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tl: eight new simplification rules

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* 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 2019-07-08 10:59:36 +02:00
parent d244ff5432
commit 0d9cc29b46
8 changed files with 203 additions and 19 deletions
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15
doc/tl/tl.tex
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@ -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}