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

Authors Jan Friso Groote , Jan Martens , Erik de Vink

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Jan Friso Groote
  • Eindhoven University of Technology, The Netherlands
Jan Martens
  • Eindhoven University of Technology, The Netherlands
Erik de Vink
  • Eindhoven University of Technology, The Netherlands


We are grateful to the anonymous reviewers of CONCUR 2021 their thorough reading and constructive feedback.

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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)


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).

Subject Classification

ACM Subject Classification
  • Theory of computation
  • Theory of computation → Interactive computation
  • Theory of computation → Design and analysis of algorithms
  • Bisimilarity
  • partition refinement
  • labeled transition system
  • lowerbound


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