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

Authors Jan Friso Groote , Jan Martens , Erik de Vink

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Author Details

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

Funding

  • Martens, Jan: AVVA project NWO 612.001.751/TOP1.17.002.

Acknowledgements

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

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.CONCUR.2021.31

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).

Subject Classification

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

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