Well-structured program equivalence is highly undecidable

Authors:
Robert Goldblatt;Marcel Jackson
Affiliations:
Victoria University of Wellington, New Zealand;La Trobe University, Australia
Venue:
ACM Transactions on Computational Logic (TOCL)
Year:
2012

Citing 2
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Effective transformations on infinite trees, with applications to high undecidability, dominoes, and fairness

Journal of the ACM (JACM) - The MIT Press scientific computation series
Dynamic Logic

Dynamic Logic

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Abstract

We show that strict deterministic propositional dynamic logic with intersection is highly undecidable, solving a problem in the Stanford Encyclopedia of Philosophy. In fact we show something quite a bit stronger. We introduce the construction of program equivalence, which returns the value ⊤ precisely when two given programs are equivalent on halting computations. We show that virtually any variant of propositional dynamic logic has a Π11-hard validity problem if it can express even just the equivalence of well-structured programs with the empty program skip. We also show, in these cases, that the set of propositional statements valid over finite models is not recursively enumerable, so there is not even an axiomatization for finitely valid propositions.