tl: add some implication-based rewritings for "<->", "->", and "xor"
This prevents an exception from being raised if NNF is not performed on Boolean properties and implication-based checks are used. * NEWS: Mention the issue. * spot/tl/simplify.cc, doc/tl/tl.tex: Add some rules. * tests/python/ltlsimple.py: Test them.
This commit is contained in:
Alexandre Duret-Lutz
parent
d8419db618
commit
126d392355
4 changed files with 113 additions and 58 deletions
7
NEWS
7
NEWS
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@ -10,6 +10,13 @@ New in spot 2.6.0.dev (not yet released)
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- scc_info::split_on_sets() did not correctly register the
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atomic propositions of the returned automata.
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- The spot::tl_simplifier class could raise an exception while
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attempting to reduce formulas containing unsimplified <->, -> or
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xor, if options nenoform_stop_on_boolean and synt_impl are both
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set. (This combinations of options is not available from
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command-line tools.)
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New in spot 2.6 (2018-07-04)
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Command-line tools:
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108
doc/tl/tl.tex
108
doc/tl/tl.tex
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@ -1744,58 +1744,62 @@ are counted as one.
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\begingroup
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\allowdisplaybreaks
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\begin{alignat*}{3}
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\text{if~} & f\simp \NOT g && \text{~then~} & f\OR g & \equiv \1 \\
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\text{if~} & f\simp \NOT g && \text{~then~} & f\AND g & \equiv \0 \\
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\text{if~} & \flessg && \text{~then~} & f\OR g & \equiv f \\
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\text{if~} & f\simp g && \text{~then~} & f\OR g & \equiv g \\
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\text{if~} & \glessf && \text{~then~} & f\AND g & \equiv g \\
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\text{if~} & f\simp g && \text{~then~} & f\AND g & \equiv f \\
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\text{if~} & \flessg && \text{~then~} & f\U g & \equiv f \\
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\text{if~} & f\simp g && \text{~then~} & f\U g & \equiv g \\
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\text{if~} & (f\U g)\Simp g && \text{~then~} & f\U g & \equiv g \\
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\text{if~} & (\NOT f)\simp g && \text{~then~} & f\U g & \equiv \F g \\
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\text{if~} & g\simp e && \text{~then~} & e\U g & \equiv \F g \\
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\text{if~} & f\simp g && \text{~then~} & f\U (g \U h) & \equiv g \U h \\
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\text{if~} & f\simp g && \text{~then~} & f\U (g \W h) & \equiv g \W h \\
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\text{if~} & g\simp f && \text{~then~} & f\U (g \U h) & \equiv f \U h \\
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\text{if~} & f\simp h && \text{~then~} & f\U (g \R (h \U k)) & \equiv g \R (h \U k) \\
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\text{if~} & f\simp h && \text{~then~} & f\U (g \R (h \W k)) & \equiv g \R (h \W k) \\
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\text{if~} & f\simp h && \text{~then~} & f\U (g \M (h \U k)) & \equiv g \M (h \U k) \\
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\text{if~} & f\simp h && \text{~then~} & f\U (g \M (h \W k)) & \equiv g \M (h \W k) \\
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\text{if~} & f\simp h && \text{~then~} & (f\U g) \U h & \equiv g \U h \\
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\text{if~} & f\simp h && \text{~then~} & (f\W g) \U h & \equiv g \U h \\
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\text{if~} & g\simp h && \text{~then~} & (f\U g) \U h & \equiv (f \U g) \OR h \\
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\text{if~} & (\NOT f)\simp g && \text{~then~} & f\W g & \equiv \1 \\
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\text{if~} & \flessg && \text{~then~} & f\W g & \equiv f \\
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\text{if~} & f\simp g && \text{~then~} & f\W g & \equiv g \\
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\text{if~} & (f\W g)\Simp g && \text{~then~} & f\W g & \equiv g \\
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\text{if~} & f\simp g && \text{~then~} & f\W (g \W h) & \equiv g \W h \\
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\text{if~} & g\simp f && \text{~then~} & f\W (g \U h) & \equiv f \W h \\
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\text{if~} & g\simp f && \text{~then~} & f\W (g \W h) & \equiv f \W h \\
