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Simplify {r1;b1}&&{r2;b2} or {b1:r1}&&{b2:r2}, or similar.

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* src/ltlvisit/simplify.cc: Add four rules.
* doc/tl/tl.tex: Document these rules.
* src/ltltest/reduccmp.test: Add tests.
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Alexandre Duret-Lutz 2011-12-05 15:41:45 +01:00
parent 2f9f274a5f
commit b03935a4cf
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doc/tl/tl.tex
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@ -1272,8 +1272,9 @@ in the OR arguments:
yet.}
The following simplification rules are used for the $n$-ary operators
$\ANDALT$, $\AND$, and $\OR$, and are of course commutative. $b$
denots a Boolean formula while $r$ or $r_i$ denote any SERE.
$\ANDALT$, $\AND$, and $\OR$. The patterns are of course commutative.
$b$ or $b_i$ denote any Boolean formula while $r$ or $r_i$ denote any
SERE.
\begin{align*}
b \ANDALT r\STAR{\mvar{i}..\mvar{j}} &\equiv
@ -1298,6 +1299,10 @@ denots a Boolean formula while $r$ or $r_i$ denote any SERE.
b \ANDALT (r_1 \OR \ldots \OR r_n) & \text{if~}\forall i,\, \varepsilon\VDash r_i\\
\0 &\text{else}\\
\end{cases}\\
\ratgroup{b_1\CONCAT r_1}\ANDALT\ratgroup{b_2\CONCAT r_2} &\equiv \ratgroup{b_1\ANDALT b_2}\CONCAT\ratgroup{r_1\ANDALT r_2} \\
\ratgroup{b_1\FUSION r_1}\ANDALT\ratgroup{b_2\FUSION r_2} &\equiv \ratgroup{b_1\ANDALT b_2}\FUSION\ratgroup{r_1\ANDALT r_2} \\
\ratgroup{r_1\CONCAT b_1}\ANDALT\ratgroup{r_2\CONCAT b_2} &\equiv \ratgroup{r_1\ANDALT r_2}\CONCAT\ratgroup{b_1\ANDALT b_2} \\
\ratgroup{r_1\FUSION b_1}\ANDALT\ratgroup{r_2\FUSION b_2} &\equiv \ratgroup{r_1\ANDALT r_2}\FUSION\ratgroup{b_1\ANDALT b_2} \\
\end{align*}
\subsection{Simplifications for Eventual and Universal Formul\ae}