Commit 0d9cc29b authored by Alexandre Duret-Lutz's avatar Alexandre Duret-Lutz

tl: eight new simplification rules

* NEWS, doc/tl/tl.tex: Document the rules.
* spot/tl/simplify.cc: Implement them.
* tests/core/reduccmp.test: Test them.
* tests/core/det.test, tests/core/ltl2tgba2.test,
tests/python/stutter-inv.ipynb, tests/core/385.test: Adjust.
parent d244ff54
......@@ -112,13 +112,21 @@ New in spot 2.7.5.dev (not yet released)
- spot::relabel_apply() makes it easier to reverse the effect
of spot::relabel() or spot::relabel_bse() on formula.
- The LTL simplifier learned the following optional rules:
- The LTL simplifier learned the following rules:
F(G(a | Fb)) = FGa | GFb (if option "favor_event_univ")
G(F(a | Gb)) = GFa | FGb (if option "favor_event_univ")
F(G(a & Fb) = FGa & GFb (unless option "reduce_size_strictly")
G(F(a & Gb)) = GFa & FGb (unless option "reduce_size_strictly")
GF(f) = GF(dnf(f)) (unless option "reduce_size_strictly")
FG(f) = FG(cnf(f)) (unless option "reduce_size_strictly")
(f & g) R h = f R h if h implies g
(f & g) M h = f M h if h implies g
(f | g) W h = f W h if g implies h
(f | g) U h = f U h if g implies h
Gf | F(g & eventual) = f W (g & eventual) if !f implies g
Ff & G(g | universal) = f M (g | universal) if f implies !g
f U (g & eventual) = F(g & eventual) if !f implies g
f R (g | universal) = G(g | universal) if f implies !g
- cleanup_parity() and colorize_parity() were cleaned up a bit,
resulting in fewer colors used in some cases. In particular,
......
......@@ -1857,6 +1857,7 @@ are counted as one.
\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~} & g\simp h & & \text{~then~} & (f\OR g) \U h & \equiv f \U h \\
\text{if~} & (\NOT f)\simp g & & \text{~then~} & f\W g & \equiv \1 \\
\text{if~} & \flessg & & \text{~then~} & f\W g & \equiv f \\
\text{if~} & f\simp g & & \text{~then~} & f\W g & \equiv g \\
......@@ -1868,6 +1869,7 @@ are counted as one.
\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 h & & \text{~then~} & (f\OR g) \W h & \equiv f \W h \\
\text{if~} & \flessg & & \text{~then~} & f\R g & \equiv f \\
\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 \\
......@@ -1879,6 +1881,7 @@ are counted as one.
\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~} & h\simp g & & \text{~then~} & (f\AND g) \R h & \equiv f \R h \\
\text{if~} & \flessg & & \text{~then~} & f\M g & \equiv f \\
\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 \\
......@@ -1888,6 +1891,7 @@ are counted as one.
\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 \\
\text{if~} & h\simp g & & \text{~then~} & (f\AND g) \M h & \equiv f \M h \\
\end{alignat*}
\endgroup
......@@ -1895,6 +1899,17 @@ Many of the above rules were collected from the
literature~\cite{somenzi.00.cav,tauriainen.03.tr,babiak.12.tacas} and
sometimes generalized to support operators such as $\M$ and $\W$.
The following rules mix implication-based checks with formulas that
are pure eventualities ($e$) or that are purely universal ($u$).
\allowdisplaybreaks
\begin{alignat*}{3}
\text{if~} & (\NOT f)\simp g & & \text{~then~} & f \U (g \AND e) & \equiv \F(g \AND e) \\
\text{if~} & f\simp \NOT g & & \text{~then~} & f \R (g \OR u) & \equiv \G(g \OR e) \\
\text{if~} & (\NOT f) \simp g & & \text{~then~} & \G(f) \OR \F(g \AND e) & \equiv f \W (g \AND e) \\
\text{if~} & f \simp\NOT g & & \text{~then~} & \F(f) \AND \G(g \OR e) & \equiv f \M (g \OR e) \\
\end{alignat*}
\appendix
\chapter{Defining LTL with only one of $\U$, $\W$, $\R$, or $\M$}
\label{sec:ltl-equiv}
......
