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Documents authored by Chodil, Miroslav


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Track B: Automata, Logic, Semantics, and Theory of Programming
The Satisfiability and Validity Problems for Probabilistic Computational Tree Logic Are Highly Undecidable

Authors: Miroslav Chodil and Antonín Kučera

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)


Abstract
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.

Cite as

Miroslav Chodil and Antonín Kučera. The Satisfiability and Validity Problems for Probabilistic Computational Tree Logic Are Highly Undecidable. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 151:1-151:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{chodil_et_al:LIPIcs.ICALP.2025.151,
  author =	{Chodil, Miroslav and Ku\v{c}era, Anton{\'\i}n},
  title =	{{The Satisfiability and Validity Problems for Probabilistic Computational Tree Logic Are Highly Undecidable}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{151:1--151:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.151},
  URN =		{urn:nbn:de:0030-drops-235281},
  doi =		{10.4230/LIPIcs.ICALP.2025.151},
  annote =	{Keywords: Satisfiability, temporal logics, probabilistic CTL}
}
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