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Implement star-normal-form rewriting.

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* src/ltlvisit/snf.cc, src/ltlvisit/snf.hh: New files.
* src/ltlvisit/Makefile.am: Distribute them.
* src/ltlvisit/simplify.cc, src/ltlvisit/simplify.hh: Call snf(f) for
all f[*].
* src/ltltest/reduccmp.test: Test it.
* doc/tl/tl.tex, doc/tl/tl.bib: Document it.
This commit is contained in:
Alexandre Duret-Lutz 2012-04-25 18:50:31 +02:00
parent e7cf7b422d
commit 6eb830c8ae
8 changed files with 327 additions and 10 deletions
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9
doc/tl/tl.bib
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@ -28,6 +28,15 @@
month = jul
}
@Article{ bruggeman.96.tcs,
author = {Anne Br{\"u}ggemann-Klein},
title = {Regular Expressions into Finite Automata},
journal = {Theoretical Computer Science},
year = {1996},
volume = {120},
pages = {87--98}
}
@InProceedings{ cerna.03.mfcs,
author = {Ivana {\v{C}}ern{\'a} and Radek Pel{\'a}nek},
title = {Relating Hierarchy of Temporal Properties to Model

24
doc/tl/tl.tex
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@ -1407,6 +1407,30 @@ SERE.
\sere{r_1\FUSION b_1}\AND \sere{r_2\FUSION b_2} &\equiv \sere{r_1\ANDALT r_2}\FUSION\sere{b_1\AND b_2} \\
\end{align*}
Stared subformul\ae{} are rewritten in Star Normal
Form~\cite{bruggeman.96.tcs} with:
\[r\STAR{\mvar{0}..\mvar{j}} \equiv r^\circ\STAR{\mvar{0}..\mvar{j}} \]
where $r^\circ$ is recursively defined as follows:
\begin{align*}
r^\circ &= r\text{~if~} \varepsilon\not\VDash r \\
\eword^\circ &= \0 &
(r_1\CONCAT r_2)^\circ &= r_1^\circ\OR r_2^\circ \text{~if~} \varepsilon\VDash r_1\text{~and~}\varepsilon\VDash r_2\\
r\STAR{\mvar{0}..\mvar{j}}^\circ &= r^\circ &
(r_1\AND r_2)^\circ &= r_1^\circ\OR r_2^\circ \text{~if~} \varepsilon\VDash r_1\text{~and~}\varepsilon\VDash r_2\\
(r_1\OR r_2)^\circ &= r_1^\circ \OR r_2^\circ &
(r_1\ANDALT r_2)^\circ &= r_1 \ANDALT r_2
\end{align*}
Note: the original SNF definition~\cite{bruggeman.96.tcs} does not
include \samp{$\FUSION$}, \samp{$\AND$}, and \samp{$\ANDALT$}
operators, and it guarantees that $\forall r,\,\varepsilon\not\VDash
r^\circ$ because $r^\circ$ is stripping all the stars and empty words
that occur in $r$. For instance $\sere{a\STAR{}\CONCAT
b\STAR{}\CONCAT\sere{\1\OR c}}^\circ\STAR{} = \sere{a\OR b\OR
c}\STAR{}$. Our extended definition still respects this property in
presence of \samp{$\FUSION$} and \samp{$\AND$} operators, but
unfortunately not when the \samp{$\ANDALT$} operator is used.
\subsection{Simplifications for Eventual and Universal Formul\ae}
\label{sec:eventunivrew}

5
src/ltltest/reduccmp.test
View file

@ -291,6 +291,11 @@ for x in ../reduccmp ../reductaustr; do
run 0 $x '{{a;b*;c}&{d;e*}&{f*;g}&{h*}} <>-> x' \
'{{f*;g}&{h*}&{{a&&d};{e* & {b*;c}}}} <>-> x'
run 0 $x '{a&b&c*}|->!Xb' '{(a&&b)|((a&&b):c*)}|-> X!b'
run 0 $x '{a;(b*;c*;([*0]+{d;e}))*}!' '{a;{b|c|{d;e}}*}!'
# 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]}!'
;;
esac

