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tl: fix the definition of ##[i:j]

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Reported by Victor Khomenko.

* NEWS, doc/tl/tl.tex, spot/tl/formula.cc: Fix the definition.
* tests/core/ltl2tgba.test: Add some test cases.
This commit is contained in:
Alexandre Duret-Lutz 2019-05-19 09:12:59 +02:00
parent 60bdf5de19
commit 66a3b6f7cb
4 changed files with 53 additions and 21 deletions
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25
doc/tl/tl.tex
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@ -775,16 +775,23 @@ $f \CONCAT \1\CONCAT g$, but the delay can be a range, and $f$ can be
omitted.
\begin{align*}
f\DELAY{\mvar{i}} g &\equiv f\DELAYR{\mvar{i}..\mvar{i}} g & {}\DELAY{\mvar{i}} g &\equiv {}\DELAYR{\mvar{i}..\mvar{i}} g\\
f\DELAYR{..} g &\equiv f\FUSION\{\STAR{}\CONCAT g\} & f\DELAYR{\mvar{i}..} g &\equiv f\FUSION\{\STAR{\mvar{i}..}\CONCAT g\} \\
f\DELAYR{..\mvar{j}} g &\equiv f\FUSION\{\STAR{0..\mvar{j}}\CONCAT g\} &
f\DELAYR{\mvar{i}..\mvar{j}} g &\equiv f\FUSION\{\STAR{\mvar{i}..\mvar{j}}\CONCAT g\} \\
{}\DELAYR{..} g &\equiv \STAR{}\CONCAT g & {}\DELAYR{\mvar{i}..} g &\equiv \STAR{\mvar{i}..}\CONCAT g \\
{}\DELAYR{..\mvar{j}} g &\equiv \STAR{0..\mvar{j}}\CONCAT g &
{}\DELAYR{\mvar{i}..\mvar{j}} g &\equiv \STAR{\mvar{i}..\mvar{j}}\CONCAT g \\
f \DELAYP{} g & \equiv f \DELAYR{1..} g & f \DELAYS{} g & \equiv f \DELAYR{0..} g \\
\DELAYP{} g & \equiv \DELAYR{1..} g & \DELAYS{} g & \equiv \DELAYR{0..} g
f\DELAYR{\mvar{i}..\mvar{j}}g & \equiv f\CONCAT{}\1\STAR{\mvar{i-1}..\mvar{j-1}}\CONCAT{}g\quad\text{if~}i>0 \\
f\DELAYR{0..\mvar{j}}g & \equiv f\FUSION(\1\STAR{0..\mvar{j}}\CONCAT{}g)\quad\text{if~}\varepsilon\nVDash f \\
f\DELAYR{0..\mvar{j}}g & \equiv (f\CONCAT{}\1\STAR{0..\mvar{j}})\FUSION{}g)\quad\text{if~}\varepsilon\VDash f \land \varepsilon\nVDash g \\
f\DELAYR{0..\mvar{j}}g & \equiv (f\FUSION{}g)\OR(f\CONCAT{}\1\STAR{0..\mvar{j-1}}\CONCAT{}g)\quad\text{if~}\varepsilon\VDash f \land \varepsilon\VDash g \\
f\DELAYR{\mvar{i}..}g & \equiv f\CONCAT{}\1\STAR{\mvar{i-1}..}\CONCAT{}g\quad\text{if~}i>0 \\
f\DELAYR{0..}g & \equiv f\FUSION(\1\STAR{}\CONCAT{}g)\quad\text{if~}\varepsilon\nVDash f \\
f\DELAYR{0..}g & \equiv (f\CONCAT{}\1\STAR{})\FUSION{}g)\quad\text{if~}\varepsilon\VDash f \land \varepsilon\nVDash g \\
f\DELAYR{0..}g & \equiv (f\FUSION{}g)\OR(f\CONCAT{}\1\STAR{}\CONCAT{}g)\quad\text{if~}\varepsilon\VDash f \land \varepsilon\VDash g
\end{align*}
\begin{align*}
f\DELAY{\mvar{i}} g & \equiv f\DELAYR{\mvar{i}..\mvar{i}} g & {}\DELAY{\mvar{i}} g & \equiv \1\DELAYR{\mvar{i}..\mvar{i}} g \\
f\DELAYP{}g & \equiv f\DELAYR{1..}g & \DELAYP{} g & \equiv\DELAYR{1..}g \\
f\DELAYS{}g & \equiv f\DELAYR{0..}g & \DELAYS{} g & \equiv\DELAYR{0..}g
f\DELAYR{..\mvar{j}} g & \equiv f\DELAYR{0..\mvar{j}} g\} & \DELAYR{..\mvar{j}} g & \equiv \1\DELAYR{0..\mvar{j}} g\} \\
f\DELAYR{..} g & \equiv f\DELAYR{0..} f g\} & \DELAYR{..} g & \equiv \1\DELAYR{0..} g\} \\
\end{align*}
\subsection{Trivial Identities (Occur Automatically)}
The following identities also hold if $j$ or $l$ are missing (assuming