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formula: add a missing trivial rewriting in SERE

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We should have [*0]|f ≡ f when f is a SERE that already accept the
empty word.  Fixes issue #454.

* spot/tl/formula.cc: Implement the rewriting.
* tests/core/reduccmp.test: Add a test case.
* doc/tl/tl.tex, NEWS: Document it.
This commit is contained in:
Alexandre Duret-Lutz 2024-07-25 17:56:04 +02:00
parent bcdfe44c44
commit 44efc96595
4 changed files with 31 additions and 17 deletions
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30
doc/tl/tl.tex
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@ -839,47 +839,47 @@ The following rules are all valid with the two arguments swapped.
%\samp{$\FUSION$}.)
\begin{align*}
\0\AND f &\equiv \0 &
\0\ANDALT f &\equiv \0 &
\0\AND f &\equiv \0 &
\0\OR f &\equiv f &
\0 \FUSION f &\equiv \0 &
\0 \CONCAT f &\equiv \0 \\
\mathllap{\0 \CONCAT f}&\equiv \0 \\
\1\ANDALT b &\equiv b &
\1\AND f&\equiv
\begin{cases}
1\mathrlap{\text{~if~} \varepsilon\VDash f} \\
f\mathrlap{\text{~if~} \varepsilon\nVDash f} \\
\end{cases} &
\1\ANDALT b &\equiv b &
\1\OR b &\equiv \1 &
\1 \FUSION f & \equiv f\mathrlap{\text{~if~}\varepsilon\nVDash f}\\
&&
\1 \FUSION f & \equiv \mathrlap{f\text{~if~}\varepsilon\nVDash f}\\
\STAR{} \ANDALT f &\equiv f &
&&
\STAR{} \OR f &\equiv \mathrlap{\STAR{}} &
&&
\STAR{} \CONCAT f &\equiv \STAR{}\text{~if~}\varepsilon\VDash f& \\
&&
\mathllap{\STAR{} \CONCAT f }&\equiv \STAR{}\text{~if~}\varepsilon\VDash f& \\
\PLUS{} \ANDALT f &\equiv f \text{~if~}\varepsilon\nVDash f&
&&
\PLUS{} \OR f &\equiv \begin{cases}
\mathrlap{\STAR{}\text{~if~} \varepsilon\VDash f} \\
\mathrlap{\PLUS{}\text{~if~} \varepsilon\nVDash f} \\
\end{cases} &
&&
&& \\
\eword\AND f &\equiv f &
\eword\ANDALT f &\equiv
\begin{cases}
\mathrlap{\eword\text{~if~} \varepsilon\VDash f} \\
\0\mathrlap{\phantom{\STAR{}}\text{~if~} \varepsilon\nVDash f} \\
\!\eword\text{~if~}\varepsilon\VDash{f} \\
\0\!\phantom{\STAR{}}\text{~if~}\varepsilon\nVDash{f} \\
\end{cases} &
&&
\mathllap{\eword}\AND f &\equiv f &
\eword\OR f &\equiv f \text{~if~} \varepsilon\VDash f&
\eword \FUSION f &\equiv \0 &
\eword \CONCAT f &\equiv f\\
f\AND f &\equiv f&
\mathllap{\eword \CONCAT f}&\equiv f\\
f\ANDALT f &\equiv f &
f\AND f &\equiv f&
f\OR f &\equiv f&
f\FUSION f&\equiv f\FSTAR{2}&
f\CONCAT f&\equiv f\STAR{2}\\
b_1 \AND b_2 &\equiv b_1\ANDALT b_2 &
b_1 \AND b_2 &\equiv \mathrlap{b_1\ANDALT b_2}&
&&
&&
b_1:b_2 &\equiv b_1\ANDALT b_2
@ -890,7 +890,7 @@ f\STAR{\mvar{i}..\mvar{j}}\CONCAT f\STAR{\mvar{k}..\mvar{l}}&\equiv f\STAR{\mvar
f\FSTAR{\mvar{i}..\mvar{j}}\FUSION f&\equiv f\FSTAR{\mvar{i+1}..\mvar{j+1}} &
f\FSTAR{\mvar{i}..\mvar{j}}\FUSION f\FSTAR{\mvar{k}..\mvar{l}}&\equiv f\FSTAR{\mvar{i+k}..\mvar{j+l}}\\
b\STAR{\mvar{i}..\mvar{j}}\FUSION b &\equiv b\STAR{\mvar{\max(i,1)}..\mvar{j}} &
b\STAR{\mvar{i}..\mvar{j}}\FUSION b\STAR{\mvar{k}..\mvar{l}} &\equiv b\mathrlap{\STAR{\mvar{\max(i,1)+\max(k,1)-1}..\mvar{j+l-1}}}
b\STAR{\mvar{i}..\mvar{j}}\FUSION b\STAR{\mvar{k}..\mvar{l}} &\equiv b\STAR{\mvar{\max(i,1)+\max(k,1)-1}..\mvar{j+l-1}}
\end{align*}
\section{SERE-LTL Binding Operators}