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arXiv · 2206.13927

On the Axiomatisation of Branching Bisimulation Congruence over CCS

Luca Aceto·Valentina Castiglioni·Anna Ingolfsdottir·Bas Luttik
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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 Ingolfsdottir, Bas Luttik. 2022-06-28. On the Axiomatisation of Branching Bisimulation Congruence over CCS. https://arxiv.org/abs/2206.13927

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