Are Two Binary Operators Necessary to Finitely Axiomatise Parallel Composition?

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Titel: Are Two Binary Operators Necessary to Finitely Axiomatise Parallel Composition?

Beteiligte: Aceto, Luca [VerfasserIn]; Castiglioni, Valentina [VerfasserIn]; Fokkink, Wan [VerfasserIn]; Ingólfsdóttir, Anna [VerfasserIn]; Luttik, Bas [VerfasserIn]

Erschienen: Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2021

Sprache: Englisch

DOI: https://doi.org/10.4230/LIPIcs.CSL.2021.8

Schlagwörter: bisimulation ; parallel composition ; CCS ; non-finitely based algebras ; Equational logic

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Beschreibung: 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.

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