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tl: add some implication-based rewritings for "<->", "->", and "xor"

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This prevents an exception from being raised if NNF is not performed
on Boolean properties and implication-based checks are used.

* NEWS: Mention the issue.
* spot/tl/simplify.cc, doc/tl/tl.tex: Add some rules.
* tests/python/ltlsimple.py: Test them.
This commit is contained in:
Alexandre Duret-Lutz 2018-08-01 15:00:45 +02:00
parent a0005cd3c9
commit 4ce0d92896
4 changed files with 113 additions and 58 deletions
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7
NEWS
View file

@ -52,6 +52,13 @@ New in spot 2.6.0.dev (not yet released)
- scc_info::split_on_sets() did not correctly register the - scc_info::split_on_sets() did not correctly register the
atomic propositions of the returned automata. atomic propositions of the returned automata.
- The spot::tl_simplifier class could raise an exception while
attempting to reduce formulas containing unsimplified <->, -> or
xor, if options nenoform_stop_on_boolean and synt_impl are both
set. (This combinations of options is not available from
command-line tools.)
New in spot 2.6 (2018-07-04) New in spot 2.6 (2018-07-04)
Command-line tools: Command-line tools:

108
doc/tl/tl.tex
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@ -1764,58 +1764,62 @@ are counted as one.
\begingroup \begingroup
\allowdisplaybreaks \allowdisplaybreaks
\begin{alignat*}{3} \begin{alignat*}{3}
\text{if~} & f\simp \NOT g && \text{~then~} & f\OR g & \equiv \1 \\ \text{if~} & f\simp \NOT g & & \text{~then~} & f\OR g & \equiv \1 \\
\text{if~} & f\simp \NOT g && \text{~then~} & f\AND g & \equiv \0 \\ \text{if~} & f\simp \NOT g & & \text{~then~} & f\AND g & \equiv \0 \\
\text{if~} & \flessg && \text{~then~} & f\OR g & \equiv f \\ \text{if~} & \flessg & & \text{~then~} & f\OR g & \equiv f \\
\text{if~} & f\simp g && \text{~then~} & f\OR g & \equiv g \\ \text{if~} & f\simp g & & \text{~then~} & f\OR g & \equiv g \\
\text{if~} & \glessf && \text{~then~} & f\AND g & \equiv g \\ \text{if~} & \glessf & & \text{~then~} & f\AND g & \equiv g \\
\text{if~} & f\simp g && \text{~then~} & f\AND g & \equiv f \\ \text{if~} & f\simp g & & \text{~then~} & f\AND g & \equiv f \\
\text{if~} & \flessg && \text{~then~} & f\U g & \equiv f \\ \text{if~} & f\simp g & & \text{~then~} & f\EQUIV g & \equiv g\IMPLIES f \\
\text{if~} & f\simp g && \text{~then~} & f\U g & \equiv g \\ \text{if~} & f\simp g & & \text{~then~} & f\IMPLIES g & \equiv \1 \\
\text{if~} & (f\U g)\Simp g && \text{~then~} & f\U g & \equiv g \\ \text{if~} & (\NOT f)\simp g & & \text{~then~} & f\XOR g & \equiv g\IMPLIES \NOT f \\
\text{if~} & (\NOT f)\simp g && \text{~then~} & f\U g & \equiv \F g \\ \text{if~} & f\simp\NOT g & & \text{~then~} & f\XOR g & \equiv (\NOT g)\IMPLIES f \\
\text{if~} & g\simp e && \text{~then~} & e\U g & \equiv \F g \\ \text{if~} & \flessg & & \text{~then~} & f\U g & \equiv f \\
\text{if~} & f\simp g && \text{~then~} & f\U (g \U h) & \equiv g \U h \\ \text{if~} & f\simp g & & \text{~then~} & f\U g & \equiv g \\
