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Add more simplification rules for AndNLM.

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* src/ltlvisit/simplify.cc: Here.
* src/ltltest/reduccmp.test: More tests.
* doc/tl/tl.tex: Document them.
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Alexandre Duret-Lutz 2012-04-18 01:00:49 +02:00
parent f7c64060c8
commit 35b41331f7
3 changed files with 240 additions and 9 deletions
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doc/tl/tl.tex
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@ -1367,7 +1367,12 @@ SERE.
\begin{cases}
b \ANDALT r &\text{if~} i\le 1\le j\\
\0 &\text{else}\\
\end{cases}\\
\end{cases} &
b \AND r &\equiV
\begin{cases}
b \OR \mathtt{\{}b\FUSION r\mathtt{\}}&\text{if~} \varepsilon\VDash r_i\\
b\FUSION r&\text{if~} \varepsilon\not\VDash r_i\\
\end{cases} \\
b \ANDALT \sere{r_1 \FUSION \ldots \FUSION r_n} &\equiv b \ANDALT r_1 \ANDALT \ldots \ANDALT r_n \\
b \ANDALT \sere{r_1 \CONCAT \ldots \CONCAT r_n} &\equiv
\begin{cases}
@ -1375,10 +1380,14 @@ SERE.
b \ANDALT (r_1 \OR \ldots \OR r_n) & \text{if~}\forall i,\, \varepsilon\VDash r_i\\
\0 &\text{else}\\
\end{cases}\\
\sere{b_1\CONCAT r_1}\ANDALT\sere{b_2\CONCAT r_2} &\equiv \sere{b_1\ANDALT b_2}\CONCAT\sere{r_1\ANDALT r_2} \\
\sere{b_1\FUSION r_1}\ANDALT\sere{b_2\FUSION r_2} &\equiv \sere{b_1\ANDALT b_2}\FUSION\sere{r_1\ANDALT r_2} \\
\sere{r_1\CONCAT b_1}\ANDALT\sere{r_2\CONCAT b_2} &\equiv \sere{r_1\ANDALT r_2}\CONCAT\sere{b_1\ANDALT b_2} \\
\sere{r_1\FUSION b_1}\ANDALT\sere{r_2\FUSION b_2} &\equiv \sere{r_1\ANDALT r_2}\FUSION\sere{b_1\ANDALT b_2} \\
\sere{b_1\CONCAT r_1}\ANDALT\sere{b_2\CONCAT r_2} &\equiv \sere{b_1\ANDALT b_2}\CONCAT\sere{r_1\ANDALT r_2} &
\sere{b_1\CONCAT r_1}\AND \sere{b_2\CONCAT r_2} &\equiv \sere{b_1\ANDALT b_2}\CONCAT\sere{r_1\AND r_2} \\
\sere{b_1\FUSION r_1}\ANDALT\sere{b_2\FUSION r_2} &\equiv \sere{b_1\ANDALT b_2}\FUSION\sere{r_1\ANDALT r_2} &
\sere{b_1\FUSION r_1}\AND \sere{b_2\FUSION r_2} &\equiv \sere{b_1\ANDALT b_2}\FUSION\sere{r_1\AND r_2} \\
\sere{r_1\CONCAT b_1}\ANDALT\sere{r_2\CONCAT b_2} &\equiv \sere{r_1\ANDALT r_2}\CONCAT\sere{b_1\ANDALT b_2} &
\sere{r_1\CONCAT b_1}\AND \sere{r_2\CONCAT b_2} &\equiv \sere{r_1\ANDALT r_2}\CONCAT\sere{b_1\AND b_2} \\
\sere{r_1\FUSION b_1}\ANDALT\sere{r_2\FUSION b_2} &\equiv \sere{r_1\ANDALT r_2}\FUSION\sere{b_1\ANDALT b_2} &
\sere{r_1\FUSION b_1}\AND \sere{r_2\FUSION b_2} &\equiv \sere{r_1\ANDALT r_2}\FUSION\sere{b_1\AND b_2} \\
\end{align*}
\subsection{Simplifications for Eventual and Universal Formul\ae}