Commit 45ba8c3e authored by Alexandre Duret-Lutz's avatar Alexandre Duret-Lutz

Add 11 implication-based simplification rules for U,W,R,M.

* src/ltlvisit/simplify.cc: Add them.
* src/ltltest/reduccmp.test: Check them.
* doc/tl/tl.tex: Document them.
parent f711f9d0
......@@ -1599,12 +1599,19 @@ option is set (otherwise the rewriting rule is not applied).
\text{if}& f\simp h &\text{then}& f\U (g \R (h \W k)) &\equiv g \R (h \W k) \\
\text{if}& f\simp h &\text{then}& f\U (g \M (h \U k)) &\equiv g \M (h \U k) \\
\text{if}& f\simp h &\text{then}& f\U (g \M (h \W k)) &\equiv g \M (h \W k) \\
\text{if}& f\simp h &\text{then}& (f\U g) \U h &\equiv g \U h \\
\text{if}& f\simp h &\text{then}& (f\W g) \U h &\equiv g \U h \\
\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 &\equiv g \\
\text{if}& (f\W g)\Simp g &\text{then}& f\W g &\equiv g \\
\text{if}& (\NOT f)\simp g &\text{then}& f\W g &\equiv \1 \\
\text{if}& f\simp g &\text{then}& f\W (g \W h) &\equiv g \W h \\
\text{if}& g\simp f &\text{then}& f\W (g \U h) &\equiv f \W h \\
\text{if}& g\simp f &\text{then}& f\W (g \W h) &\equiv f \W h \\
\text{if}& f\simp h &\text{then}& (f\U g) \W h &\equiv g \W h \\
\text{if}& f\simp h &\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 h &\text{then}& (f\U g) \W h &\equiv (f \U g) \OR h \\
\text{if}& g\simp f &\text{then}& f\R g &\equiv g \\
\text{if}& g\simp \NOT f &\text{then}& f\R g &\equiv \G g \\
\text{if}& g\simp f &\text{then}& f\R (g \R h) &\equiv g \R h \\
......@@ -1612,12 +1619,16 @@ option is set (otherwise the rewriting rule is not applied).
\text{if}& f\simp g &\text{then}& f\R (g \R h) &\equiv f \R h \\
\text{if}& h\simp f &\text{then}& (f\R g) \R h &\equiv g \R h \\
\text{if}& h\simp f &\text{then}& (f\M 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 h &\text{then}& (f\M g) \R h &\equiv (f \AND g) \R h \\
\text{if}& g\simp f &\text{then}& f\M g &\equiv g \\
\text{if}& g\simp \NOT f &\text{then}& f\M g &\equiv \0 \\
\text{if}& g\simp f &\text{then}& f\M (g \M h) &\equiv 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{array}
\end{equation*}
......
......@@ -229,6 +229,25 @@ for x in ../reduccmp ../reductaustr; do
run 0 $x '(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
# Eventuality and universality class reductions
run 0 $x 'Fa M b' 'Fa & b'
run 0 $x 'GFa M b' 'GFa & b'
......
......@@ -1848,6 +1848,29 @@ namespace spot
}
}
}
// if a => b, then (a U c) U b = c U b
// if a => b, then (a W c) U b = c U b
// if c => b, then (a U c) U b = (a U c) | b
if (const binop* bo = is_binop(a))
{
if ((bo->op() == binop::U || bo->op() == binop::W)
&& c_->implication(bo->first(), b))
{
result_ = recurse_destroy
(binop::instance(binop::U,
bo->second()->clone(),
b));
a->destroy();
return;
}
else if ((bo->op() == binop::U)
&& c_->implication(bo->second(), b))
{
result_ = recurse_destroy
(multop::instance(multop::Or, a, b));
return;
}
}
break;
case binop::R:
......@@ -1889,20 +1912,35 @@ namespace spot
return;
}
}
if (a->kind() == formula::BinOp)
// if b => a, then (a R c) R b = c R b
// if b => a, then (a M c) R b = c R b
// if c => b, then (a R c) R b = (a & c) R b
// if c => b, then (a M c) R b = (a & c) R b
if (const binop* bo = is_binop(a))
{
// if b => a then (a R c) R b = c R b
// if b => a then (a M c) R b = c R b
const binop* bo = static_cast<const binop*>(a);
if ((bo->op() == binop::R || bo->op() == binop::M)
&& c_->implication(b, bo->first()))
if (bo->op() == binop::M || bo->op() == binop::R)
{
result_ = recurse_destroy
(binop::instance(binop::R,
bo->second()->clone(),
b));
a->destroy();
return;
if (c_->implication(b, bo->first()))
{
result_ = recurse_destroy
(binop::instance(binop::R,
bo->second()->clone(),
b));
a->destroy();
return;
}
else if (c_->implication(bo->second(), b))
{
const formula* ac =
multop::instance(multop::And,
bo->first()->clone(),
bo->second()->clone());
a->destroy();
result_ = recurse_destroy
(binop::instance(binop::R, ac, b));
return;
}
}
}
......@@ -1954,6 +1992,31 @@ namespace spot
return;
}
}
// if a => b, then (a U c) W b = c W b
// if a => b, then (a W c) W b = c W b
// if c => b, then (a W c) W b = (a W c) | b
// if c => b, then (a U c) W b = (a U c) | b
if (const binop* bo = is_binop(a))
{
if ((bo->op() == binop::U || bo->op() == binop::W))
{
if (c_->implication(bo->first(), b))
{
result_ = recurse_destroy
(binop::instance(binop::W,
bo->second()->clone(),
b));
a->destroy();
return;
}
else if (c_->implication(bo->second(), b))
{
result_ = recurse_destroy
(multop::instance(multop::Or, a, b));
return;
}
}
}
break;
case binop::M:
......@@ -1996,11 +2059,13 @@ namespace spot
return;
}
}
if (a->kind() == formula::BinOp)
// if b => a, then (a R c) M b = c M b
// if b => a, then (a M c) M b = c M b
// if c => b, then (a M c) M b = (a & c) M b
if (const binop* bo = is_binop(a))
{
// if b => a then (a M c) M b = c M b
const binop* bo = static_cast<const binop*>(a);
if (bo->op() == binop::M
if ((bo->op() == binop::M || bo->op() == binop::R)
&& c_->implication(b, bo->first()))
{
result_ = recurse_destroy
......@@ -2010,6 +2075,18 @@ namespace spot
a->destroy();
return;
}
else if ((bo->op() == binop::M)
&& c_->implication(bo->second(), b))
{
const formula* ac =
multop::instance(multop::And,
bo->first()->clone(),
bo->second()->clone());
a->destroy();
result_ = recurse_destroy
(binop::instance(binop::M, ac, b));
return;
}
}
break;
}
......
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