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.
This commit is contained in:
Alexandre Duret-Lutz
parent
d244ff5432
commit
0d9cc29b46
8 changed files with 203 additions and 19 deletions
10
NEWS
10
NEWS
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@ -112,13 +112,21 @@ New in spot 2.7.5.dev (not yet released)
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- spot::relabel_apply() makes it easier to reverse the effect
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of spot::relabel() or spot::relabel_bse() on formula.
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- The LTL simplifier learned the following optional rules:
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- The LTL simplifier learned the following rules:
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F(G(a | Fb)) = FGa | GFb (if option "favor_event_univ")
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G(F(a | Gb)) = GFa | FGb (if option "favor_event_univ")
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F(G(a & Fb) = FGa & GFb (unless option "reduce_size_strictly")
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G(F(a & Gb)) = GFa & FGb (unless option "reduce_size_strictly")
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GF(f) = GF(dnf(f)) (unless option "reduce_size_strictly")
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FG(f) = FG(cnf(f)) (unless option "reduce_size_strictly")
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(f & g) R h = f R h if h implies g
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(f & g) M h = f M h if h implies g
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(f | g) W h = f W h if g implies h
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(f | g) U h = f U h if g implies h
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Gf | F(g & eventual) = f W (g & eventual) if !f implies g
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Ff & G(g | universal) = f M (g | universal) if f implies !g
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f U (g & eventual) = F(g & eventual) if !f implies g
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f R (g | universal) = G(g | universal) if f implies !g
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- cleanup_parity() and colorize_parity() were cleaned up a bit,
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resulting in fewer colors used in some cases. In particular,
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@ -1857,6 +1857,7 @@ are counted as one.
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\text{if~} & f\simp h & & \text{~then~} & (f\U g) \U h & \equiv g \U h \\
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\text{if~} & f\simp h & & \text{~then~} & (f\W g) \U h & \equiv g \U h \\
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\text{if~} & g\simp h & & \text{~then~} & (f\U g) \U h & \equiv (f \U g) \OR h \\
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\text{if~} & g\simp h & & \text{~then~} & (f\OR g) \U h & \equiv f \U h \\
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\text{if~} & (\NOT f)\simp g & & \text{~then~} & f\W g & \equiv \1 \\
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\text{if~} & \flessg & & \text{~then~} & f\W g & \equiv f \\
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\text{if~} & f\simp g & & \text{~then~} & f\W g & \equiv g \\
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@ -1868,6 +1869,7 @@ are counted as one.
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\text{if~} & f\simp h & & \text{~then~} & (f\W g) \W h & \equiv g \W h \\
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\text{if~} & g\simp h & & \text{~then~} & (f\W g) \W h & \equiv (f \W g) \OR h \\
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\text{if~} & g\simp h & & \text{~then~} & (f\U g) \W h & \equiv (f \U g) \OR h \\
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\text{if~} & g\simp h & & \text{~then~} & (f\OR g) \W h & \equiv f \W h \\
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\text{if~} & \flessg & & \text{~then~} & f\R g & \equiv f \\
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\text{if~} & g\simp f & & \text{~then~} & f\R g & \equiv g \\
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\text{if~} & g\simp \NOT f & & \text{~then~} & f\R g & \equiv \G g \\
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@ -1879,6 +1881,7 @@ are counted as one.
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\text{if~} & h\simp f & & \text{~then~} & (f\M g) \R h & \equiv g \R h \\
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\text{if~} & g\simp h & & \text{~then~} & (f\R g) \R h & \equiv (f \AND g) \R h \\
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\text{if~} & g\simp h & & \text{~then~} & (f\M g) \R h & \equiv (f \AND g) \R h \\
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\text{if~} & h\simp g & & \text{~then~} & (f\AND g) \R h & \equiv f \R h \\
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\text{if~} & \flessg & & \text{~then~} & f\M g & \equiv f \\
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\text{if~} & g\simp f & & \text{~then~} & f\M g & \equiv g \\
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\text{if~} & g\simp \NOT f & & \text{~then~} & f\M g & \equiv \0 \\
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@ -1888,6 +1891,7 @@ are counted as one.
