Are Two Binary Operators Necessary to Obtain a Finite Axiomatisation of Parallel Composition?
Authors: 
Luca Aceto, Valentina Castiglioni, 
Wan Fokkink, Anna Ingólfsdóttir, Bas LuttikAuthors Info & Claims
Luca Aceto, Valentina Castiglioni, Wan Fokkink, Anna Ingólfsdóttir, Bas LuttikAuthors Info & ClaimsArticle No.: 22, Pages 1 - 56
Abstract
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. We contribute to answering this question in the simplified setting of the recursion-, relabelling-, and restriction-free fragment of CCS. We formulate three natural assumptions pertaining to the operational semantics of auxiliary operators and their relationship to parallel composition and prove that an auxiliary binary operator facilitating a finite axiomatisation of bisimilarity in the simplified setting cannot satisfy all three assumptions.
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Index Terms
- Are Two Binary Operators Necessary to Obtain a Finite Axiomatisation of Parallel Composition?
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Publication History
Published: 20 October 2022
Online AM: 20 April 2022
Accepted: 29 March 2022
Revised: 04 March 2022
Received: 31 May 2021
Published in TOCL Volume 23, Issue 4
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