9
src/ltlvisit/Makefile.am
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@ -1,7 +1,8 @@
## Copyright (C) 2010, 2011 Laboratoire de Recherche et Developpement de
## l'Epita (LRDE).
## -*- coding: utf-8 -*-
## Copyright (C) 2010, 2011, 2012 Laboratoire de Recherche et
## Developpement de l'Epita (LRDE).
## Copyright (C) 2004, 2005, 2006 Laboratoire d'Informatique de Paris 6 (LIP6),
## département Systèmes Répartis Coopératifs (SRC), Université Pierre
## département Systèmes Répartis Coopératifs (SRC), Université Pierre
## et Marie Curie.
##
## This file is part of Spot, a model checking library.
@ -42,6 +43,7 @@ ltlvisit_HEADERS = \
reduce.hh \
simpfg.hh \
simplify.hh \
snf.hh \
tostring.hh \
tunabbrev.hh
@ -62,5 +64,6 @@ libltlvisit_la_SOURCES = \
reduce.cc \
simpfg.cc \
simplify.cc \
snf.cc \
tostring.cc \
tunabbrev.cc

52
src/ltlvisit/simplify.cc
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@ -32,6 +32,7 @@
#include "ltlast/visitor.hh"
#include "ltlvisit/contain.hh"
#include "ltlvisit/tostring.hh"
#include "ltlvisit/snf.hh"
#include <cassert>
namespace spot
@ -95,6 +96,16 @@ namespace spot
old->first.second->destroy();
}
}
{
snf_cache::iterator i = snf_cache_.begin();
snf_cache::iterator end = snf_cache_.end();
while (i != end)
{
snf_cache::iterator old = i++;
old->second->destroy();
old->first->destroy();
}
}
dict->unregister_all_my_variables(this);
}
@ -184,8 +195,8 @@ namespace spot
break;
}
case multop::AndNLM:
case multop::AndRat:
case multop::OrRat:
case multop::AndRat:
case multop::OrRat:
case multop::Concat:
case multop::Fusion:
assert(!"Unsupported operator");
@ -327,11 +338,18 @@ namespace spot
simplified_[orig->clone()] = simplified->clone();
}
const formula*
star_normal_form(const formula* f)
{
return ltl::star_normal_form(f, &snf_cache_);
}
private:
f2b_map as_bdd_;
f2f_map simplified_;
f2f_map nenoform_;
syntimpl_cache_t syntimpl_;
snf_cache snf_cache_;
};
@ -437,11 +455,10 @@ namespace spot
void
visit(bunop* bo)
{
// !(a*) is not simplified, whatever that means
// !(a*) should never occur.
assert(!negated_);
result_ = bunop::instance(bo->op(), recurse_(bo->child(), false),
bo->min(), bo->max());
if (negated_)
result_ = unop::instance(unop::Not, result_);
}
formula* equiv_or_xor(bool equiv, formula* f1, formula* f2)
@ -1002,8 +1019,23 @@ namespace spot
void
visit(bunop* bo)
{
result_ = bunop::instance(bo->op(), recurse(bo->child()),
bo->min(), bo->max());
bunop::type op = bo->op();
unsigned min = bo->min();
formula* h = recurse(bo->child());
switch (op)
{
case bunop::Star:
if (h->accepts_eword())
min = 0;
if (min == 0)
{
const formula* s = c_->star_normal_form(h);
h->destroy();
h = const_cast<formula*>(s);
}
result_ = bunop::instance(op, h, min, bo->max());
break;
}
}
void
@ -3724,6 +3756,12 @@ namespace spot
return cache_->as_bdd(f);
}
const formula*
ltl_simplifier::star_normal_form(const formula* f)
{
return cache_->star_normal_form(f);
}
bdd_dict*
ltl_simplifier::get_dict() const
{

3
src/ltlvisit/simplify.hh
View file

@ -132,6 +132,9 @@ namespace spot
/// Return the bdd_dict used.
bdd_dict* get_dict() const;
/// Cached version of spot::ltl::star_normal_form().
const formula* star_normal_form(const formula* f);
private:
ltl_simplifier_cache* cache_;
// Copy disallowed.

