals.cc reduccmp_SOURCES = equalsf.cc
reduccmp_CPPFLAGS = $(AM_CPPFLAGS) -DREDUC reduccmp_CPPFLAGS = $(AM_CPPFLAGS) -DREDUC
reduceu_SOURCES = equals.cc reduceu_SOURCES = equals.cc
reduceu_CPPFLAGS = $(AM_CPPFLAGS) -DREDUC -DEVENT_UNIV reduceu_CPPFLAGS = $(AM_CPPFLAGS) -DREDUC -DEVENT_UNIV
reductau_SOURCES = equals.cc reductau_SOURCES = equals.cc
reductau_CPPFLAGS = $(AM_CPPFLAGS) -DREDUC_TAU reductau_CPPFLAGS = $(AM_CPPFLAGS) -DREDUC_TAU
reductaustr_SOURCES = equals.cc reductaustr_SOURCES = equalsf.cc
reductaustr_CPPFLAGS = $(AM_CPPFLAGS) -DREDUC_TAUSTR reductaustr_CPPFLAGS = $(AM_CPPFLAGS) -DREDUC_TAUSTR
syntimpl_SOURCES = syntimpl.cc syntimpl_SOURCES = syntimpl.cc
tostring_SOURCES = tostring.cc tostring_SOURCES = tostring.cc

251
src/ltltest/equalsf.cc Normal file
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@ -0,0 +1,251 @@
// -*- coding: utf-8 -*-
// Copyright (C) 2008, 2009, 2010, 2011, 2012, 2014 Laboratoire de
// Recherche et Développement de l'Epita (LRDE).
// Copyright (C) 2003, 2004, 2006 Laboratoire d'Informatique de
// Paris 6 (LIP6), département Systèmes Répartis Coopératifs (SRC),
// Université Pierre et Marie Curie.
//
// This file is part of Spot, a model checking library.
//
// Spot is free software; you can redistribute it and/or modify it
// under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 3 of the License, or
// (at your option) any later version.
//
// Spot is distributed in the hope that it will be useful, but WITHOUT
// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
// or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
// License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program. If not, see <http://www.gnu.org/licenses/>.
#include <iostream>
#include <fstream>
#include <sstream>
#include <cassert>
#include <cstdlib>
#include <cstring>
#include "ltlparse/public.hh"
#include "ltlvisit/lunabbrev.hh"
#include "ltlvisit/tunabbrev.hh"
#include "ltlvisit/dump.hh"
#include "ltlvisit/wmunabbrev.hh"
#include "ltlvisit/nenoform.hh"
#include "ltlast/allnodes.hh"
#include "ltlvisit/simplify.hh"
#include "ltlvisit/tostring.hh"
void
syntax(char* prog)
{
std::cerr << prog << " [-E] file" << std::endl;
exit(2);
}
int
main(int argc, char** argv)
{
bool check_first = true;
if (argc > 1 && !strcmp(argv[1], "-E"))
{
check_first = false;
argv[1] = argv[0];
++argv;
--argc;
}
if (argc != 2)
syntax(argv[0]);
std::ifstream input(argv[1]);
std::string s;
unsigned line = 0;
while (std::getline(input, s))
{
++line;
std::cerr << line << ": " << s << '\n';
if (s[0] == '#') // Skip comments
continue;
std::vector<std::string> formulas;
{
std::istringstream ss(s);
std::string form;
while (std::getline(ss, form, ','))
formulas.push_back(form);
}
unsigned size = formulas.size();
if (size == 0) // Skip empty lines
continue;
if (size == 1)
{
std::cerr << "Not enough formulas on line " << line << '\n';
return 2;
}
spot::ltl::parse_error_list p2;
const spot::ltl::formula* f2 = spot::ltl::parse(formulas[size - 1], p2);
if (spot::ltl::format_parse_errors(std::cerr, formulas[size - 1], p2))
return 2;
for (unsigned n = 0; n < size - 1; ++n)
{
