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simplifier: new PSL simplifications

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{e[*0..j]}<>->f = {e[*1..j]}<>->f
{e[*0..j]}[]->f = {e[*1..j]}[]->f

Fixes #81.

This required a small change to the bounded-star-normal-form to prevent
infinite recursion.

* spot/tl/simplify.cc: Implement these rules.
* doc/tl/tl.tex, NEWS: Document them.
* tests/core/reduccmp.test: Add tests, and adjust others.
* tests/core/unambig.test: Replace formula that used to generated an
ambiguous automaton, but now generates a deterministic one.
This commit is contained in:
Alexandre Duret-Lutz 2016-07-19 16:40:59 +02:00
parent d5b2de7fa8
commit abff7eba8e
5 changed files with 38 additions and 16 deletions
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7
doc/tl/tl.tex
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@ -1565,7 +1565,8 @@ presence of \samp{$\AND$} operators, but unfortunately not when the
We extend the above definition to bounded repetitions with:
\begin{align*}
r\STAR{\mvar{i}..\mvar{j}} & \equiv r^\square\STAR{\0..\mvar{j}}\quad\text{if}\quad\varepsilon\VDash r\STAR{\mvar{i}..\mvar{j}}
r\STAR{\mvar{i}..\mvar{j}} & \equiv r^\square\STAR{0..\mvar{j}}\quad\text{if}\quad\varepsilon\VDash r\STAR{\mvar{i}..\mvar{j}}\text{~and~}\varepsilon\not\VDash r^\square\\
r\STAR{\mvar{i}..\mvar{j}} & \equiv r^\square\STAR{1..\mvar{j}}\quad\text{if}\quad\varepsilon\VDash r\STAR{\mvar{i}..\mvar{j}}\text{~and~}\varepsilon\VDash r^\square
\end{align*}
where $r^\square$ is recursively defined as follows:
\begin{align*}
@ -1603,6 +1604,7 @@ denoted with $\equiV$ can be disabled by setting the
\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{0..\mvar{j}}}\Asuffix f &\equiv \sere{r\STAR{1..\mvar{j}}}\Asuffix f \\
\sere{r\STAR{\mvar{i}..\mvar{j}}}\Asuffix f &\equiV
\sere{r}\Asuffix \X(
\sere{r}\Asuffix \X(\ldots
@ -1618,6 +1620,7 @@ denoted with $\equiV$ can be disabled by setting the
\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{0..\mvar{j}}}\Esuffix f &\equiv \sere{r\STAR{1..\mvar{j}}}\Esuffix f \\
\sere{r\STAR{\mvar{i}..\mvar{j}}}\Esuffix f &\equiV
\sere{r}\Esuffix \X(
\sere{r}\Esuffix \X(\ldots
@ -1632,7 +1635,7 @@ denoted with $\equiV$ can be disabled by setting the
\sere{r_1\OR r_2}\Esuffix f &\equiV (\sere{r_1}\Esuffix f)\OR(\sere{r_2}\Esuffix f)
\end{align*}
Here are basic the rewritings for the weak closure and its negation:
Here are the basic rewritings for the weak closure and its negation:
\begin{align*}
\sere{r\STAR{}}&\equiv \sere{r}&
\nsere{r\STAR{}}&\equiv \nsere{r}\\