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LTL/SVA->Buechi: reject error traces early #1223

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Aug 6, 2025
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@kroening kroening commented Aug 4, 2025

The Buechi automaton accepts counterexamples to the original property. The Buechi acceptance condition requires a lasso where the loop contains an accepting state. A proof of that requires satisfying the looping condition, which may require a very long counterexample.

This adds a shortcut using a sufficient condition for a counterexample: we can reject the property when we reach a state in which the Buechi automaton transitions into an accepting state that has an unconditional self-loop on it. Such traces can always be extended to a lasso as above.

@kroening kroening force-pushed the incomplete-buechi branch from 4c01e47 to 7a79dce Compare August 4, 2025 22:14
@kroening kroening marked this pull request as ready for review August 4, 2025 22:23
@kroening kroening force-pushed the incomplete-buechi branch 4 times, most recently from 3bab967 to 367b584 Compare August 5, 2025 17:55
--
^warning: ignoring
--
Back-end support is missing.
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What does this comment mean when the lines above suggest that the properties are proved and refuted, respectively?

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It's a leftover; removed

--
^warning: ignoring
--
SMT-back end doesn't do cast from bool to bool.
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How does this become apparent when this test isn't excluded from the tests run with the SMT back-end?

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Another leftover; removed

@@ -155,6 +174,37 @@ ltl_to_buechi(const exprt &property, message_handlert &message_handler)
message.debug() << "Buechi liveness signal: " << format(liveness_signal)
<< messaget::eom;

// construct the error signal -- true when the next automaton state
// is nonaccepting with an unconditional self-loop.
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Should this say "accepting" instead of "nonaccepting"?

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Indeed; fixed

The Buechi automaton accepts counterexamples to the original property.  The
Buechi acceptance condition requires a lasso where the loop contains an
accepting state.  A proof of that requires satisfying the looping condition,
which may require a very long counterexample.

This adds a shortcut using a sufficient condition for a counterexample: we
can reject the property when we reach a state in which the Buechi automaton
transitions into an accepting state that has an unconditional self-loop on
it.  Such traces can always be extended to a lasso as above.
@kroening kroening force-pushed the incomplete-buechi branch from 367b584 to 9633ac8 Compare August 6, 2025 16:05
@kroening kroening merged commit f817354 into main Aug 6, 2025
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@kroening kroening deleted the incomplete-buechi branch August 6, 2025 16:14
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2 participants