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formula: new trivial simplifications

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Add the following rules:
  - f|[+] = [+] if f rejects [*0]
  - f|[*] = [*] if f accepts [*0]
  - f&&[+] = f if f rejects [*0]
  - b:b[*i..j] = b[*max(i,1)..j]
  - b[*i..j]:b[*k..l] = b[*max(i,1)+max(k,1)-1,1), j+l-1]

* spot/tl/formula.cc: Implement the new rules.
* doc/tl/tl.tex: Document them.
* tests/core/equals.test: Test them.
* NEWS: Add them
This commit is contained in:
Alexandre Duret-Lutz 2022-12-08 13:54:19 +01:00
parent 8ed9e3381f
commit 720c380412
4 changed files with 147 additions and 14 deletions
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18
doc/tl/tl.tex
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@ -853,10 +853,18 @@ The following rules are all valid with the two arguments swapped.
\1\OR b &\equiv \1 &
\1 \FUSION f & \equiv f\mathrlap{\text{~if~}\varepsilon\nVDash f}\\
&&
\STAR{} \AND f &\equiv f &
\STAR{} \OR f &\equiv \1\mathrlap{\STAR{}} &
\STAR{} \ANDALT f &\equiv f &
\STAR{} \OR f &\equiv \mathrlap{\STAR{}} &
&&
\STAR{} \CONCAT f &\equiv \STAR{}\mathrlap{\text{~if~}\varepsilon\VDash f}& \\
\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}
@ -880,7 +888,9 @@ The following rules are all valid with the two arguments swapped.
f\STAR{\mvar{i}..\mvar{j}}\CONCAT f&\equiv f\STAR{\mvar{i+1}..\mvar{j+1}} &
f\STAR{\mvar{i}..\mvar{j}}\CONCAT f\STAR{\mvar{k}..\mvar{l}}&\equiv f\STAR{\mvar{i+k}..\mvar{j+l}}\\
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}}
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}}}
\end{align*}
\section{SERE-LTL Binding Operators}