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\text{if~} & h\simp f & & \text{~then~} & (f\M g) \M h & \equiv g \M h \\
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\text{if~} & h\simp f & & \text{~then~} & (f\R g) \M h & \equiv g \M h \\
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\text{if~} & g\simp h & & \text{~then~} & (f\M g) \M h & \equiv (f \AND g) \M h \\
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\text{if~} & h\simp g & & \text{~then~} & (f\AND g) \M h & \equiv f \M h \\
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\end{alignat*}
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\endgroup
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@ -1895,6 +1899,17 @@ Many of the above rules were collected from the
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literature~\cite{somenzi.00.cav,tauriainen.03.tr,babiak.12.tacas} and
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sometimes generalized to support operators such as $\M$ and $\W$.
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The following rules mix implication-based checks with formulas that
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are pure eventualities ($e$) or that are purely universal ($u$).
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\allowdisplaybreaks
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\begin{alignat*}{3}
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\text{if~} & (\NOT f)\simp g & & \text{~then~} & f \U (g \AND e) & \equiv \F(g \AND e) \\
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\text{if~} & f\simp \NOT g & & \text{~then~} & f \R (g \OR u) & \equiv \G(g \OR e) \\
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\text{if~} & (\NOT f) \simp g & & \text{~then~} & \G(f) \OR \F(g \AND e) & \equiv f \W (g \AND e) \\
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\text{if~} & f \simp\NOT g & & \text{~then~} & \F(f) \AND \G(g \OR e) & \equiv f \M (g \OR e) \\
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\end{alignat*}
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\appendix
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\chapter{Defining LTL with only one of $\U$, $\W$, $\R$, or $\M$}
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\label{sec:ltl-equiv}
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@ -2160,6 +2160,31 @@ namespace spot
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// if c => b, then (a U c) U b = (a U c) | b
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if (a.is(op::U) && c_->implication(a[1], b))
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return recurse(formula::Or({a, b}));
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// if g => h, then (f|g) U h = f U h
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if (a.is(op::Or))
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{
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unsigned n = a.size();
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for (unsigned child = 0; child < n; ++child)
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if (c_->implication(a[child], b))
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return recurse(formula::U(a.all_but(child), b));
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}
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// a U (b & e) = F(b & e) if !b => a
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if (b.is(op::And))
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for (formula c: b)
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if (c.is_eventual())
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{
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// We know there is one pure eventuality
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// formula but we might have more. So lets
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// extract everything else.
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vec rest;
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rest.reserve(c.size());
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for (formula cc: b)
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if (!cc.is_eventual())
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rest.emplace_back(cc);
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if (c_->implication_neg(formula::And(rest), a, false))
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return recurse(formula::F(b));
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break;
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}
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break;
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case op::R:
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@ -2198,6 +2223,31 @@ namespace spot
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return recurse(formula::R(ac, b));
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}
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}
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// if h => g, then (f&g) R h = f R h
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if (a.is(op::And))
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{
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unsigned n = a.size();
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for (unsigned child = 0; child < n; ++child)
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if (c_->implication(b, a[child]))
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return recurse(formula::R(a.all_but(child), b));
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}
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// a R (b | u) = G(b | u) if b => !a
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if (b.is(op::Or))
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for (formula c: b)
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if (c.is_universal())
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{
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// We know there is one purely universal
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// formula but we might have more. So lets
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// extract everything else.
