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Implement dual rewritings rules for <>->.

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* src/ltlvisit/simplify.cc (reduce_sere_ltl): New function,
to factor the code of the []-> and <>-> rewrittings.
* src/ltltest/reduccmp.test: Add more tests.
* doc/tl/tl.tex: Document these rewritings.
This commit is contained in:
Alexandre Duret-Lutz 2012-04-26 18:12:01 +02:00
parent 6f46345c3a
commit d6587cf531
3 changed files with 307 additions and 248 deletions
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17
doc/tl/tl.tex
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@ -1456,7 +1456,22 @@ denoted with $\equiV$ can be disabled by setting the
\sere{b\STAR{}\CONCAT r}\Asuffix f &\equiV (\NOT b)\R(\sere{r}\Asuffix f) \text{~if~}\varepsilon\not\VDash r\\
\sere{r_1\CONCAT r_2}\Asuffix f &\equiV \sere{r_1}\Asuffix\X(\sere{r_2}\Asuffix f)\text{~if~}\varepsilon\not\VDash r_1\text{~and~}\varepsilon\not\VDash r_2\\
\sere{r_1\FUSION r_2}\Asuffix f &\equiV \sere{r_1}\Asuffix(\sere{r_2}\Asuffix f)\\
\sere{r_1\OR r_2}\Asuffix f &\equiV (\sere{r_1}\Asuffix f)\AND(\sere{r_2}\Asuffix f)
\sere{r_1\OR r_2}\Asuffix f &\equiV (\sere{r_1}\Asuffix f)\AND(\sere{r_2}\Asuffix f)\\
\sere{\STAR{}}\Esuffix f &\equiv \F f\\
\sere{b\STAR{}}\Esuffix f &\equiv f \M b\\
\sere{b\PLUS{}}\Esuffix f &\equiv f \M b\\
\sere{r\STAR{\mvar{i}..\mvar{j}}}\Esuffix f &\equiV
\sere{r}\Esuffix \X(
\sere{r}\Esuffix \X(\ldots
\Esuffix\X(r\STAR{\mvar{1}..\mvar{j-i+1}})))
\text{~if~}i\ge 1\text{~and~}\varepsilon\not\VDash r\\
\sere{r\CONCAT \STAR{}}\Esuffix f &\equiv \sere{r}\Esuffix \F f\\
\sere{r\CONCAT b\STAR{}}\Esuffix f &\equiV \sere{r}\Esuffix (f\OR \X(f \M b)) \text{~if~}\varepsilon\not\VDash r\\
\sere{\STAR{}\CONCAT r}\Esuffix f &\equiV \F(\sere{r}\Esuffix f)\\
\sere{b\STAR{}\CONCAT r}\Esuffix f &\equiV b\U(\sere{r}\Esuffix f) \text{~if~}\varepsilon\not\VDash r\\
\sere{r_1\CONCAT r_2}\Esuffix f &\equiV \sere{r_1}\Esuffix\X(\sere{r_2}\Esuffix f)\text{~if~}\varepsilon\not\VDash r_1\text{~and~}\varepsilon\not\VDash r_2\\
\sere{r_1\FUSION r_2}\Esuffix f &\equiV \sere{r_1}\Esuffix(\sere{r_2}\Esuffix f)\\
\sere{r_1\OR r_2}\Esuffix f &\equiV (\sere{r_1}\Esuffix f)\OR(\sere{r_2}\Esuffix f)
\end{align*}
\subsection{Simplifications for Eventual and Universal Formul\ae}