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ltlcross: give an example of accepted word for nonempty cross-products

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* src/tgbaalgos/word.cc, src/tgbaalgos/word.hh: New files.
* src/tgbaalgos/Makefile.am: Add them.
* src/tgbatest/ltlcrossce.test: New file.
* src/tgbatest/Makefile.am: Add it.
* src/bin/ltlcross.cc: Compute and display an accepted word
for nonempty cross-products.
* NEWS, doc/org/ltlcross.org: Document it.
This commit is contained in:
Alexandre Duret-Lutz 2013-07-20 18:55:45 +02:00
parent 4bafa4e1b0
commit e7522056ca
8 changed files with 324 additions and 37 deletions
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44
doc/org/ltlcross.org
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@ -396,28 +396,32 @@ positive and negative formulas by the ith translator).
A single failing translator might generate a lot of lines of
the form:
: error: P0*N1 is nonempty
: error: P1*N0 is nonempty
: error: P1*N1 is nonempty
: error: P1*N2 is nonempty
: error: P1*N3 is nonempty
: error: P1*N4 is nonempty
: error: P1*N5 is nonempty
: error: P1*N6 is nonempty
: error: P1*N7 is nonempty
: error: P1*N8 is nonempty
: error: P1*N9 is nonempty
: error: P2*N1 is nonempty
: error: P3*N1 is nonempty
: error: P4*N1 is nonempty
: error: P5*N1 is nonempty
: error: P6*N1 is nonempty
: error: P7*N1 is nonempty
: error: P8*N1 is nonempty
: error: P9*N1 is nonempty
: error: P0*N1 is nonempty; both automata accept the infinite word
: cycle{p0 & !p1}
: error: P1*N0 is nonempty; both automata accept the infinite word
: p0; !p1; cycle{p0 & p1}
: error: P1*N1 is nonempty; both automata accept the infinite word
: p0; cycle{!p1 & !p0}
: error: P1*N2 is nonempty; both automata accept the infinite word
: p0; !p1; cycle{p0 & p1}
: error: P1*N3 is nonempty; both automata accept the infinite word
: p0; !p1; cycle{p0 & p1}
: error: P1*N4 is nonempty; both automata accept the infinite word
: p0; cycle{!p1 & !p0}
: error: P2*N1 is nonempty; both automata accept the infinite word
: p0; !p1; !p0; cycle{!p1 & !p0; p0 & !p1; !p1; !p1; p0 & !p1}
: error: P3*N1 is nonempty; both automata accept the infinite word
: p0; !p1; !p1 & !p0; cycle{p0 & !p1}
: error: P4*N1 is nonempty; both automata accept the infinite word
: p0; !p1; !p1 & !p0; cycle{p0 & !p1}
In this example, translator number =1= looks clearly faulty
(at least the other 9 translators do not contradict each other).
(at least the other 4 translators do not contradict each other).
Examples of infinite words that are accepted by both automata
always have the form of a lasso: a (possibly empty) finite prefix
followed by a cycle that should be repeated infinitely often.
The cycle part is denoted by =cycle{...}=.
- Cross-comparison checks: for some state-space $S$,
all $P_i\otimes S$ are either all empty, or all non-empty.