The Satisfiability and Validity Problems for Probabilistic Computational Tree Logic Are Highly Undecidable
| Authors | |
|---|---|
| Year of publication | 2025 |
| Type | Article in Proceedings |
| Conference | 52nd International Colloquium on Automata, Languages, and Programming |
| MU Faculty or unit | |
| Citation | |
| Doi | https://doi.org/10.4230/LIPIcs.ICALP.2025.151 |
| Keywords | pctl; probablistic computation tree logic; markov chains; modal and temporal logics; probabilistic verification |
| Description | The Probabilistic Computational Tree Logic (PCTL) is the main specification formalism for discrete probabilistic systems modeled by Markov chains. Despite serious research attempts, the decidability of PCTL satisfiability and validity problems remained unresolved for 30 years. We show that both problems are highly undecidable, i.e., beyond the arithmetical hierarchy. Consequently, there is no sound and complete deductive system for PCTL. |
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