spot::ltl::parse_error_list p1;
const spot::ltl::formula* f1 = spot::ltl::parse(formulas[n], p1);
if (check_first &&
spot::ltl::format_parse_errors(std::cerr, formulas[n], p1))
return 2;
int exit_code = 0;
{
#if defined LUNABBREV || defined TUNABBREV || defined NENOFORM || defined WM
const spot::ltl::formula* tmp;
#endif
#ifdef LUNABBREV
tmp = f1;
f1 = spot::ltl::unabbreviate_logic(f1);
tmp->destroy();
spot::ltl::dump(std::cout, f1);
std::cout << std::endl;
#endif
#ifdef TUNABBREV
tmp = f1;
f1 = spot::ltl::unabbreviate_ltl(f1);
tmp->destroy();
spot::ltl::dump(std::cout, f1);
std::cout << std::endl;
#endif
#ifdef WM
tmp = f1;
f1 = spot::ltl::unabbreviate_wm(f1);
tmp->destroy();
spot::ltl::dump(std::cout, f1);
std::cout << std::endl;
#endif
#ifdef NENOFORM
tmp = f1;
f1 = spot::ltl::negative_normal_form(f1);
tmp->destroy();
spot::ltl::dump(std::cout, f1);
std::cout << std::endl;
#endif
#ifdef REDUC
spot::ltl::ltl_simplifier_options opt(true, true, true,
false, false);
# ifdef EVENT_UNIV
opt.favor_event_univ = true;
# endif
spot::ltl::ltl_simplifier simp(opt);
{
const spot::ltl::formula* tmp;
tmp = f1;
f1 = simp.simplify(f1);
if (!simp.are_equivalent(f1, tmp))
{
std::cerr
<< "Source and simplified formulae are not equivalent!\n";
std::cerr
<< "Simplified: " << spot::ltl::to_string(f1) << '\n';
exit_code = 1;
}
tmp->destroy();
}
spot::ltl::dump(std::cout, f1);
std::cout << std::endl;
#endif
#ifdef REDUC_TAU
spot::ltl::ltl_simplifier_options opt(false, false, false,
true, false);
spot::ltl::ltl_simplifier simp(opt);
{
const spot::ltl::formula* tmp;
tmp = f1;
f1 = simp.simplify(f1);
if (!simp.are_equivalent(f1, tmp))
{
std::cerr
<< "Source and simplified formulae are not equivalent!\n";
std::cerr
<< "Simplified: " << spot::ltl::to_string(f1) << '\n';
exit_code = 1;
}
tmp->destroy();
}
spot::ltl::dump(std::cout, f1);
std::cout << std::endl;
#endif
#ifdef REDUC_TAUSTR
spot::ltl::ltl_simplifier_options opt(false, false, false,
true, true);
spot::ltl::ltl_simplifier simp(opt);
{
const spot::ltl::formula* tmp;
tmp = f1;
f1 = simp.simplify(f1);
if (!simp.are_equivalent(f1, tmp))
{
std::cerr
<< "Source and simplified formulae are not equivalent!\n";
std::cerr
<< "Simplified: " << spot::ltl::to_string(f1) << '\n';
exit_code = 1;
}
tmp->destroy();
}
spot::ltl::dump(std::cout, f1);
std::cout << std::endl;
#endif
exit_code |= f1 != f2;
#if (!defined(REDUC) && !defined(REDUC_TAU) && !defined(REDUC_TAUSTR))
spot::ltl::ltl_simplifier simp;
#endif
if (!simp.are_equivalent(f1, f2))
{
#if (!defined(REDUC) && !defined(REDUC_TAU) && !defined(REDUC_TAUSTR))
std::cerr
<< "Source and destination formulae are not equivalent!\n";
#else
std::cerr
<< "Simpl. and destination formulae are not equivalent!\n";
#endif
exit_code = 1;
}
if (exit_code)
{
spot::ltl::dump(std::cerr, f1) << std::endl;
spot::ltl::dump(std::cerr, f2) << std::endl;
return exit_code;
}
}
f1->destroy();
}
f2->destroy();
}
spot::ltl::atomic_prop::dump_instances(std::cerr);
spot::ltl::unop::dump_instances(std::cerr);
spot::ltl::binop::dump_instances(std::cerr);
spot::ltl::multop::dump_instances(std::cerr);
assert(spot::ltl::atomic_prop::instance_count() == 0);
