The General and Finite Satisfiability Problems for PCTL are Undecidable

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Miroslav Chodil, Antonín Kucera

Published: 01 Jan 2024, Last Modified: 23 Jul 2025CoRR 2024EveryoneRevisionsBibTeXCC BY-SA 4.0
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.