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Implement 11 rewritings for []->.

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* src/ltlvisit/simplify.cc: Here.
* doc/tl/tl.tex: Document then.
* src/ltlast/bunop.hh (as_KleenStar): New helper function.
* src/ltltest/reduccmp.test: Add more tests.
* src/ltltest/reduc.cc: Also display the resulting formula
without reduce_size_stricly.
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Alexandre Duret-Lutz 2012-04-26 17:13:56 +02:00
parent 6eb830c8ae
commit 6f46345c3a
5 changed files with 291 additions and 8 deletions
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32
doc/tl/tl.tex
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@ -1183,7 +1183,7 @@ would invalidate the results stored in the caches).
This is implemented by the `\verb|ltl_simplifier::negative_normal_form|`
method.
A formula in negative normal form can only have only have negation
A formula in negative normal form can only have negation
operators ($\NOT$) in front of atomic properties, and does not use any
of the $\XOR$, $\IMPLIES$ and $\EQUIV$ operators. The following
rewriting arrange any PSL formula into negative normal form.
@ -1256,7 +1256,7 @@ The goals in most of these simplification are to:
limit the sources of indeterminism.
\end{itemize}
\subsection{Basic Simplifications}
\subsection{Basic Simplifications}\label{sec:basic-simp}
These simplifications are enabled with
\verb|ltl_simplifier_options::reduce_basics|'. A couple of them may
@ -1431,6 +1431,34 @@ that occur in $r$. For instance $\sere{a\STAR{}\CONCAT
presence of \samp{$\FUSION$} and \samp{$\AND$} operators, but
unfortunately not when the \samp{$\ANDALT$} operator is used.
\subsubsection{Basic Simplifications SERE-LTL Binding Operators}
The following rewritings are applied to the operators $\Asuffix$ and
$\Esuffix$. They assume that $b$, denote a Boolean formula.
As noted at the beginning for section~\ref{sec:basic-simp}, rewritings
denoted with $\equiV$ can be disabled by setting the
\verb|ltl_simplifier_options::reduce_size_strictly|' option to
\texttt{true}.
\begin{align*}
\sere{\STAR{}}\Asuffix f &\equiv \G f\\
\sere{b\STAR{}}\Asuffix f &\equiv f \W \NOT b\\
\sere{b\PLUS{}}\Asuffix f &\equiv f \W \NOT b\\
\sere{r\STAR{\mvar{i}..\mvar{j}}}\Asuffix f &\equiV
\sere{r}\Asuffix \X(
\sere{r}\Asuffix \X(\ldots
\Asuffix\X(r\STAR{\mvar{1}..\mvar{j-i+1}})))
\text{~if~}i\ge 1\text{~and~}\varepsilon\not\VDash r\\
\sere{r\CONCAT \STAR{}}\Asuffix f &\equiv \sere{r}\Asuffix \G f\\
\sere{r\CONCAT b\STAR{}}\Asuffix f &\equiV \sere{r}\Asuffix (f\AND \X(f \W \NOT b)) \text{~if~}\varepsilon\not\VDash r\\
\sere{\STAR{}\CONCAT r}\Asuffix f &\equiV \G(\sere{r}\Asuffix f)\\
\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)
\end{align*}
\subsection{Simplifications for Eventual and Universal Formul\ae}
\label{sec:eventunivrew}