assert(spot::ltl::unop::instance_count() == 0);
assert(spot::ltl::binop::instance_count() == 0);
assert(spot::ltl::multop::instance_count() == 0);
return 0;
}

595
src/ltltest/reduccmp.test
View file

@ -25,368 +25,373 @@
# Check LTL reductions # Check LTL reductions
. ./defs || exit 1 . ./defs || exit 1
set -e
for x in ../reduccmp ../reductaustr; do cat >common.txt <<EOF
# No reduction # No reduction
run 0 $x 'a U b' 'a U b' a U b, a U b
run 0 $x 'a R b' 'a R b' a R b, a R b
run 0 $x 'a & b' 'a & b' a & b, a & b
run 0 $x 'a | b' 'a | b' a | b, a | b
run 0 $x 'a & (a U b)' 'a & (a U b)' a & (a U b), a & (a U b)
run 0 $x 'a | (a U b)' 'a | (a U b)' a | (a U b), a | (a U b)
# Syntactic reduction # Syntactic reduction
run 0 $x 'a & (!b R !a)' 'false' a & (!b R !a), false
run 0 $x '(!b R !a) & a' 'false' (!b R !a) & a, false
run 0 $x 'a & (!b R !a) & c' 'false' a & (!b R !a) & c, false
run 0 $x 'c & (!b R !a) & a' 'false' c & (!b R !a) & a, false
run 0 $x 'a & (!b M !a)' 'false' a & (!b M !a), false
run 0 $x '(!b M !a) & a' 'false' (!b M !a) & a, false
run 0 $x 'a & (!b M !a) & c' 'false' a & (!b M !a) & c, false
run 0 $x 'c & (!b M !a) & a' 'false' c & (!b M !a) & a, false
run 0 $x 'a & (b U a)' 'a' a & (b U a), a
run 0 $x '(b U a) & a' 'a' (b U a) & a, a
run 0 $x 'a | (b U a)' '(b U a)' a | (b U a), (b U a)
run 0 $x '(b U a) | a' '(b U a)' (b U a) | a, (b U a)
run 0 $x 'a U (b U a)' '(b U a)' a U (b U a), (b U a)
run 0 $x 'a & (b W a)' 'a' a & (b W a), a
run 0 $x '(b W a) & a' 'a' (b W a) & a, a
run 0 $x 'a | (b W a)' '(b W a)' a | (b W a), (b W a)
run 0 $x '(b W a) | a' '(b W a)' (b W a) | a, (b W a)
run 0 $x 'a W (b W a)' '(b W a)' a W (b W a), (b W a)
run 0 $x 'a & (b U a) & a' 'a' a & (b U a) & a, a
run 0 $x 'a & (b U a) & a' 'a' a & (b U a) & a, a
run 0 $x 'a | (b U a) | a' '(b U a)' a | (b U a) | a, (b U a)
run 0 $x 'a | (b U a) | a' '(b U a)' a | (b U a) | a, (b U a)
run 0 $x 'a U (b U a)' '(b U a)' a U (b U a), (b U a)
run 0 $x 'a & c & (b W a)' 'a & c' a & c & (b W a), a & c
run 0 $x 'a & d & c & e & f & g & b & (x W (g & f))' 'a&b&c&d&e&f&g' a & d & c & e & f & g & b & (x W (g & f)), a&b&c&d&e&f&g
run 0 $x '(F!a & X(!b R a)) | (Ga & X(b U !a))' 'F!a & X(!b R a)' (F!a & X(!b R a)) | (Ga & X(b U !a)), F!a & X(!b R a)
run 0 $x 'd & ((!a & d) | (a & d))' '(!a & d) | (a & d)' d & ((!a & d) | (a & d)), (!a & d) | (a & d)
run 0 $x 'a <-> !a' '0' a <-> !a, 0
run 0 $x 'a <-> a' '1' a <-> a, 1
run 0 $x 'a ^ a' '0' a ^ a, 0
run 0 $x 'a ^ !a' '1' a ^ !a, 1
run 0 $x 'GFa | FGa' 'GFa' GFa | FGa, GFa
run 0 $x 'XXGa | GFa' 'GFa' XXGa | GFa, GFa
run 0 $x 'GFa & FGa' 'FGa' GFa & FGa, FGa
run 0 $x 'XXGa & GFa' 'XXGa' XXGa & GFa, XXGa
# Basic reductions # Basic reductions
run 0 $x 'X(true)' 'true' X(true), true
run 0 $x 'X(false)' 'false' X(false), false
run 0 $x 'F(true)' 'true' F(true), true
run 0 $x 'F(false)' 'false' F(false), false
run 0 $x 'XGF(f)' 'GF(f)' XGF(f), GF(f)
case $x in # not reduced
*tau*);; a R (b W G(c)), a R (b W G(c))
*) # not reduced.
run 0 $x 'G(true)' 'true' a M ((a&b) R c), a M ((a&b) R c)
run 0 $x 'G(false)' 'false' # not reduced.
