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* doc/org/ltlfilt.org: Add an example with --stutter-invariant.

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Alexandre Duret-Lutz 2013-05-13 16:10:09 +02:00
parent 54b25b8c8e
commit b457e78fb0
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@ -216,10 +216,44 @@ ltlfilt -f 'a U (b U a)' --equivalent-to 'b U a'
#+RESULTS:
: a U (b U a)
The commands prints the formula and returns an exit status of 0 if the
The command prints the formula and returns an exit status of 0 if the
two formulas are equivalent. It would print nothing and set the exit
status to 1, were the two formulas not equivalent.
If the formula =F(a & X(!a & Gb))= stutter-invariant?
#+BEGIN_SRC sh :results verbatim :exports both
ltlfilt -f 'F(a & X(!a & Gb))' --stutter-invariant
#+END_SRC
#+RESULTS:
: F(a & X(!a & Gb))
Yes it is. And since it is stutter-invariant, there exist some
equivalent formulas that do not use =X= operator. The =--remove-x=
option gives one:
#+BEGIN_SRC sh :results verbatim :exports both
ltlfilt -f 'F(a & X(!a & Gb))' --remove-x
#+END_SRC
#+RESULTS:
: F(a & ((a & (a U (!a & Gb)) & ((!b U !a) | (b U !a))) | (!a & (!a U (a & !a & Gb)) & ((!b U a) | (b U a))) | (b & (b U (!a & Gb & !b)) & ((!a U !b) | (a U !b))) | (!b & (!b U (!a & b & Gb)) & ((!a U b) | (a U b))) | (!a & Gb & (G!a | Ga) & (Gb | G!b))))
We could even verify that the resulting horrible formula is equivalent
to the original one:
#+BEGIN_SRC sh :results verbatim :exports both
ltlfilt -f 'F(a & X(!a & Gb))' --remove-x | ltlfilt --equivalent-to 'F(a & X(!a & Gb))'
#+END_SRC
#+RESULTS:
: F(a & ((a & (a U (!a & Gb)) & ((!b U !a) | (b U !a))) | (!a & (!a U (a & !a & Gb)) & ((!b U a) | (b U a))) | (b & (b U (!a & Gb & !b)) & ((!a U !b) | (a U !b))) | (!b & (!b U (!a & b & Gb)) & ((!a U b) | (a U b))) | (!a & Gb & (G!a | Ga) & (Gb | G!b))))
It is therefore equivalent, but that is not a surprise since the
=--stutter-invariant= filter is actually implemented using exactly
[[http://homepages.inf.ed.ac.uk/kousha/note_on_stut_tl_lpi.ps][this procedure]] (calling the =remove_x()= function, and checking the
equivalence of the resulting formula with the original one).
# LocalWords: ltlfilt num toc LTL PSL syntaxes LBT's SRC GFp scheck
# LocalWords: ltl EOF lbt Gp Fp Xp XFp XXp randltl ary nnf wm abc
# LocalWords: pnn Xb Fc XFb XXd sed boolean bsize nox Gb Fb Xa XGb