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The General and Finite Satisfiability Problems for PCTL are Undecidable (2404.10648v1)
Published 16 Apr 2024 in cs.LO
Abstract: The general/finite PCTL satisfiability problem asks whether a given PCTL formula has a general/finite model. We show that the finite PCTL satisfiability problem is undecidable, and the general PCTL satisfiability problem is even highly undecidable (beyond the arithmetical hierarchy). Consequently, there are no sound deductive systems proving all generally/finitely valid PCTL formulae.
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