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Comparing Labelled Markov Decision Processes

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 Oxford, UK

Funding

  • Kiefer, Stefan: Supported by a Royal Society University Fellowship.

Acknowledgements

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

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Stefan Kiefer and Qiyi Tang. Comparing Labelled Markov Decision Processes. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 49:1-49:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.FSTTCS.2020.49

Abstract

A labelled Markov decision process is a labelled Markov chain with nondeterminism, i.e., together with a strategy a labelled MDP induces a labelled Markov chain. The model is related to interval Markov chains. Motivated by applications of equivalence checking for the verification of anonymity, we study the algorithmic comparison of two labelled MDPs, in particular, whether there exist strategies such that the MDPs become equivalent/inequivalent, both in terms of trace equivalence and in terms of probabilistic bisimilarity. We provide the first polynomial-time algorithms for computing memoryless strategies to make the two labelled MDPs inequivalent if such strategies exist. We also study the computational complexity of qualitative problems about making the total variation distance and the probabilistic bisimilarity distance less than one or equal to one.

Subject Classification

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

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