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\text{if~} & f\simp h && \text{~then~} & (f\U g) \W h & \equiv g \W h \\
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\text{if~} & f\simp h && \text{~then~} & (f\W g) \W h & \equiv g \W h \\
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\text{if~} & g\simp h && \text{~then~} & (f\W g) \W h & \equiv (f \W g) \OR h \\
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\text{if~} & g\simp h && \text{~then~} & (f\U g) \W h & \equiv (f \U g) \OR h \\
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\text{if~} & \flessg && \text{~then~} & f\R g & \equiv f \\
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\text{if~} & g\simp f && \text{~then~} & f\R g & \equiv g \\
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\text{if~} & g\simp \NOT f && \text{~then~} & f\R g & \equiv \G g \\
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\text{if~} & u\simp g && \text{~then~} & u\R g & \equiv \G g \\
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\text{if~} & g\simp f && \text{~then~} & f\R (g \R h) & \equiv g \R h \\
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\text{if~} & g\simp f && \text{~then~} & f\R (g \M h) & \equiv g \M h \\
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\text{if~} & f\simp g && \text{~then~} & f\R (g \R h) & \equiv f \R h \\
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\text{if~} & h\simp f && \text{~then~} & (f\R g) \R h & \equiv g \R h \\
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\text{if~} & h\simp f && \text{~then~} & (f\M g) \R h & \equiv g \R h \\
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\text{if~} & g\simp h && \text{~then~} & (f\R g) \R h & \equiv (f \AND g) \R h \\
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\text{if~} & g\simp h && \text{~then~} & (f\M g) \R h & \equiv (f \AND g) \R h \\
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\text{if~} & \flessg && \text{~then~} & f\M g & \equiv f \\
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\text{if~} & g\simp f && \text{~then~} & f\M g & \equiv g \\
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\text{if~} & g\simp \NOT f && \text{~then~} & f\M g & \equiv \0 \\
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\text{if~} & g\simp f && \text{~then~} & f\M (g \M h) & \equiv g \M h \\
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\text{if~} & f\simp g && \text{~then~} & f\M (g \M h) & \equiv f \M h \\
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\text{if~} & f\simp g && \text{~then~} & f\M (g \R h) & \equiv f \M h \\
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\text{if~} & h\simp f && \text{~then~} & (f\M g) \M h & \equiv g \M h \\
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\text{if~} & h\simp f && \text{~then~} & (f\R g) \M h & \equiv g \M h \\
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\text{if~} & g\simp h && \text{~then~} & (f\M g) \M h & \equiv (f \AND g) \M h \\
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\text{if~} & f\simp \NOT g & & \text{~then~} & f\OR g & \equiv \1 \\
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\text{if~} & f\simp \NOT g & & \text{~then~} & f\AND g & \equiv \0 \\
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\text{if~} & \flessg & & \text{~then~} & f\OR g & \equiv f \\
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\text{if~} & f\simp g & & \text{~then~} & f\OR g & \equiv g \\
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\text{if~} & \glessf & & \text{~then~} & f\AND g & \equiv g \\
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\text{if~} & f\simp g & & \text{~then~} & f\AND g & \equiv f \\
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\text{if~} & f\simp g & & \text{~then~} & f\EQUIV g & \equiv g\IMPLIES f \\
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\text{if~} & f\simp g & & \text{~then~} & f\IMPLIES g & \equiv \1 \\
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\text{if~} & (\NOT f)\simp g & & \text{~then~} & f\XOR g & \equiv g\IMPLIES \NOT f \\
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\text{if~} & f\simp\NOT g & & \text{~then~} & f\XOR g & \equiv (\NOT g)\IMPLIES f \\
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\text{if~} & \flessg & & \text{~then~} & f\U g & \equiv f \\
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\text{if~} & f\simp g & & \text{~then~} & f\U g & \equiv g \\
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\text{if~} & (f\U g)\Simp g & & \text{~then~} & f\U g & \equiv g \\
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\text{if~} & (\NOT f)\simp g & & \text{~then~} & f\U g & \equiv \F g \\
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\text{if~} & g\simp e & & \text{~then~} & e\U g & \equiv \F g \\
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\text{if~} & f\simp g & & \text{~then~} & f\U (g \U h) & \equiv g \U h \\
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\text{if~} & f\simp g & & \text{~then~} & f\U (g \W h) & \equiv g \W h \\
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\text{if~} & g\simp f & & \text{~then~} & f\U (g \U h) & \equiv f \U h \\
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\text{if~} & f\simp h & & \text{~then~} & f\U (g \R (h \U k)) & \equiv g \R (h \U k) \\