(a&b) W (a U c), (a&b) W (a U c)
run 0 $x 'a M 1' 'Fa' # Eventuality and universality class reductions
run 0 $x 'a W 0' 'Ga' FFa, Fa
run 0 $x '1 U a' 'Fa' FGFa, GFa
run 0 $x '0 R a' 'Ga' b U Fa, Fa
b U GFa, GFa
Ga, Ga
run 0 $x 'G(a R b)' 'G(b)' a U XXXFb, XXXFb
EOF
run 0 $x 'FX(a)' 'XF(a)' cp common.txt nottau.txt
run 0 $x 'GX(a)' 'XG(a)' cat >>nottau.txt<<EOF
G(true), true
G(false), false
run 0 $x '(Xf W 0) | X(f W 0)' 'XGf' a M 1, Fa
run 0 $x 'XFa & FXa' 'XFa' a W 0, Ga
1 U a, Fa
0 R a, Ga
run 0 $x 'GF(a | Xb)' 'GF(a | b)' G(a R b), G(b)
run 0 $x 'GF(a | Fb)' 'GF(a | b)'
run 0 $x 'GF(Xa | Fb)' 'GF(a | b)'
run 0 $x 'FG(a & Xb)' 'FG(a & b)'
run 0 $x 'FG(a & Gb)' 'FG(a & b)'
run 0 $x 'FG(Xa & Gb)' 'FG(a & b)'
run 0 $x 'X(a) U X(b)' 'X(a U b)' FX(a), XF(a)
run 0 $x 'X(a) R X(b)' 'X(a R b)' GX(a), XG(a)
run 0 $x 'Xa & Xb' 'X(a & b)'
run 0 $x 'Xa | Xb' 'X(a | b)'
run 0 $x 'X(a) M X(b)' 'X(a M b)' (Xf W 0) | X(f W 0), XGf
run 0 $x 'X(a) W X(b)' 'X(a W b)' XFa & FXa, XFa
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)'
run 0 $x '(a U b) & (c U b)' '(a & c) U b' GF(a | Xb), GF(a | b)
run 0 $x '(a R b) & (a R c)' 'a R (b & c)' GF(a | Fb), GF(a | b)
run 0 $x '(a U b) | (a U c)' 'a U (b | c)' GF(Xa | Fb), GF(a | b)
run 0 $x '(a R b) | (c R b)' '(a | c) R 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)' X(a) U X(b), X(a U b)
run 0 $x 'Xa | FGb' 'X(a | FGb)' X(a) R X(b), X(a R b)
run 0 $x 'Xa & GFb' 'X(a & GFb)' Xa & Xb, X(a & b)
run 0 $x 'Xa | GFb' 'X(a | GFb)' 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 # The following is not reduced to F(a) & GFb. because
# (1) is does not help the translate the formula into a # (1) is does not help the translate the formula into a
# smaller automaton, and ... # 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 # (2) ... it would hinder this useful reduction (that helps to
# produce a smaller automaton) # 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? # FIXME: Don't we want the opposite rewriting?
# rewriting Fa & GFb as F(a & GFb) seems better, but # rewriting Fa & GFb as F(a & GFb) seems better, but
# it not clear how that scales to Fa & Fb & GFc... # it not clear how that scales to Fa & Fb & GFc...
run 0 $x 'Fa & GFb' 'Fa & GFb' Fa & GFb, Fa & GFb
run 0 $x 'G(a | GFb)' 'Ga | GFb' G(a | GFb), Ga | GFb
# The following is not reduced to F(a & c) & GF(b) for the same # The following is not reduced to F(a & c) & GF(b) for the same
# reason as above. # reason as above.
run 0 $x 'F(a & GFb & c)' 'F(a & GFb & c)' F(a & GFb & c), F(a & GFb & c)
run 0 $x 'G(a | GFb | c)' 'G(a | c) | GFb' 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' Gb W a, Gb|a
run 0 $x 'Fb M Fa' 'Fa & Fb' Fb M Fa, Fa & Fb
run 0 $x 'a U (b | G(a) | c)' 'a W (b | c)' a U (b | G(a) | c), a W (b | c)
run 0 $x 'a U (G(a))' 'Ga' a U (G(a)), Ga
run 0 $x '(a U b) | (a W c)' 'a W (b | c)' (a U b) | (a W c), a W (b | c)
run 0 $x '(a U b) | Ga' 'a W b' (a U b) | Ga, a W b
run 0 $x 'a R (b & F(a) & c)' 'a M (b & c)' a R (b & F(a) & c), a M (b & c)