\text{if~} & f\simp g && \text{~then~} & f\U (g \W h) & \equiv g \W h \\ \text{if~} & (f\U g)\Simp g & & \text{~then~} & f\U g & \equiv g \\
\text{if~} & g\simp f && \text{~then~} & f\U (g \U h) & \equiv f \U h \\ \text{if~} & (\NOT f)\simp g & & \text{~then~} & f\U g & \equiv \F g \\
\text{if~} & f\simp h && \text{~then~} & f\U (g \R (h \U k)) & \equiv g \R (h \U k) \\ \text{if~} & g\simp e & & \text{~then~} & e\U g & \equiv \F g \\
\text{if~} & f\simp h && \text{~then~} & f\U (g \R (h \W k)) & \equiv g \R (h \W k) \\ \text{if~} & f\simp g & & \text{~then~} & f\U (g \U h) & \equiv g \U h \\
\text{if~} & f\simp h && \text{~then~} & f\U (g \M (h \U k)) & \equiv g \M (h \U k) \\ \text{if~} & f\simp g & & \text{~then~} & f\U (g \W h) & \equiv g \W h \\
\text{if~} & f\simp h && \text{~then~} & f\U (g \M (h \W k)) & \equiv g \M (h \W k) \\ \text{if~} & g\simp f & & \text{~then~} & f\U (g \U h) & \equiv f \U h \\
\text{if~} & f\simp h && \text{~then~} & (f\U g) \U h & \equiv g \U h \\ \text{if~} & f\simp h & & \text{~then~} & f\U (g \R (h \U k)) & \equiv g \R (h \U k) \\
\text{if~} & f\simp h && \text{~then~} & (f\W g) \U h & \equiv g \U h \\ \text{if~} & f\simp h & & \text{~then~} & f\U (g \R (h \W k)) & \equiv g \R (h \W k) \\
\text{if~} & g\simp h && \text{~then~} & (f\U g) \U h & \equiv (f \U g) \OR h \\ \text{if~} & f\simp h & & \text{~then~} & f\U (g \M (h \U k)) & \equiv g \M (h \U k) \\
\text{if~} & (\NOT f)\simp g && \text{~then~} & f\W g & \equiv \1 \\ \text{if~} & f\simp h & & \text{~then~} & f\U (g \M (h \W k)) & \equiv g \M (h \W k) \\
\text{if~} & \flessg && \text{~then~} & f\W g & \equiv f \\ \text{if~} & f\simp h & & \text{~then~} & (f\U g) \U h & \equiv g \U h \\
\text{if~} & f\simp g && \text{~then~} & f\W g & \equiv g \\ \text{if~} & f\simp h & & \text{~then~} & (f\W g) \U h & \equiv g \U h \\
\text{if~} & (f\W g)\Simp g && \text{~then~} & f\W g & \equiv g \\ \text{if~} & g\simp h & & \text{~then~} & (f\U g) \U h & \equiv (f \U g) \OR h \\
\text{if~} & f\simp g && \text{~then~} & f\W (g \W h) & \equiv g \W h \\ \text{if~} & (\NOT f)\simp g & & \text{~then~} & f\W g & \equiv \1 \\
\text{if~} & g\simp f && \text{~then~} & f\W (g \U h) & \equiv f \W h \\ \text{if~} & \flessg & & \text{~then~} & f\W g & \equiv f \\
\text{if~} & g\simp f && \text{~then~} & f\W (g \W h) & \equiv f \W h \\ \text{if~} & f\simp g & & \text{~then~} & f\W g & \equiv g \\
\text{if~} & f\simp h && \text{~then~} & (f\U g) \W h & \equiv g \W h \\ \text{if~} & (f\W g)\Simp g & & \text{~then~} & f\W g & \equiv g \\
\text{if~} & f\simp h && \text{~then~} & (f\W g) \W h & \equiv g \W h \\ \text{if~} & f\simp g & & \text{~then~} & f\W (g \W h) & \equiv g \W h \\
\text{if~} & g\simp h && \text{~then~} & (f\W g) \W h & \equiv (f \W g) \OR h \\ \text{if~} & g\simp f & & \text{~then~} & f\W (g \U h) & \equiv f \W h \\
\text{if~} & g\simp h && \text{~then~} & (f\U g) \W h & \equiv (f \U g) \OR h \\ \text{if~} & g\simp f & & \text{~then~} & f\W (g \W h) & \equiv f \W h \\
\text{if~} & \flessg && \text{~then~} & f\R g & \equiv f \\ \text{if~} & f\simp h & & \text{~then~} & (f\U g) \W h & \equiv g \W h \\
