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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).

Cite as

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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