Abstract Congruence Criteria for Weak Bisimilarity

Authors Stelios Tsampas , Christian Williams , Andreas Nuyts , Dominique Devriese , Frank Piessens

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Stelios Tsampas
  • KU Leuven, Belgium
Christian Williams
  • University of California, Riverside, CA, USA
Andreas Nuyts
  • Vrije Universiteit Brussel, Belgium
Dominique Devriese
  • Vrije Universiteit Brussel, Belgium
Frank Piessens
  • KU Leuven, Belgium


This research was partially funded by the Research Fund KU Leuven. Andreas Nuyts was supported by a grant of the Research Foundation – Flanders (FWO).

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Stelios Tsampas, Christian Williams, Andreas Nuyts, Dominique Devriese, and Frank Piessens. Abstract Congruence Criteria for Weak Bisimilarity. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 88:1-88:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We introduce three general compositionality criteria over operational semantics and prove that, when all three are satisfied together, they guarantee weak bisimulation being a congruence. Our work is founded upon Turi and Plotkin’s mathematical operational semantics and the coalgebraic approach to weak bisimulation by Brengos. We demonstrate each criterion with various examples of success and failure and establish a formal connection with the simply WB cool rule format of Bloom and van Glabbeek. In addition, we show that the three criteria induce lax models in the sense of Bonchi et al.

Subject Classification

ACM Subject Classification
  • Theory of computation → Categorical semantics
  • Structural Operational Semantics
  • distributive laws
  • weak bisimilarity


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