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vec rest;
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rest.reserve(c.size());
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for (formula cc: b)
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if (!cc.is_universal())
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rest.emplace_back(cc);
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if (c_->implication_neg(formula::Or(rest), a, true))
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return recurse(formula::G(b));
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break;
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}
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break;
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case op::W:
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@ -2234,6 +2284,14 @@ namespace spot
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// if c => b, then (a U c) W b = (a U c) | b
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if (a.is(op::U, op::W) && c_->implication(a[1], b))
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return recurse(formula::Or({a, b}));
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// if g => h, then (f|g) W h = f M h
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if (a.is(op::Or))
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{
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unsigned n = a.size();
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for (unsigned child = 0; child < n; ++child)
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if (c_->implication(a[child], b))
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return recurse(formula::W(a.all_but(child), b));
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}
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break;
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case op::M:
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@ -2265,6 +2323,14 @@ namespace spot
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return
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recurse(formula::M(formula::And({a[0], a[1]}),
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b));
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// if h => g, then (f&g) M h = f M h
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if (a.is(op::And))
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{
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unsigned n = a.size();
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for (unsigned child = 0; child < n; ++child)
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if (c_->implication(b, a[child]))
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return recurse(formula::M(a.all_but(child), b));
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}
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break;
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default:
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@ -2680,6 +2746,7 @@ namespace spot
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// F(a) & (a M b) = a M b
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// F(b) & (a W b) = a U b
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// F(b) & (a U b) = a U b
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// F(c) & G(phi | e) = c M (phi | e) if c => !phi.
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typedef std::unordered_map<formula, vec::iterator> fmap_t;
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fmap_t uwmap; // associates "b" to "a U b" or "a W b"
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fmap_t rmmap; // associates "a" to "a R b" or "a M b"
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@ -2762,6 +2829,43 @@ namespace spot
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assert(j->second->is(op::M));
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}
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}
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if (opt_.synt_impl | opt_.containment_checks)
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{
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// if the input looks like o1|u1|u2|o2,
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// return o1 | o2. The input must have at
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// least on universal formula.
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auto extract_not_un =
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[&](formula f) {
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if (f.is(op::Or))
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for (auto u: f)
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if (u.is_universal())
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{
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vec phi;
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phi.reserve(f.size());
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for (auto uu: f)
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if (!uu.is_universal())
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phi.push_back(uu);
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return formula::Or(phi);
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}
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return formula(nullptr);
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};
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// F(c) & G(phi | e) = c M (phi | e) if c => !phi.
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for (auto in_g = s.res_G->begin();
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in_g != s.res_G->end();)
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{
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if (formula phi = extract_not_un(*in_g))
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if (c_->implication_neg(phi, c, true))
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{
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s.res_other->push_back(formula::M(c,
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*in_g));
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in_g = s.res_G->erase(in_g);
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superfluous = true;
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continue;
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}
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++in_g;
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}
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}
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if (superfluous)
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f = nullptr;
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}
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@ -3273,6 +3377,7 @@ namespace spot
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// G(a) | (a W b) = a W b
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// G(b) | (a R b) = a R b.
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// G(b) | (a M b) = a R b.
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// G(c) | F(phi & e) = c W (phi & e) if !c => phi.
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typedef std::unordered_map<formula, vec::iterator> fmap_t;
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fmap_t uwmap; // associates "a" to "a U b" or "a W b"
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fmap_t rmmap; // associates "b" to "a R b" or "a M b"
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@ -3355,6 +3460,43 @@ namespace spot
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assert(j->second->is(op::R));
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}
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}
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if (opt_.synt_impl | opt_.containment_checks)
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{
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// if the input looks like o1&e1&e2&o2,
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// return o1 & o2. The input must have at
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// least on eventual formula.
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auto extract_not_ev =
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[&](formula f) {
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if (f.is(op::And))
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for (auto e: f)
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if (e.is_eventual())
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{
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vec phi;
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phi.reserve(f.size());
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for (auto ee: f)
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if (!ee.is_eventual())
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phi.push_back(ee);
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return formula::And(phi);
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}
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return formula(nullptr);
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};
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// G(c) | F(phi & e) = c W (phi & e) if !c => phi.
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for (auto in_f = s.res_F->begin();
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in_f != s.res_F->end();)
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{
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if (formula phi = extract_not_ev(*in_f))
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if (c_->implication_neg(c, phi, false))
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{
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s.res_other->push_back(formula::W(c,
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*in_f));
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in_f = s.res_F->erase(in_f);
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superfluous = true;
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continue;
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}
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++in_f;
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}
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}
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if (superfluous)
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f = nullptr;
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}
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@ -36,7 +36,7 @@ EOF
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# Some of the following are still not optimal.