run 0 $x 'a R (F(a))' 'Fa' a R (F(a)), Fa
run 0 $x '(a R b) & (a M c)' 'a M (b & c)' (a R b) & (a M c), a M (b & c)
run 0 $x '(a R b) & Fa' 'a M b' (a R b) & Fa, a M b
run 0 $x '(a U b) & (c W b)' '(a & c) U b' (a U b) & (c W b), (a & c) U b
run 0 $x '(a W b) & (c W b)' '(a & c) W b' (a W b) & (c W b), (a & c) W b
run 0 $x '(a R b) | (c M b)' '(a | c) R b' (a R b) | (c M b), (a | c) R b
run 0 $x '(a M b) | (c M b)' '(a | c) M b' (a M b) | (c M b), (a | c) M b
run 0 $x '(a R b) | Gb' 'a R b' (a R b) | Gb, a R b
run 0 $x '(a M b) | Gb' 'a R b' (a M b) | Gb, a R b
run 0 $x '(a U b) & Fb' 'a U b' (a U b) & Fb, a U b
run 0 $x '(a W b) & Fb' 'a U b' (a W b) & Fb, a U b
run 0 $x '(a M b) | Gb | (c M b)' '(a | c) R b' (a M b) | Gb | (c M b), (a | c) R b
run 0 $x 'GFGa' 'FGa' GFGa, FGa
run 0 $x 'b R Ga' 'Ga' b R Ga, Ga
run 0 $x 'b R FGa' 'FGa' b R FGa, FGa
run 0 $x 'G(!a M a) M 1' '0' G(!a M a) M 1, 0
run 0 $x 'G(!a M a) U 1' '1' G(!a M a) U 1, 1
run 0 $x 'a R (!a M a)' '0' a R (!a M a), 0
run 0 $x 'a W (!a M a)' 'Ga' a W (!a M a), Ga
run 0 $x 'F(a U b)' 'Fb' F(a U b), Fb
run 0 $x 'F(a M b)' 'F(a & b)' F(a M b), F(a & b)
run 0 $x 'G(a R b)' 'Gb' G(a R b), Gb
run 0 $x 'G(a W b)' 'G(a | b)' G(a W b), G(a | b)
run 0 $x 'Fa W Fb' 'F(GFa | b)' Fa W Fb, F(GFa | b)
run 0 $x 'Ga M Gb' 'FGa & Gb' Ga M Gb, FGa & Gb
run 0 $x 'a & XGa' 'Ga' a & XGa, Ga
run 0 $x 'a & XG(a&b)' '(XGb)&(Ga)' a & XG(a&b), (XGb)&(Ga)
run 0 $x 'a & b & XG(a&b)' 'G(a&b)' a & b & XG(a&b), G(a&b)
run 0 $x 'a & b & X(Ga&Gb)' 'G(a&b)' a & b & X(Ga&Gb), G(a&b)
run 0 $x 'a & b & XGa &XG(b)' 'G(a&b)' a & b & XGa &XG(b), G(a&b)
run 0 $x 'a & b & XGa & XGc' 'b & Ga & XGc' 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))' 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' 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)' 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' a | (Xa R b) | c, (b W a) | c
run 0 $x 'a | (Xa M b) | c' '(b U a) | c' 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)' a | (Xa M b) | (Xa R c), (b U a) | (c W a)
run 0 $x 'a | (Xa M b) | XF(a)' 'Fa' a | (Xa M b) | XF(a), Fa
run 0 $x 'a | (Xa R b) | XF(a)' '(b W a) | Fa' # Gb | Fa ? # Gb | Fa ?
run 0 $x 'a & (Xa W b) & c' '(b R a) & c' a | (Xa R b) | XF(a), (b W a) | Fa
run 0 $x 'a & (Xa U b) & c' '(b M a) & c' a & (Xa W b) & c, (b R a) & c
run 0 $x 'a & (Xa W b) & (Xa U c)' '(b R a) & (c M a)' a & (Xa U b) & c, (b M a) & c
run 0 $x 'a & (Xa W b) & XGa' 'Ga' a & (Xa W b) & (Xa U c), (b R a) & (c M a)
run 0 $x 'a & (Xa U b) & XGa' '(b M a) & Ga' # Fb & Ga ? a & (Xa W b) & XGa, Ga
run 0 $x 'a|(c&b&X((b&c) U a))|d' '((b&c) U a)|d' # Fb & Ga ?
run 0 $x 'a|(c&X((b&c) W a)&b)|d' '((b&c) W a)|d' a & (Xa U b) & XGa, (b M a) & Ga
run 0 $x 'a&(c|b|X((b|c) M a))&d' '((b|c) M a)&d' a|(c&b&X((b&c) U a))|d, ((b&c) U a)|d
run 0 $x 'a&(c|X((b|c) R a)|b)&d' '((b|c) R a)&d' a|(c&X((b&c) W a)&b)|d, ((b&c) W a)|d
run 0 $x 'g R (f|g|h)' '(f|h) W g' a&(c|b|X((b|c) M a))&d, ((b|c) M a)&d
run 0 $x 'g M (f|g|h)' '(f|h) U g' a&(c|X((b|c) R a)|b)&d, ((b|c) R a)&d
