Strategies for MDP Bisimilarity Equivalence and Inequivalence

Authors Stefan Kiefer , Qiyi Tang

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Author Details

Stefan Kiefer
  • Department of Computer Science, University of Oxford, UK
Qiyi Tang
  • Department of Computer Science, University of Liverpool, UK


We thank the anonymous reviewers of this paper for their constructive feedback.

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Stefan Kiefer and Qiyi Tang. Strategies for MDP Bisimilarity Equivalence and Inequivalence. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 32:1-32:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


A labelled Markov decision process (MDP) is a labelled Markov chain with nondeterminism; i.e., together with a strategy a labelled MDP induces a labelled Markov chain. Motivated by applications to the verification of probabilistic noninterference in security, we study problems whether there exist strategies such that the labelled MDPs become bisimilarity equivalent/inequivalent. We show that the equivalence problem is decidable; in fact, it is EXPTIME-complete and becomes NP-complete if one of the MDPs is a Markov chain. Concerning the inequivalence problem, we show that (1) it is decidable in polynomial time; (2) if there are strategies for inequivalence then there are memoryless strategies for inequivalence; (3) such memoryless strategies can be computed in polynomial time.

Subject Classification

ACM Subject Classification
  • Theory of computation → Program verification
  • Theory of computation → Models of computation
  • Mathematics of computing → Probability and statistics
  • Markov decision processes
  • Markov chains


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