Approximate Bisimulation Minimisation

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


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

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Stefan Kiefer and Qiyi Tang. Approximate Bisimulation Minimisation. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 48:1-48:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We propose polynomial-time algorithms to minimise labelled Markov chains whose transition probabilities are not known exactly, have been perturbed, or can only be obtained by sampling. Our algorithms are based on a new notion of an approximate bisimulation quotient, obtained by lumping together states that are exactly bisimilar in a slightly perturbed system. We present experiments that show that our algorithms are able to recover the structure of the bisimulation quotient of the unperturbed system.

Subject Classification

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


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