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arXiv · 2404.10648

The General and Finite Satisfiability Problems for PCTL are Undecidable

Miroslav Chodil·Antonín Kučera
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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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Miroslav Chodil, Antonín Kučera. 2024-04-16. The General and Finite Satisfiability Problems for PCTL are Undecidable. https://arxiv.org/abs/2404.10648

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