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simplify: add four simplification rules for GF and FG

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GF(a|Xb) = GF(a|b)      GF(a|Fb) = GF(a|b)
FG(a&Xb) = FG(a&b)      FG(a&Gb) = FG(a&b)

* src/ltlvisit/simplify.cc: Implement them.
* NEWS, doc/tl/tl.tex: Document them.
* src/ltltest/reduccmp.test: Test then.
This commit is contained in:
Alexandre Duret-Lutz 2013-01-11 16:07:10 +01:00
parent 2580fc6f91
commit e4ecc2d465
4 changed files with 107 additions and 8 deletions
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8
doc/tl/tl.tex
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@ -1313,9 +1313,11 @@ instead of $\equiv$, and they can be disabled by setting the
The following are simplification rules for unary operators (applied
from left to right, as usual):
\begin{align*}
\X\F\G f & \equiv \F\G f & \F\X f & \equiv \X\F f & \G\X f & \equiv \X\G f\\
\X\G\F f & \equiv \G\F f & \F(f\U g) & \equiv \F g & \G(f \R g) & \equiv \G g \\
& & \F(f\M g) & \equiv \F (f\AND g) & \G(f \W g) & \equiv \G(f\OR g)
\X\F\G f & \equiv \F\G f & \F\X f & \equiv \X\F f & \G\X f & \equiv \X\G f \\
\X\G\F f & \equiv \G\F f & \F(f\U g) & \equiv \F g & \G(f \R g) & \equiv \G g \\
& & \F(f\M g) & \equiv \F (f\AND g) & \G(f \W g) & \equiv \G(f\OR g) \\
& & \F\G(f\AND \X g) & \equiv \F\G(f\AND g) & \G\F(f\OR \X g) & \equiv \G\F(f\OR g) \\
& & \F\G(f\AND \G g) & \equiv \F\G(f\AND g) & \G\F(f\OR \F g) & \equiv \G\F(f\OR g) \\
\end{align*}
\begin{align*}
\G(f_1\OR\ldots\OR f_n \OR \G\F(g_1)\OR\ldots\OR \G\F(g_m)) & \equiv \G(f_1\OR\ldots\OR f_n)\OR \G\F(g_1\OR\ldots\OR g_m)