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DOI: 10.4230/LIPIcs.CONCUR.2020.8

A Near-Linear-Time Algorithm for Weak Bisimilarity on Markov Chains

Authors: David N. Jansen, Jan Friso Groote, Ferry Timmers, and Pengfei Yang

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

Abstract

This article improves the time bound for calculating the weak/branching bisimulation minimisation quotient on state-labelled discrete-time Markov chains from O(m n) to an expected-time O(m log⁴ n), where n is the number of states and m the number of transitions. For these results we assume that the set of state labels AP is small (|AP| ∈ O(m/n log⁴ n)). It follows the ideas of Groote et al. (ACM ToCL 2017) in combination with an efficient algorithm to handle decremental strongly connected components (Bernstein et al., STOC 2019).

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David N. Jansen, Jan Friso Groote, Ferry Timmers, and Pengfei Yang. A Near-Linear-Time Algorithm for Weak Bisimilarity on Markov Chains. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{jansen_et_al:LIPIcs.CONCUR.2020.8,
  author =	{Jansen, David N. and Groote, Jan Friso and Timmers, Ferry and Yang, Pengfei},
  title =	{{A Near-Linear-Time Algorithm for Weak Bisimilarity on Markov Chains}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{8:1--8:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.8},
  URN =		{urn:nbn:de:0030-drops-128209},
  doi =		{10.4230/LIPIcs.CONCUR.2020.8},
  annote =	{Keywords: Behavioural Equivalence, weak Bisimulation, Markov Chain}
}

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A Near-Linear-Time Algorithm for Weak Bisimilarity on Markov Chains

Abstract

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