175
src/ltlvisit/snf.cc Normal file
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@ -0,0 +1,175 @@
// -*- coding: utf-8 -*-
// Copyright (C) 2012 Laboratoire de Recherche et Developpement
// de l'Epita (LRDE).
//
// 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 Spot; see the file COPYING. If not, write to the Free
// Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
// 02111-1307, USA.
#include "snf.hh"
#include "ltlast/allnodes.hh"
#include "ltlast/visitor.hh"
#include "ltlvisit/tostring.hh"
namespace spot
{
namespace ltl
{
namespace
{
// E°
class snf_visitor: public visitor
{
formula* result_;
snf_cache* cache_;
public:
snf_visitor(snf_cache* c): cache_(c)
{
}
formula*
result() const
{
return result_;
}
void
visit(atomic_prop*)
{
assert(!"unexpected operator");
}
void
visit(constant* c)
{
assert(c == constant::empty_word_instance());
result_ = constant::false_instance();
}
void
visit(bunop* bo)
{
bunop::type op = bo->op();
switch (op)
{
case bunop::Star:
assert(bo->accepts_eword());
// Strip the star.
result_ = recurse(bo->child());
break;
}
}
void
visit(unop*)
{
assert(!"unexpected operator");
}
void
visit(binop*)
{
assert(!"unexpected operator");
}
void
visit(automatop*)
{
assert(!"unexpected operator");
}
void
visit(multop* mo)
{
multop::type op = mo->op();
switch (op)
{
case multop::And:
case multop::Or:
case multop::Fusion:
assert(!"unexpected operator");
break;
case multop::Concat:
case multop::AndNLM:
// Let F designate expressions that accept [*0],
// and G designate expressions that do not.
// (G₁;G₂;G₃)° = G₁;G₂;G₃
// (G₁;F₂;G₃)° = (G₁°);F₂;(G₃°) = G₁;F₂;G₃
// because there is nothing to do recursively on a G.
//
// AndNLM can be dealt with similarly.
//
// This case is already handled in recurse().
// if we reach this switch, we only have to
// deal with...
//
// (F₁;F₂;F₃)° = (F₁°)|(F₂°)|(F₃°)
// (F₁&F₂&F₃)° = (F₁°)|(F₂°)|(F₃°)
// so we fall through to the OrRat case...
case multop::OrRat:
assert(mo->accepts_eword());
{
unsigned s = mo->size();
multop::vec* v = new multop::vec;
v->reserve(s);
for (unsigned pos = 0; pos < s; ++pos)
v->push_back(recurse(mo->nth(pos)));
result_ = multop::instance(multop::OrRat, v);
}
break;
case multop::AndRat:
// FIXME: Can we deal with AndRat in a better way
// when it accepts [*0].
result_ = mo->clone();
break;
}
}
formula*
recurse(formula* f)
{
if (!f->accepts_eword())
return f->clone();
if (cache_)
{
snf_cache::const_iterator i = cache_->find(f);
if (i != cache_->end())
return i->second->clone();
}
f->accept(*this);
if (cache_)
(*cache_)[f->clone()] = result_->clone();
return result_;
}
};
}
formula*
star_normal_form(const formula* sere, snf_cache* cache)
{
snf_visitor v(cache);
return v.recurse(const_cast<formula*>(sere));
}
}
}

60
src/ltlvisit/snf.hh Normal file
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@ -0,0 +1,60 @@
// -*- coding: utf-8 -*-
// Copyright (C) 2012 Laboratoire de Recherche et Developpement
// de l'Epita (LRDE).
//
// 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 Spot; see the file COPYING. If not, write to the Free
// Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
// 02111-1307, USA.
#ifndef SPOT_LTLVISIT_SNF_HH
#define SPOT_LTLVISIT_SNF_HH
#include "ltlast/formula.hh"
#include "misc/hash.hh"
namespace spot
{
namespace ltl
{
typedef Sgi::hash_map<const formula*, const formula*,
ptr_hash<formula> > snf_cache;
/// Helper to rewrite a sere in Star Normal Form.
///
/// This should only be called on children of a Star operator. It
/// corresponds to the E° operation defined in the following
/// paper.
///
/// \verbatim
/// @Article{ bruggeman.96.tcs,
/// author = {Anne Br{\"u}ggemann-Klein},
/// title = {Regular Expressions into Finite Automata},
/// journal = {Theoretical Computer Science},
/// year = {1996},
/// volume = {120},
/// pages = {87--98}
/// }
/// \endverbatim
///
/// \param sere the SERE to rewrite
/// \param cache an optional cache
formula* star_normal_form(const formula* sere,
snf_cache* cache = 0);
}
}
#endif // SPOT_LTLVISIT_SNF_HH