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DOI: 10.4230/LIPIcs.CONCUR.2021.31

Bisimulation by Partitioning Is Ω((m+n)log n)

Authors: Jan Friso Groote, Jan Martens, and Erik de Vink

Published in: LIPIcs, Volume 203, 32nd International Conference on Concurrency Theory (CONCUR 2021)

Abstract

An asymptotic lowerbound of Ω((m+n)log n) is established for partition refinement algorithms that decide bisimilarity on labeled transition systems. The lowerbound is obtained by subsequently analysing two families of deterministic transition systems - one with a growing action set and another with a fixed action set. For deterministic transition systems with a one-letter action set, bisimilarity can be decided with fundamentally different techniques than partition refinement. In particular, Paige, Tarjan, and Bonic give a linear algorithm for this specific situation. We show, exploiting the concept of an oracle, that the approach of Paige, Tarjan, and Bonic is not of help to develop a generic algorithm for deciding bisimilarity on labeled transition systems that is faster than the established lowerbound of Ω((m+n)log n).

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Jan Friso Groote, Jan Martens, and Erik de Vink. Bisimulation by Partitioning Is Ω((m+n)log n). In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{groote_et_al:LIPIcs.CONCUR.2021.31,
  author =	{Groote, Jan Friso and Martens, Jan and de Vink, Erik},
  title =	{{Bisimulation by Partitioning Is \Omega((m+n)log n)}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{31:1--31:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2021.31},
  URN =		{urn:nbn:de:0030-drops-144087},
  doi =		{10.4230/LIPIcs.CONCUR.2021.31},
  annote =	{Keywords: Bisimilarity, partition refinement, labeled transition system, lowerbound}
}

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Bisimulation by Partitioning Is Ω((m+n)log n)

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