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Rewrite "a U (a&b)" as "b M a", and "a W (a&b)" as "b R a".

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* src/ltlvisit/simplify.cc (simplify_visitor): Implement these
rules.
* doc/tl/tl.tex: Document these rules.
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Alexandre Duret-Lutz 2012-01-05 13:13:32 +01:00
parent 55a1c6c12f
commit c2ab4e781b
2 changed files with 41 additions and 11 deletions
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17
doc/tl/tl.tex
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@ -1326,14 +1326,15 @@ verified, there is no need to worry about the $\G\F g$ term.
Here are the basic rewriting rules for binary operators (excluding $\OR$ and
$\AND$ which are considered in Spot as $n$-ary operators):
\begin{align*}
\1 \U f &\equiv \F f & f \W \0 &\equiv \G f \\
f \M \1 &\equiv \F f & \0 \R f &\equiv \G f \\
(\X f)\U (\X g) &\equiv \X(f\U g) & (\X f)\W(\X g) &\equiv \X(f\W g) \\
(\X f)\M (\X g) &\equiv \X(f\M g) & (\X f)\R(\X g) &\equiv \X(f\R g) \\
f \U(\G f) &\equiv \G f & f \W(\G f) &\equiv \G f \\
f \M(\F f) &\equiv \F f & f \R(\F f) &\equiv \F f \\
f \U (g \OR \G(f)) &\equiv f\W g & f \W (g \OR \G(f)) &\equiv f\W g\\
f \M (g \AND \F(f)) &\equiv f\M g & f \R (g \AND \F(f)) &\equiv f\M g
\1 \U f & \equiv \F f & f \W \0 & \equiv \G f \\
f \M \1 & \equiv \F f & \0 \R f & \equiv \G f \\
(\X f)\U (\X g) & \equiv \X(f\U g) & (\X f)\W(\X g) & \equiv \X(f\W g) \\
(\X f)\M (\X g) & \equiv \X(f\M g) & (\X f)\R(\X g) & \equiv \X(f\R g) \\
f \U(\G f) & \equiv \G f & f \W(\G f) & \equiv \G f \\
f \M(\F f) & \equiv \F f & f \R(\F f) & \equiv \F f \\
f \U (g \OR \G(f)) & \equiv f\W g & f \W (g \OR \G(f)) & \equiv f\W g \\
f \M (g \AND \F(f)) & \equiv f\M g & f \R (g \AND \F(f)) & \equiv f\M g \\
f \U (g \AND f) & \equiv g\M f & f \W (g \AND f) & \equiv g\R f
\end{align*}
Here are the basic rewriting rules for $n$-ary operators ($\AND$ and