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Implement rewritings for {f|g} and !{f|g}.

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* src/ltlvisit/simplify.cc: Here.
* src/ltltest/reduccmp.test: Test them.
* doc/tl/tl.tex: Document them.
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Alexandre Duret-Lutz 2012-04-29 23:36:12 +02:00
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doc/tl/tl.tex
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@ -1502,7 +1502,9 @@ Here are basic the rewritings for the weak closure and its negation:
\sere{b\STAR{\mvar{i}..\mvar{j}};r}&\equiV \underbrace{b\AND \X(b\ldots}_{\mathclap{i\text{~occurences of~}b}}\AND\X\sere{b\STAR{\mvar{0}..\mvar{j-i}}\CONCAT r})&
\nsere{b\STAR{\mvar{i}..\mvar{j}};r}&\equiV \underbrace{(\NOT b)\OR \X((\NOT b)\ldots}_{\mathclap{i\text{~occurences of~}\NOT b}}\OR\X\nsere{b\STAR{\mvar{0}..\mvar{j-i}}\CONCAT r}) \\
\sere{b\STAR{\mvar{i}..\mvar{j}}}&\equiV \underbrace{b\AND \X(b\AND \X(\ldots b))}_{i\text{~occurences of~}b}&
\nsere{b\STAR{\mvar{i}..\mvar{j}}}&\equiV \underbrace{(\NOT b)\OR \X((\NOT b)\OR \X(\ldots(\NOT b)))}_{i\text{~occurences of~}\NOT b}
\nsere{b\STAR{\mvar{i}..\mvar{j}}}&\equiV \underbrace{(\NOT b)\OR \X((\NOT b)\OR \X(\ldots(\NOT b)))}_{i\text{~occurences of~}\NOT b}\\
\sere{r_1\OR r_2}&\equiV\sere{r_1}\OR\sere{r_2} &
\nsere{r_1\OR r_2}&\equiV\nsere{r_1}\AND\nsere{r_2}
\end{align*}
\subsection{Simplifications for Eventual and Universal Formul\ae}