Are Two Binary Operators Necessary to Finitely Axiomatise Parallel Composition?

Authors Luca Aceto , Valentina Castiglioni , Wan Fokkink , Anna Ingólfsdóttir , Bas Luttik

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Author Details

Luca Aceto
  • Reykjavik University, Iceland
  • Gran Sasso Science Institute, L'Aquila, Italy
Valentina Castiglioni
  • Reykjavik University, Iceland
Wan Fokkink
  • Vrije Universiteit Amsterdam, The Netherlands
Anna Ingólfsdóttir
  • Reykjavik University, Iceland
Bas Luttik
  • Eindhoven University of Technology, The Netherlands


We thank the anonymous reviewers for their valuable comments.

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Luca Aceto, Valentina Castiglioni, Wan Fokkink, Anna Ingólfsdóttir, and Bas Luttik. Are Two Binary Operators Necessary to Finitely Axiomatise Parallel Composition?. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Bergstra and Klop have shown that bisimilarity has a finite equational axiomatisation over ACP/CCS extended with the binary left and communication merge operators. Moller proved that auxiliary operators are necessary to obtain a finite axiomatisation of bisimilarity over CCS, and Aceto et al. showed that this remains true when Hennessy’s merge is added to that language. These results raise the question of whether there is one auxiliary binary operator whose addition to CCS leads to a finite axiomatisation of bisimilarity. This study provides a negative answer to that question based on three reasonable assumptions.

Subject Classification

ACM Subject Classification
  • Theory of computation → Equational logic and rewriting
  • Theory of computation → Process calculi
  • Theory of computation → Operational semantics
  • Equational logic
  • CCS
  • bisimulation
  • parallel composition
  • non-finitely based algebras


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