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\text{if~} & f\simp h & & \text{~then~} & f\U (g \R (h \W k)) & \equiv g \R (h \W k) \\
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\text{if~} & f\simp h & & \text{~then~} & f\U (g \M (h \U k)) & \equiv g \M (h \U k) \\
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\text{if~} & f\simp h & & \text{~then~} & f\U (g \M (h \W k)) & \equiv g \M (h \W k) \\
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\text{if~} & f\simp h & & \text{~then~} & (f\U g) \U h & \equiv g \U h \\
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\text{if~} & f\simp h & & \text{~then~} & (f\W g) \U h & \equiv g \U h \\
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\text{if~} & g\simp h & & \text{~then~} & (f\U g) \U h & \equiv (f \U g) \OR h \\
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\text{if~} & (\NOT f)\simp g & & \text{~then~} & f\W g & \equiv \1 \\
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\text{if~} & \flessg & & \text{~then~} & f\W g & \equiv f \\
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\text{if~} & f\simp g & & \text{~then~} & f\W g & \equiv g \\
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\text{if~} & (f\W g)\Simp g & & \text{~then~} & f\W g & \equiv g \\
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\text{if~} & f\simp g & & \text{~then~} & f\W (g \W h) & \equiv g \W h \\
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\text{if~} & g\simp f & & \text{~then~} & f\W (g \U h) & \equiv f \W h \\
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\text{if~} & g\simp f & & \text{~then~} & f\W (g \W h) & \equiv f \W h \\
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\text{if~} & f\simp h & & \text{~then~} & (f\U g) \W h & \equiv g \W h \\
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\text{if~} & f\simp h & & \text{~then~} & (f\W g) \W h & \equiv g \W h \\
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\text{if~} & g\simp h & & \text{~then~} & (f\W g) \W h & \equiv (f \W g) \OR h \\
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\text{if~} & g\simp h & & \text{~then~} & (f\U g) \W h & \equiv (f \U g) \OR h \\
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\text{if~} & \flessg & & \text{~then~} & f\R g & \equiv f \\
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\text{if~} & g\simp f & & \text{~then~} & f\R g & \equiv g \\
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\text{if~} & g\simp \NOT f & & \text{~then~} & f\R g & \equiv \G g \\
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\text{if~} & u\simp g & & \text{~then~} & u\R g & \equiv \G g \\
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\text{if~} & g\simp f & & \text{~then~} & f\R (g \R h) & \equiv g \R h \\
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\text{if~} & g\simp f & & \text{~then~} & f\R (g \M h) & \equiv g \M h \\
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\text{if~} & f\simp g & & \text{~then~} & f\R (g \R h) & \equiv f \R h \\
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\text{if~} & h\simp f & & \text{~then~} & (f\R g) \R h & \equiv g \R h \\
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\text{if~} & h\simp f & & \text{~then~} & (f\M g) \R h & \equiv g \R h \\
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\text{if~} & g\simp h & & \text{~then~} & (f\R g) \R h & \equiv (f \AND g) \R h \\
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\text{if~} & g\simp h & & \text{~then~} & (f\M g) \R h & \equiv (f \AND g) \R h \\
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\text{if~} & \flessg & & \text{~then~} & f\M g & \equiv f \\
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\text{if~} & g\simp f & & \text{~then~} & f\M g & \equiv g \\
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\text{if~} & g\simp \NOT f & & \text{~then~} & f\M g & \equiv \0 \\
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\text{if~} & g\simp f & & \text{~then~} & f\M (g \M h) & \equiv g \M h \\
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\text{if~} & f\simp g & & \text{~then~} & f\M (g \M h) & \equiv f \M h \\
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\text{if~} & f\simp g & & \text{~then~} & f\M (g \R h) & \equiv f \M h \\
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\text{if~} & h\simp f & & \text{~then~} & (f\M g) \M h & \equiv g \M h \\
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\text{if~} & h\simp f & & \text{~then~} & (f\R g) \M h & \equiv g \M h \\
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\text{if~} & g\simp h & & \text{~then~} & (f\M g) \M h & \equiv (f \AND g) \M h \\
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\end{alignat*}
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\endgroup
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@ -1775,12 +1775,38 @@ namespace spot
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trace << "bo: trying inclusion-based rules" << std::endl;
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switch (o)
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{
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case op::Xor:
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case op::Equiv:
