License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2020.8
URN: urn:nbn:de:0030-drops-128209
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12820/
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Jansen, David N. ; Groote, Jan Friso ; Timmers, Ferry ; Yang, Pengfei

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

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LIPIcs-CONCUR-2020-8.pdf (0.6 MB)


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).

BibTeX - Entry

@InProceedings{jansen_et_al:LIPIcs:2020:12820,
  author =	{David N. Jansen and Jan Friso Groote and Ferry Timmers and Pengfei Yang},
  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 =	{Igor Konnov and Laura Kov{\'a}cs},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12820},
  URN =		{urn:nbn:de:0030-drops-128209},
  doi =		{10.4230/LIPIcs.CONCUR.2020.8},
  annote =	{Keywords: Behavioural Equivalence, weak Bisimulation, Markov Chain}
}

Keywords: Behavioural Equivalence, weak Bisimulation, Markov Chain
Collection: 31st International Conference on Concurrency Theory (CONCUR 2020)
Issue Date: 2020
Date of publication: 26.08.2020


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