run 0 $x 'g U (f&g&h)' '(f&h) M g' g R (f|g|h), (f|h) W g
run 0 $x 'g W (f&g&h)' '(f&h) R 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 # Syntactic implication
run 0 $x '(a & b) R (a R c)' '(a & b)R c' (a & b) R (a R c), (a & b)R c
run 0 $x 'a R ((a & b) R c)' '(a & b)R c' a R ((a & b) R c), (a & b)R c
run 0 $x 'a R ((a & b) M c)' '(a & b)M c' a R ((a & b) M c), (a & b)M c
run 0 $x 'a M ((a & b) M c)' '(a & b)M c' a M ((a & b) M c), (a & b)M c
run 0 $x '(a & b) M (a R c)' '(a & b)M c' (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) M (a M c), (a & b)M c
run 0 $x 'a U ((a & b) U c)' 'a U c' 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)' (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)' (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)' (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&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)' (a R c) R (b & a), c R (b & a)
run 0 $x '(a M 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' 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) 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' ((a&c) U b) U c, b U c
run 0 $x '((a&c) W b) U c' 'b U c' ((a&c) W b) U c, b U c
run 0 $x '((a&c) U b) W c' 'b W c' ((a&c) U b) W c, b W c
run 0 $x '((a&c) W b) W c' 'b W c' ((a&c) W b) W c, b W c
run 0 $x '(a R b) R (c&a)' 'b R (c&a)' (a R b) R (c&a), b R (c&a)
run 0 $x '(a M b) R (c&a)' 'b R (c&a)' (a M b) R (c&a), b R (c&a)
run 0 $x '(a R b) M (c&a)' 'b M (c&a)' (a R b) M (c&a), b M (c&a)
run 0 $x '(a M b) M (c&a)' 'b M (c&a)' (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 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 # Eventuality and universality class reductions
run 0 $x 'Fa M b' 'Fa & b' Fa M b, Fa & b
run 0 $x 'GFa M b' 'GFa & b' GFa M b, GFa & b
run 0 $x 'Fa|Xb|GFc' 'Fa | X(b|GFc)' Fa|Xb|GFc, Fa | X(b|GFc)
run 0 $x 'Fa|GFc' 'F(a|GFc)' Fa|GFc, F(a|GFc)
run 0 $x 'FGa|GFc' 'F(Ga|GFc)' FGa|GFc, F(Ga|GFc)
run 0 $x 'Ga&Xb&FGc' 'Ga & X(b&FGc)' Ga&Xb&FGc, Ga & X(b&FGc)
run 0 $x 'Ga&Xb&GFc' 'Ga & X(b&GFc)' Ga&Xb&GFc, Ga & X(b&GFc)
run 0 $x 'Ga&GFc' 'G(a&Fc)' Ga&GFc, G(a&Fc)
run 0 $x '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)
run 0 $x '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)
run 0 $x 'X(a|b)|GFc|GFd|FGe|FGf' 'X(a|b|GF(c|d)|F(Ge|Gf))' 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' Xa&Xb&GFc&GFd&Ge, X(a&b&G(Fc&Fd))&Ge
# F comes in front when possible... # F comes in front when possible...
run 0 $x 'GFc|GFd|FGe|FGf' 'F(GF(c|d)|Ge|Gf)' GFc|GFd|FGe|FGf, F(GF(c|d)|Ge|Gf)
run 0 $x 'G(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, # Because reduccmp will translate the formula,
# this also check for an old bug in ltl2tgba_fm. # 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, # Tricky case that used to break the translator,
# because it was translating closer on-the-fly # because it was translating closer on-the-fly
# without pruning the rational automaton. # 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' {a && b && c*} <>-> d, a&b&c&d
run 0 $x '{a && b && c[*1..3]} <>-> d' 'a&b&c&d' {a && b && c[*1..3]} <>-> d, a&b&c&d
