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Computing Probabilistic Bisimilarity Distances for Probabilistic Automata

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

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Author Details

Giorgio Bacci
  • Department of Computer Science, Aalborg University, DK
Giovanni Bacci
  • Department of Computer Science, Aalborg University, DK
Kim G. Larsen
  • Department of Computer Science, Aalborg University, DK
Radu Mardare
  • Department of Computer Science, Aalborg University, DK
Qiyi Tang
  • Department of Computing, Imperial College, London, UK
Franck van Breugel
  • DisCoVeri Group, Dept. of Electrical Engineering and Computer Science, York University, Canada

Funding

Giovanni Bacci and Kim G. Larsen are funded by the ERC-Project LASSO, Radu Mardare is funded by the ASAP Project, Franck van Breugel is supported by Natural Sciences and Engineering Research Council of Canada.

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Giorgio Bacci, Giovanni Bacci, Kim G. Larsen, Radu Mardare, Qiyi Tang, and Franck van Breugel. Computing Probabilistic Bisimilarity Distances for Probabilistic Automata. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.CONCUR.2019.9

Abstract

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 cap 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Program verification
  • Theory of computation → Models of computation
  • Mathematics of computing → Probability and statistics
Keywords
  • Probabilistic automata
  • Behavioural metrics
  • Simple stochastic games
  • Simple policy iteration algorithm

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