\text{if~} & g\simp f && \text{~then~} & f\R g & \equiv g \\ \text{if~} & f\simp h & & \text{~then~} & (f\W g) \W h & \equiv g \W h \\
\text{if~} & g\simp \NOT f && \text{~then~} & f\R g & \equiv \G g \\ \text{if~} & g\simp h & & \text{~then~} & (f\W g) \W h & \equiv (f \W g) \OR h \\
\text{if~} & u\simp g && \text{~then~} & u\R g & \equiv \G g \\ \text{if~} & g\simp h & & \text{~then~} & (f\U g) \W h & \equiv (f \U g) \OR h \\
\text{if~} & g\simp f && \text{~then~} & f\R (g \R h) & \equiv g \R h \\ \text{if~} & \flessg & & \text{~then~} & f\R g & \equiv f \\
\text{if~} & g\simp f && \text{~then~} & f\R (g \M h) & \equiv g \M h \\ \text{if~} & g\simp f & & \text{~then~} & f\R g & \equiv g \\
\text{if~} & f\simp g && \text{~then~} & f\R (g \R h) & \equiv f \R h \\ \text{if~} & g\simp \NOT f & & \text{~then~} & f\R g & \equiv \G g \\
\text{if~} & h\simp f && \text{~then~} & (f\R g) \R h & \equiv g \R h \\ \text{if~} & u\simp g & & \text{~then~} & u\R g & \equiv \G g \\
\text{if~} & h\simp f && \text{~then~} & (f\M g) \R h & \equiv g \R h \\ \text{if~} & g\simp f & & \text{~then~} & f\R (g \R h) & \equiv g \R h \\
\text{if~} & g\simp h && \text{~then~} & (f\R g) \R h & \equiv (f \AND g) \R h \\ \text{if~} & g\simp f & & \text{~then~} & f\R (g \M h) & \equiv g \M h \\
\text{if~} & g\simp h && \text{~then~} & (f\M g) \R h & \equiv (f \AND g) \R h \\ \text{if~} & f\simp g & & \text{~then~} & f\R (g \R h) & \equiv f \R h \\
\text{if~} & \flessg && \text{~then~} & f\M g & \equiv f \\ \text{if~} & h\simp f & & \text{~then~} & (f\R g) \R h & \equiv g \R h \\
\text{if~} & g\simp f && \text{~then~} & f\M g & \equiv g \\ \text{if~} & h\simp f & & \text{~then~} & (f\M g) \R h & \equiv g \R h \\
\text{if~} & g\simp \NOT f && \text{~then~} & f\M g & \equiv \0 \\ \text{if~} & g\simp h & & \text{~then~} & (f\R g) \R h & \equiv (f \AND g) \R h \\
\text{if~} & g\simp f && \text{~then~} & f\M (g \M h) & \equiv g \M h \\ \text{if~} & g\simp h & & \text{~then~} & (f\M g) \R h & \equiv (f \AND g) \R h \\
\text{if~} & f\simp g && \text{~then~} & f\M (g \M h) & \equiv f \M h \\ \text{if~} & \flessg & & \text{~then~} & f\M g & \equiv f \\
\text{if~} & f\simp g && \text{~then~} & f\M (g \R h) & \equiv f \M h \\ \text{if~} & g\simp f & & \text{~then~} & f\M g & \equiv g \\
\text{if~} & h\simp f && \text{~then~} & (f\M g) \M h & \equiv g \M h \\ \text{if~} & g\simp \NOT f & & \text{~then~} & f\M g & \equiv \0 \\
\text{if~} & h\simp f && \text{~then~} & (f\R g) \M h & \equiv g \M h \\ \text{if~} & g\simp f & & \text{~then~} & f\M (g \M h) & \equiv g \M h \\
\text{if~} & g\simp h && \text{~then~} & (f\M g) \M h & \equiv (f \AND g) \M h \\ \text{if~} & f\simp g & & \text{~then~} & f\M (g \M h) & \equiv f \M h \\
\text{if~} & f\simp g & & \text{~then~} & f\M (g \R h) & \equiv f \M h \\
\text{if~} & h\simp f & & \text{~then~} & (f\M g) \M h & \equiv g \M h \\
\text{if~} & h\simp f & & \text{~then~} & (f\R g) \M h & \equiv g \M h \\
\text{if~} & g\simp h & & \text{~then~} & (f\M g) \M h & \equiv (f \AND g) \M h \\
\end{alignat*} \end{alignat*}
\endgroup \endgroup

