License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2021.31
URN: urn:nbn:de:0030-drops-144087
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Groote, Jan Friso ; Martens, Jan ; de Vink, Erik

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

LIPIcs-CONCUR-2021-31.pdf (0.8 MB)


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).

BibTeX - Entry

  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 =		{},
  URN =		{urn:nbn:de:0030-drops-144087},
  doi =		{10.4230/LIPIcs.CONCUR.2021.31},
  annote =	{Keywords: Bisimilarity, partition refinement, labeled transition system, lowerbound}

Keywords: Bisimilarity, partition refinement, labeled transition system, lowerbound
Collection: 32nd International Conference on Concurrency Theory (CONCUR 2021)
Issue Date: 2021
Date of publication: 13.08.2021

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