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cat >expected <<EOF
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1,GF(!a | !d | !e)
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6,G(Gc | F(a | (!c & F!e)))
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6,G(Fa | (c W (!c & F!e)))
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2,Ge | G(Fd & FGe & Fc)
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1,F(G(Fb & FGc) | Ge)
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4,G(F!d | (!c & G!b))
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@ -26,7 +26,7 @@ cat >formulas <<'EOF'
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1,5,X(((a & b) R (!a U !c)) R b)
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1,8,XXG(Fa U Xb)
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1,5,(!a M !b) W F!c
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1,3,(b & Fa & GFc) R a
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1,3,(b & GFc) R a
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1,2,(a R (b W a)) W G(!a M (b | c))
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1,11,(Fa W b) R (!a | Fc)
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1,6,X(G(!a M !b) | G(a | G!a))
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@ -77,7 +77,7 @@ dac-patterns,37, 4,56, 4,56, 4,56, 4,56
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dac-patterns,38, 4,56, 4,56, 4,56, 4,56
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dac-patterns,39, 4,112, 4,112, 4,112, 4,112
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dac-patterns,40, 3,88, 3,88, 3,88, 3,88
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dac-patterns,41, 6,54, 6,54, 7,56, 7,56
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dac-patterns,41, 4,32, 4,32, 4,32, 4,32
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dac-patterns,42, 6,96, 6,96, 6,96, 6,96
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dac-patterns,43, 5,80, 5,80, 5,80, 5,80
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dac-patterns,44, 10,300, 10,300, 13,372, 13,372
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@ -298,17 +298,36 @@ a W ((a&b) W c), a W c
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(a R b) M (c&a), b M (c&a)
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(a M b) M (c&a), b M (c&a)
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(a R (b&c)) R (c), (a&b&c) R c
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(a M (b&c)) R (c), (a&b&c) R c
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(x M y) M y, x M y
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(x R y) R y, x R y
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(x & y) M y, x M y
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(x & y) R y, x R y
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(a R (b&c)) R (c), (a&b) R c
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(a M (b&c)) R (c), (a&b) R c
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# not reduced
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(a R (b&c)) M (c), (a R (b&c)) M (c)
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(a M (b&c)) M (c), (a&b&c) M c
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(a M (b&c)) M (c), (a&b) M c
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(a W (c&b)) W b, (a W (c&b)) | b
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(a U (c&b)) W b, (a U (c&b)) | b
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(a U (c&b)) U b, (a U (c&b)) | b
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# not reduced
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(a W (c&b)) U b, (a W (c&b)) U b
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!x U (x & Fa), F(x & Fa)
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!x R (x | Ga), G(x | Ga)
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!x U ((x | c) & Fa & Fb), F((x | c) & Fa & Fb)
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!x R ((x & c) | Ga | Gb), G((x & c) | Ga | Gb)
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G!f | F((f|g) & Fa & Fb), !f W ((f | g) & Fa & Fb)
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F!f & G((f&g) | Ga | Gb), !f M ((f & g) | Ga | Gb)
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(x|b) W (x|a), b W (x|a)
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(x|b) U (x|a), b U (x|a)
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!x U ((x | c) & Fa & Fb), F((x | c) & Fa & Fb)
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!x R ((x & c) | Ga | Gb), G((x & c) | Ga | Gb)
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# Eventuality and universality class reductions
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Fa M b, Fa & b
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GFa M b, GFa & b
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@ -302,7 +302,7 @@
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"</svg>\n"
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],
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"text/plain": [
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"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f691c29f3f0> >"
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"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc090629840> >"
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]
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},
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"metadata": {},
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@ -603,7 +603,7 @@
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"</svg>\n"
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],
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"text/plain": [
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"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f691c31c360> >"
|
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"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc090629db0> >"
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]
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},
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"metadata": {},
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@ -812,7 +812,7 @@
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"</svg>\n"
|
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],
|
||||
"text/plain": [
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"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f691c31c360> >"
|
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"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc090629db0> >"
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||||
]
|
||||
},
|
||||
"metadata": {},
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@ -964,7 +964,7 @@
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"</svg>\n"
|
||||
],
|
||||
"text/plain": [
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"<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": {},
|
||||
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@ -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,
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue