Computing probabilistic bisimilarity distances for probabilistic automata

Giorgio Bacci, Giovanni Bacci, Kim G. Larsen, Radu Mardare, Qiyi Tang, Franck van Breugel

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

6 Citations (Scopus)
60 Downloads (Pure)


The probabilistic bisimilarity distance of Deng et al. has been proposed as a robust quantitative generalization of Segala and Lynch’s probabilistic bisimilarity for probabilistic automata. In this paper, we present a novel characterization of the bisimilarity distance as the solution of a simple stochastic game. The characterization gives us an algorithm to compute the distances by applying Condon’s simple policy iteration on these games. The correctness of Condon’s approach, however, relies on the assumption that the games are stopping. Our games may be non-stopping in general, yet we are able to prove termination for this extended class of games. Already other algorithms have been proposed in the literature to compute these distances, with complexity in UP ∩ coUP and PPAD. Despite the theoretical relevance, these algorithms are inefficient in practice. To the best of our knowledge, our algorithm is the first practical solution. In the proofs of all the above-mentioned results, an alternative presentation of the Hausdorff distance due to Mémoli plays a central rôle.

Original languageEnglish
Title of host publication30th International Conference on Concurrency Theory, CONCUR 2019
EditorsWan Fokkink, Rob van Glabbeek
Place of PublicationDagstuhl, Germany
Number of pages17
ISBN (Electronic)9783959771214
Publication statusPublished - 1 Aug 2019
Event30th International Conference on Concurrency Theory, CONCUR 2019 - Amsterdam, Netherlands
Duration: 27 Aug 201930 Aug 2019


Conference30th International Conference on Concurrency Theory, CONCUR 2019


  • behavioural metrics
  • probabilistic automata
  • simple policy iteration algorithm
  • simple stochastic games


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