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Deciding Probabilistic Bisimilarity Distance One for Probabilistic Automata

Authors Qiyi Tang, Franck van Breugel

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Author Details

Qiyi Tang
  • Department of Computing, Imperial College, London, United Kingdom
Franck van Breugel
  • Department of Electrical Engineering and Computer Science, York University, Toronto, Canada

Funding

Natural Sciences and Engineering Research Council of Canada

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Qiyi Tang and Franck van Breugel. Deciding Probabilistic Bisimilarity Distance One for Probabilistic Automata. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.CONCUR.2018.9

Abstract

Probabilistic bisimilarity, due to Segala and Lynch, is an equivalence relation that captures which states of a probabilistic automaton behave exactly the same. Deng, Chothia, Palamidessi and Pang proposed a robust quantitative generalization of probabilistic bisimilarity. Their probabilistic bisimilarity distances of states of a probabilistic automaton capture the similarity of their behaviour. The smaller the distance, the more alike the states behave. In particular, states are probabilistic bisimilar if and only if their distance is zero.
Although the complexity of computing probabilistic bisimilarity distances for probabilistic automata has already been studied and shown to be in NP cap coNP and PPAD, we are not aware of any practical algorithm to compute those distances. In this paper we provide several key results towards algorithms to compute probabilistic bisimilarity distances for probabilistic automata. In particular, we present a polynomial time algorithm that decides distance one. Furthermore, we give an alternative characterization of the probabilistic bisimilarity distances as a basis for a policy iteration algorithm.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Markov processes
  • Theory of computation → Concurrency
Keywords
  • probabilistic automaton
  • probabilistic bisimilarity
  • distance

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