34
spot/tl/simplify.cc
View file

@ -1775,12 +1775,38 @@ namespace spot
trace << "bo: trying inclusion-based rules" << std::endl; trace << "bo: trying inclusion-based rules" << std::endl;
switch (o) switch (o)
{ {
case op::Xor:
case op::Equiv: case op::Equiv:
{
if (c_->implication(a, b))
return recurse(formula::Implies(b, a));
if (c_->implication(b, a))
return recurse(formula::Implies(a, b));
break;
}
case op::Implies: case op::Implies:
SPOT_UNIMPLEMENTED(); {
break; if (c_->implication(a, b))
return formula::tt();
break;
}
case op::Xor:
{
// if (!a)->b then a xor b = b->!a = a->!b
if (c_->implication_neg(a, b, false))
{
if (b.is(op::Not))
return recurse(formula::Implies(a, b[0]));
return recurse(formula::Implies(b, formula::Not(a)));
}
// if a->!b then a xor b = (!b)->a = (!a)->b
if (c_->implication_neg(a, b, true))
{
if (b.is(op::Not))
return recurse(formula::Implies(b[0], a));
return recurse(formula::Implies(formula::Not(a), b));
}
break;
}
case op::U: case op::U:
// if a => b, then a U b = b // if a => b, then a U b = b
if (c_->implication(a, b)) if (c_->implication(a, b))

22
tests/python/ltlsimple.py
View file

@ -1,6 +1,6 @@
# -*- mode: python; coding: utf-8 -*- # -*- mode: python; coding: utf-8 -*-
# Copyright (C) 2009, 2010, 2012, 2015 Laboratoire de Recherche et Développement # Copyright (C) 2009, 2010, 2012, 2015, 2018 Laboratoire de Recherche et
# de l'Epita (LRDE). # Développement de l'Epita (LRDE).
# Copyright (C) 2003, 2004 Laboratoire d'Informatique de Paris 6 (LIP6), # Copyright (C) 2003, 2004 Laboratoire d'Informatique de Paris 6 (LIP6),
# département Systemes Répartis Coopératifs (SRC), Université Pierre # département Systemes Répartis Coopératifs (SRC), Université Pierre
# et Marie Curie. # et Marie Curie.
@ -116,3 +116,21 @@ Default for shell: echo 'a U (b U "$strange[0]=name")' | ...
LBT for shell: echo 'U "a" U "b" "$strange[0]=name"' | ... LBT for shell: echo 'U "a" U "b" "$strange[0]=name"' | ...
Default for CSV: ...,"a U (b U ""$strange[0]=name"")",... Default for CSV: ...,"a U (b U ""$strange[0]=name"")",...
Wring, centered: ~~~~~(a=1) U ((b=1) U ("$strange[0]=name"=1))~~~~~""" Wring, centered: ~~~~~(a=1) U ((b=1) U ("$strange[0]=name"=1))~~~~~"""
opt = spot.tl_simplifier_options(False, True, True,
True, True, True,
False, False, False)
for (input, output) in [('(a&b)<->b', 'b->(a&b)'),
('b<->(a&b)', 'b->(a&b)'),
('(a&b)->b', '1'),
('b->(a&b)', 'b->(a&b)'),
('(!(a&b)) xor b', 'b->(a&b)'),
('(a&b) xor !b', 'b->(a&b)'),
('b xor (!(a&b))', 'b->(a&b)'),
('!b xor (a&b)', 'b->(a&b)')]:
f = spot.tl_simplifier(opt).simplify(input)
print(input, f, output)
assert(f == output)
assert(spot.are_equivalent(input, output))