Work

The Finite Satisfiability Problem for PCTL is Undecidable

Year: 2026

Type: article

Abstract: We show that the problem of whether a given PCTL formula has a finite model is undecidable. The undecidability result holds even for formulae of the form \(\varphi _1 \wedge {\pmb {\mathtt {G}}}_{=1} \varphi _2\) where the validity of \(\varphi _1,\varphi _2\) depends only on the states reachable in at most two transitions. Consequently, the problem of whether a given PCTL formula is valid in all finite-state Markov chains is not even semi-decidable.

Source: Journal of the ACM

DOI: 10.1145/3787496

Authors: Miroslav Chodil, Antonín Kučera

Institution: Masaryk University

Language: English

Topic: Formal Methods in Verification

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Funder: Grantová Agentura České Republiky

Award: G4381856722