......@@ -2160,6 +2160,31 @@ namespace spot
// if c => b, then (a U c) U b = (a U c) | b
if (a.is(op::U) && c_->implication(a[1], b))
return recurse(formula::Or({a, b}));
// if g => h, then (f|g) U h = f U h
if (a.is(op::Or))
{
unsigned n = a.size();
for (unsigned child = 0; child < n; ++child)
if (c_->implication(a[child], b))
return recurse(formula::U(a.all_but(child), b));
}
// a U (b & e) = F(b & e) if !b => a
if (b.is(op::And))
for (formula c: b)
if (c.is_eventual())
{
// We know there is one pure eventuality
// formula but we might have more. So lets
// extract everything else.
vec rest;
rest.reserve(c.size());
for (formula cc: b)
if (!cc.is_eventual())
rest.emplace_back(cc);
if (c_->implication_neg(formula::And(rest), a, false))
return recurse(formula::F(b));
break;
}
break;
case op::R:
......@@ -2198,6 +2223,31 @@ namespace spot
return recurse(formula::R(ac, b));
}
}
// if h => g, then (f&g) R h = f R h
if (a.is(op::And))
{
unsigned n = a.size();
for (unsigned child = 0; child < n; ++child)
if (c_->implication(b, a[child]))
return recurse(formula::R(a.all_but(child), b));
}
// a R (b | u) = G(b | u) if b => !a
if (b.is(op::Or))
for (formula c: b)
if (c.is_universal())
{
// We know there is one purely universal
// formula but we might have more. So lets
// extract everything else.
vec rest;
rest.reserve(c.size());
for (formula cc: b)
if (!cc.is_universal())
rest.emplace_back(cc);
if (c_->implication_neg(formula::Or(rest), a, true))
return recurse(formula::G(b));
break;
}
break;
case op::W:
......@@ -2234,6 +2284,14 @@ namespace spot
// if c => b, then (a U c) W b = (a U c) | b
if (a.is(op::U, op::W) && c_->implication(a[1], b))
return recurse(formula::Or({a, b}));
// if g => h, then (f|g) W h = f M h
if (a.is(op::Or))
{
unsigned n = a.size();
for (unsigned child = 0; child < n; ++child)
if (c_->implication(a[child], b))
return recurse(formula::W(a.all_but(child), b));
}
break;
case op::M:
......@@ -2265,6 +2323,14 @@ namespace spot
return
recurse(formula::M(formula::And({a[0], a[1]}),
b));
// if h => g, then (f&g) M h = f M h
if (a.is(op::And))
{
unsigned n = a.size();
for (unsigned child = 0; child < n; ++child)
if (c_->implication(b, a[child]))
return recurse(formula::M(a.all_but(child), b));
}
break;
default:
......@@ -2680,6 +2746,7 @@ namespace spot
// F(a) & (a M b) = a M b
// F(b) & (a W b) = a U b
// F(b) & (a U b) = a U b
// F(c) & G(phi | e) = c M (phi | e) if c => !phi.
typedef std::unordered_map<formula, vec::iterator> fmap_t;
fmap_t uwmap; // associates "b" to "a U b" or "a W b"
fmap_t rmmap; // associates "a" to "a R b" or "a M b"
......@@ -2762,6 +2829,43 @@ namespace spot
assert(j->second->is(op::M));
}
}
if (opt_.synt_impl | opt_.containment_checks)
{
// if the input looks like o1|u1|u2|o2,
// return o1 | o2. The input must have at
// least on universal formula.
auto extract_not_un =
[&](formula f) {
if (f.is(op::Or))
for (auto u: f)
if (u.is_universal())
{
vec phi;
phi.reserve(f.size());
for (auto uu: f)
if (!uu.is_universal())
phi.push_back(uu);
return formula::Or(phi);
}
return formula(nullptr);
};
// F(c) & G(phi | e) = c M (phi | e) if c => !phi.
for (auto in_g = s.res_G->begin();
in_g != s.res_G->end();)
{
if (formula phi = extract_not_un(*in_g))
if (c_->implication_neg(phi, c, true))
{
s.res_other->push_back(formula::M(c,
*in_g));
in_g = s.res_G->erase(in_g);
superfluous = true;
continue;
}
++in_g;
}
}
if (superfluous)
f = nullptr;
}
......@@ -3273,6 +3377,7 @@ namespace spot
// G(a) | (a W b) = a W b
// G(b) | (a R b) = a R b.
// G(b) | (a M b) = a R b.
// G(c) | F(phi & e) = c W (phi & e) if !c => phi.
typedef std::unordered_map<formula, vec::iterator> fmap_t;
fmap_t uwmap; // associates "a" to "a U b" or "a W b"
fmap_t rmmap; // associates "b" to "a R b" or "a M b"
......@@ -3355,6 +3460,43 @@ namespace spot
assert(j->second->is(op::R));
}
}
if (opt_.synt_impl | opt_.containment_checks)
{
// if the input looks like o1&e1&e2&o2,
// return o1 & o2. The input must have at
// least on eventual formula.
auto extract_not_ev =
[&](formula f) {
if (f.is(op::And))
for (auto e: f)
if (e.is_eventual())
{
vec phi;
phi.reserve(f.size());
for (auto ee: f)
if (!ee.is_eventual())
phi.push_back(ee);
return formula::And(phi);
}
return formula(nullptr);
};
// G(c) | F(phi & e) = c W (phi & e) if !c => phi.
for (auto in_f = s.res_F->begin();
in_f != s.res_F->end();)
{
if (formula phi = extract_not_ev(*in_f))
if (c_->implication_neg(c, phi, false))
{
s.res_other->push_back(formula::W(c,
*in_f));
in_f = s.res_F->erase(in_f);
superfluous = true;
continue;
}
++in_f;
}
}
if (superfluous)
f = nullptr;
}
......
......@@ -36,7 +36,7 @@ EOF
# Some of the following are still not optimal.
cat >expected <<EOF
1,GF(!a | !d | !e)
6,G(Gc | F(a | (!c & F!e)))
6,G(Fa | (c W (!c & F!e)))
2,Ge | G(Fd & FGe & Fc)
1,F(G(Fb & FGc) | Ge)
4,G(F!d | (!c & G!b))
......
......@@ -26,7 +26,7 @@ cat >formulas <<'EOF'
1,5,X(((a & b) R (!a U !c)) R b)
1,8,XXG(Fa U Xb)
1,5,(!a M !b) W F!c
1,3,(b & Fa & GFc) R a
1,3,(b & GFc) R a
1,2,(a R (b W a)) W G(!a M (b | c))
1,11,(Fa W b) R (!a | Fc)
1,6,X(G(!a M !b) | G(a | G!a))
......
......@@ -77,7 +77,7 @@ dac-patterns,37, 4,56, 4,56, 4,56, 4,56
dac-patterns,38, 4,56, 4,56, 4,56, 4,56
dac-patterns,39, 4,112, 4,112, 4,112, 4,112
dac-patterns,40, 3,88, 3,88, 3,88, 3,88
dac-patterns,41, 6,54, 6,54, 7,56, 7,56
dac-patterns,41, 4,32, 4,32, 4,32, 4,32
dac-patterns,42, 6,96, 6,96, 6,96, 6,96
dac-patterns,43, 5,80, 5,80, 5,80, 5,80
dac-patterns,44, 10,300, 10,300, 13,372, 13,372
......
......@@ -298,17 +298,36 @@ a W ((a&b) W c), a W c
(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
(x M y) M y, x M y
(x R y) R y, x R y
(x & y) M y, x M y
(x & y) R y, x R y
(a R (b&c)) R (c), (a&b) R c
(a M (b&c)) R (c), (a&b) 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 M (b&c)) M (c), (a&b) 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
!x U (x & Fa), F(x & Fa)
!x R (x | Ga), G(x | Ga)
!x U ((x | c) & Fa & Fb), F((x | c) & Fa & Fb)
!x R ((x & c) | Ga | Gb), G((x & c) | Ga | Gb)
G!f | F((f|g) & Fa & Fb), !f W ((f | g) & Fa & Fb)
F!f & G((f&g) | Ga | Gb), !f M ((f & g) | Ga | Gb)
(x|b) W (x|a), b W (x|a)
(x|b) U (x|a), b U (x|a)
!x U ((x | c) & Fa & Fb), F((x | c) & Fa & Fb)
!x R ((x & c) | Ga | Gb), G((x & c) | Ga | Gb)
# Eventuality and universality class reductions
Fa M b, Fa & b
GFa M b, GFa & b
......
......@@ -302,7 +302,7 @@
"</svg>\n"
],
"text/plain": [
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f691c29f3f0> >"
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc090629840> >"
]
},
"metadata": {},
......@@ -603,7 +603,7 @@
"</svg>\n"
],
"text/plain": [
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f691c31c360> >"
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc090629db0> >"
]
},
"metadata": {},
......@@ -812,7 +812,7 @@
"</svg>\n"
],
"text/plain": [
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f691c31c360> >"
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc090629db0> >"
]
},
"metadata": {},
......@@ -964,7 +964,7 @@
"</svg>\n"
],
"text/plain": [
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f691c29f840> >"
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc0905b5960> >"
]
},
"metadata": {},
......@@ -1062,7 +1062,7 @@
"</svg>\n"
],
"text/plain": [
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f691c29f690> >"
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc0905b5840> >"
]
},
"metadata": {},
......@@ -1272,7 +1272,7 @@
"</svg>\n"
],
"text/plain": [
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f691c29f7e0> >"
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc0905c34e0> >"
]
},
"metadata": {},
......@@ -1401,7 +1401,7 @@
"</svg>\n"
],
"text/plain": [
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f691c29f780> >"
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc0905c3570> >"
]
},
"metadata": {},
......@@ -1532,7 +1532,7 @@
"</svg>\n"
],
"text/plain": [
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f691c29f810> >"
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc0905c3f90> >"
]
},
"metadata": {},
......@@ -1792,7 +1792,7 @@
"</svg>\n"
],
"text/plain": [
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f691c23bb10> >"
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc0905c3240> >"
]
},
"metadata": {},
......@@ -2106,7 +2106,7 @@
"</svg>\n"
],
"text/plain": [
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f691c23bb10> >"
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc0905c3240> >"
]
},
"metadata": {},
......@@ -2192,7 +2192,7 @@
"G!p0 | (!p0 U (p0 & (F(p1 & XFp2) -> (!p 4 2 1\n",
"G((p0 & Fp1) -> (!(!p1 & p2 & X(!p1 U (! 4 1 1\n",
"G(p0 -> ((!(!p1 & p2 & X(!p1 U (!p1 & p3 3 0 1\n",
"G((p0 & XFp1) -> XF(p1 & Fp2)) 6 1 1\n",
"G((p0 & XFp1) -> XF(p1 & Fp2)) 4 0 1\n",
"Fp0 -> (((p1 & X(!p0 U p2)) -> X(!p0 U ( 6 2 1\n",
"G(p0 -> G((p1 & XFp2) -> X(!p2 U (p2 & F 5 0 1\n",
"G((p0 & Fp1) -> (((p2 & X(!p1 U p3)) -> 10 2 1\n",
......@@ -2318,7 +2318,7 @@
{
"data": {
"text/plain": [
"55.749128919860624"
"55.78947368421053"
]
},
"execution_count": 31,
......
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