run 0 $x '{a && b && c[->0..2]} <>-> d' 'a&b&c&d' {a && b && c[->0..2]} <>-> d, a&b&c&d
run 0 $x '{a && b && c[+]} <>-> d' 'a&b&c&d' {a && b && c[+]} <>-> d, a&b&c&d
run 0 $x '{a && b && c[=1]} <>-> d' 'a&b&c&d' {a && b && c[=1]} <>-> d, a&b&c&d
run 0 $x '{a && b && d[=2]} <>-> d' '0' {a && b && d[=2]} <>-> d, 0
run 0 $x '{a && b && d[*2..]} <>-> d' '0' {a && b && d[*2..]} <>-> d, 0
run 0 $x '{a && b && d[->2..4]} <>-> d' '0' {a && b && d[->2..4]} <>-> d, 0
run 0 $x '{a && { c* : b* : (g|h)*}} <>-> d' 'a & c & b & (g | h) & d' {a && { c* : b* : (g|h)*}} <>-> d, a & c & b & (g | h) & d
run 0 $x '{a && {b;c}} <>-> d' '0' {a && {b;c}} <>-> d, 0
run 0 $x '{a && {(b;c):e}} <>-> d' '0' {a && {(b;c):e}} <>-> d, 0
run 0 $x '{a && {b*;c*}} <>-> d' '{a && {b*|c*}} <>-> d' # until better # until better
run 0 $x '{a && {(b*;c*):e}} <>-> d' '{a && {b*|c*} && e} <>-> d' # idem {a && {b*;c*}} <>-> d, {a && {b*|c*}} <>-> d
run 0 $x '{a && {b*;c}} <>-> d' 'a & c & d' # until better
run 0 $x '{a && {(b*;c):e}} <>-> d' 'a & c & d & e' {a && {(b*;c*):e}} <>-> d, {a && {b*|c*} && e} <>-> d
run 0 $x '{a && {b;c*}} <>-> d' 'a & b & d' {a && {b*;c}} <>-> d, a & c & d
run 0 $x '{a && {(b;c*):e}} <>-> d' 'a & b & d & e' {a && {(b*;c):e}} <>-> d, a & c & d & e
run 0 $x '{{{b1;r1*}&&{b2;r2*}};c}' 'b1&b2&X{{r1*&&r2*};c}' {a && {b;c*}} <>-> d, a & b & d
run 0 $x '{{b1:r1*}&&{b2:r2*}}' '{{b1&&b2}:{r1*&&r2*}}' {a && {(b;c*):e}} <>-> d, a & b & d & e
run 0 $x '{{r1*;b1}&&{r2*;b2}}' '{{r1*&&r2*};{b1&&b2}}' {{{b1;r1*}&&{b2;r2*}};c}, b1&b2&X{{r1*&&r2*};c}
run 0 $x '{{r1*:b1}&&{r2*:b2}}' '{{r1*&&r2*}:{b1&&b2}}' {{b1:r1*}&&{b2:r2*}}, {{b1&&b2}:{r1*&&r2*}}
run 0 $x '{{a;b*;c}&&{d;e*}&&{f*;g}&&{h*}}' \ {{r1*;b1}&&{r2*;b2}}, {{r1*&&r2*};{b1&&b2}}
'{{f*;g}&&{h*}&&{{a&&d};{e* && {b*;c}}}}' {{r1*:b1}&&{r2*:b2}}, {{r1*&&r2*}:{b1&&b2}}
run 0 $x '{{{b1;r1*}&{b2;r2*}};c}' 'b1&b2&X{{r1*&r2*};c}' {{a;b*;c}&&{d;e*}&&{f*;g}&&{h*}}, {{f*;g}&&{h*}&&{{a&&d};{e* && {b*;c}}}}
run 0 $x '{{b1:(r1;x1*)}&{b2:(r2;x2*)}}' '{{b1&&b2}:{{r1&&r2};{x1*&x2*}}}' {{{b1;r1*}&{b2;r2*}};c}, b1&b2&X{{r1*&r2*};c}
run 0 $x '{{b1:r1*}&{b2:r2*}}' '{{b1:r1*}&{b2:r2*}}' # Not reduced {{b1:(r1;x1*)}&{b2:(r2;x2*)}}, {{b1&&b2}:{{r1&&r2};{x1*&x2*}}}
run 0 $x '{{r1*;b1}&{r2*;b2}}' '{{r1*;b1}&{r2*;b2}}' # Not reduced # Not reduced
run 0 $x '{{r1*:b1}&{r2*:b2}}' '{{r1*:b1}&{r2*:b2}}' # Not reduced {{b1:r1*}&{b2:r2*}}, {{b1:r1*}&{b2:r2*}}
run 0 $x '{{a;b*;c}&{d;e*}&{f*;g}&{h*}}' \ # Not reduced
'{{f*;g}&{h*}&{{a&&d};{e* & {b*;c}}}}' {{r1*;b1}&{r2*;b2}}, {{r1*;b1}&{r2*;b2}}
run 0 $x '{a;(b*;c*;([*0]+{d;e}))*}!' '{a;{b|c|{d;e}}*}!' # Not reduced
run 0 $x '{a&b&c*}|->!Xb' '(X!b | !(a & b)) & (!(a & b) | !c | X(!c R !b))' {{r1*:b1}&{r2*:b2}}, {{r1*:b1}&{r2*:b2}}
run 0 $x '{[*]}[]->b' 'Gb' {{a;b*;c}&{d;e*}&{f*;g}&{h*}}, {{f*;g}&{h*}&{{a&&d};{e* & {b*;c}}}}
run 0 $x '{a;[*]}[]->b' 'Gb | !a' {a;(b*;c*;([*0]+{d;e}))*}!, {a;{b|c|{d;e}}*}!
run 0 $x '{[*];a}[]->b' 'G(b | !a)' {a&b&c*}|->!Xb, (X!b | !(a & b)) & (!(a & b) | !c | X(!c R !b))
run 0 $x '{a;b;[*]}[]->c' '!a | X(!b | Gc)' {[*]}[]->b, Gb
run 0 $x '{a;a;[*]}[]->c' '!a | X(!a | Gc)' {a;[*]}[]->b, Gb | !a
run 0 $x '{s[*]}[]->b' 'b W !s' {[*];a}[]->b, G(b | !a)
run 0 $x '{s[+]}[]->b' 'b W !s' {a;b;[*]}[]->c, !a | X(!b | Gc)
run 0 $x '{s[*2..]}[]->b' '!s | X(b W !s)' {a;a;[*]}[]->c, !a | X(!a | Gc)
run 0 $x '{a;b*;c;d*}[]->e' '!a | X(!b R ((e & X(e W !d)) | !c))' {s[*]}[]->b, b W !s
run 0 $x '{a:b*:c:d*}[]->e' '!a | ((!c | (e W !d)) W !b)' {s[+]}[]->b, b W !s
run 0 $x '{a|b*|c|d*}[]->e' '(e | !(a | c)) & (e W !b) & (e W !d)' {s[*2..]}[]->b, !s | X(b W !s)
run 0 $x '{{[*0] | a};b;{[*0] | a};c;e[*]} []-> f' \ {a;b*;c;d*}[]->e, !a | X(!b R ((e & X(e W !d)) | !c))
'{{[*0] | a};b;{[*0] | a}} []-> X((f & X(f W !e)) | !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)
run 0 $x '{a&b&c*}<>->!Xb' '(a & b & X!b) | (a & b & c & X(c U !b))' {{[*0]|a};b;{[*0]|a};c;e[*]}[]->f,{{[*0]|a};b;{[*0]|a}}[]->X((f&X(f W !e))|!c)
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*}<>->!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 # not reduced
run 0 $x '{a;(b[*2..4];c*;([*0]+{d;e}))*}!' \ {a;(b[*2..4];c*;([*0]+{d;e}))*}!, {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]}!
run 0 $x '{((a*;b)+[*0])[*4..6]}!' '{((a*;b))[*0..6]}!' {c[*];e[*]}[]-> a, {c[*];e[*]}[]-> a
run 0 $x '{c[*];e[*]}[]-> a' '{c[*];e[*]}[]-> a' EOF
;;
esac
run 0 $x 'a R (b W G(c))' 'a R (b W G(c))' #not reduced run 0 ../reduccmp nottau.txt
run 0 ../reductaustr common.txt
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

63
src/ltltest/uwrm.test
View file

@ -1,5 +1,5 @@
#! /bin/sh #! /bin/sh
# Copyright (C) 2012 Laboratoire de Recherche et Developpement # Copyright (C) 2012, 2014 Laboratoire de Recherche et Developpement
# de l'Epita (LRDE). # de l'Epita (LRDE).
# #
# This file is part of Spot, a model checking library. # This file is part of Spot, a model checking library.
@ -22,52 +22,39 @@
# These formulas comes from an appendix of tl/tl.tex # These formulas comes from an appendix of tl/tl.tex
. ./defs || exit 1 . ./defs || exit 1
set -e set -e
equiv() cat >input.txt<<EOF
{
dst=$1
shift
for src in "$@"; do
../reduccmp "$src" "$dst"
done
}
# Equivalences with U # Equivalences with U
1 U f, Ff
equiv Ff '1 U f' !F!f, !(1 U!f), Gf
equiv Gf '!F!f' '!(1 U!f)' (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
equiv 'f W g' '(f U g) | (G f)' '(f U g) | !(1 U ! f)' \ g U (f & g), f M g
'f U (g | G f)' 'f U (g | !(1 U ! f ))' g W (f & g), (g U (f & g)) | !(1 U ! g), g U ((f & g) | !(1 U ! g)), f R g
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))'
# Equivalences with W # Equivalences with W
!G!f, !((! f) W 0), Ff
equiv Ff '!G!f' '!((! f) W 0)' 0 R f, f W 0, Gf
equiv Gf '0 R f' 'f W 0' (f W g) & (F g), (f W g) & !((! g) W 0), f U g
equiv 'f U g' '(f W g) & (F g)' '(f W g) & !((! g) W 0)' (g W (f & g)) & (F f), (g W (f & g)) & !((!f) W 0), f M g
equiv 'f M g' '(g W (f & g)) & (F f)' '(g W (f & g)) & !((!f) W 0)' g W (f & g), f R g
equiv 'f R g' 'g W (f & g)'
# Equivalences with R # 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 # Equivalences with M
f M 1, Ff
equiv Ff 'f M 1' !F!f, !((!f) M 1), Gf
equiv Gf '!F!f' '!((!f) M 1)' ((X g) M f) | g, g M (f | g), f U g
equiv 'f U g' '((X g) M f) | g' 'g M (f | g)' (f U g) | G f, ((X g) M f) | g | !((! f ) M 1), f W g
equiv 'f W g' '(f U g) | G f' '((X g) M f) | g | !((! f ) M 1)' (f M g) | G g, (f M g) | !((! g) M 1), f R g
equiv 'f R g' '(f M g) | G g' '(f M g) | !((! g) M 1)'
# Example from tl.tex # Example from tl.tex
#(((f U (Xg & f))|!(1 U !f))&(1 U Xg)) | g, f U g
EOF
# equiv 'f U g' '(((f U (Xg & f))|!(1 U !f))&(1 U Xg)) | g' run 0 ../reduccmp input.txt