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{
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if (c_->implication(a, b))
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return recurse(formula::Implies(b, a));
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if (c_->implication(b, a))
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return recurse(formula::Implies(a, b));
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break;
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}
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case op::Implies:
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SPOT_UNIMPLEMENTED();
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break;
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{
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if (c_->implication(a, b))
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return formula::tt();
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break;
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}
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case op::Xor:
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{
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// if (!a)->b then a xor b = b->!a = a->!b
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if (c_->implication_neg(a, b, false))
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{
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if (b.is(op::Not))
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return recurse(formula::Implies(a, b[0]));
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return recurse(formula::Implies(b, formula::Not(a)));
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}
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// if a->!b then a xor b = (!b)->a = (!a)->b
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if (c_->implication_neg(a, b, true))
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{
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if (b.is(op::Not))
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return recurse(formula::Implies(b[0], a));
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return recurse(formula::Implies(formula::Not(a), b));
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}
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break;
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}
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case op::U:
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// if a => b, then a U b = b
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if (c_->implication(a, b))
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@ -1,6 +1,6 @@
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# -*- mode: python; coding: utf-8 -*-
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# Copyright (C) 2009, 2010, 2012, 2015 Laboratoire de Recherche et Développement
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# de l'Epita (LRDE).
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# Copyright (C) 2009, 2010, 2012, 2015, 2018 Laboratoire de Recherche et
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# Développement de l'Epita (LRDE).
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# Copyright (C) 2003, 2004 Laboratoire d'Informatique de Paris 6 (LIP6),
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# département Systemes Répartis Coopératifs (SRC), Université Pierre
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# et Marie Curie.
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@ -116,3 +116,21 @@ Default for shell: echo 'a U (b U "$strange[0]=name")' | ...
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LBT for shell: echo 'U "a" U "b" "$strange[0]=name"' | ...
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Default for CSV: ...,"a U (b U ""$strange[0]=name"")",...
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Wring, centered: ~~~~~(a=1) U ((b=1) U ("$strange[0]=name"=1))~~~~~"""
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opt = spot.tl_simplifier_options(False, True, True,
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True, True, True,
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False, False, False)
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for (input, output) in [('(a&b)<->b', 'b->(a&b)'),
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('b<->(a&b)', 'b->(a&b)'),
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('(a&b)->b', '1'),
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('b->(a&b)', 'b->(a&b)'),
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('(!(a&b)) xor b', 'b->(a&b)'),
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('(a&b) xor !b', 'b->(a&b)'),
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('b xor (!(a&b))', 'b->(a&b)'),
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('!b xor (a&b)', 'b->(a&b)')]:
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f = spot.tl_simplifier(opt).simplify(input)
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print(input, f, output)
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assert(f == output)
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assert(spot.are_equivalent(input, output))
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