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On the Axiomatisation of Branching Bisimulation Congruence over CCS

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

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ACM Subject Classification
  • Theory of computation → Equational logic and rewriting
Keywords
  • Equational basis
  • Weak semantics
  • CCS
  • Parallel composition

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Abstract

In this paper we investigate the equational theory of (the restriction, relabelling, and recursion free fragment of) CCS modulo rooted branching bisimilarity, which is a classic, bisimulation-based notion of equivalence that abstracts from internal computational steps in process behaviour. Firstly, we show that CCS is not finitely based modulo the considered congruence. As a key step of independent interest in the proof of that negative result, we prove that each CCS process has a unique parallel decomposition into indecomposable processes modulo branching bisimilarity. As a second main contribution, we show that, when the set of actions is finite, rooted branching bisimilarity has a finite equational basis over CCS enriched with the left merge and communication merge operators from ACP.

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Luca Aceto, Valentina Castiglioni, Anna Ingólfsdóttir, and Bas Luttik. On the Axiomatisation of Branching Bisimulation Congruence over CCS. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.CONCUR.2022.6

Author Details

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

Funding

This work has been partially supported by the project "Open Problems in the Equational Logic of Processes" (OPEL) of the Icelandic Research Fund (grant No. 196050-051). V. Castiglioni has been supported by the project "Programs in the wild: Uncertainties, adaptabiLiTy and veRificatiON" (ULTRON) of the Icelandic Research Fund (grant No. 228376-051).

Acknowledgements

We thank the reviewers for their valuable comments that helped us to improve our contribution.

References

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