In search of lost time: Axiomatising parallel composition in process algebras

This survey reviews some of the most recent achievements in the saga of the axiomatisation of parallel composition, along with some classic results. We focus on the recursion, relabelling and restriction free fragment of CCS and we discuss the solutions to three problems that were open for many year...

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Veröffentlicht in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science S. 1 - 14
Hauptverfasser: Aceto, Luca, Anastasiadi, Elli, Castiglioni, Valentina, Ingolfsdottir, Anna, Luttik, Bas
Format: Tagungsbericht
Sprache:Englisch
Veröffentlicht: IEEE 29.06.2021
Schlagworte:
Algebra
bisimilarity
CCS
Computer science
Equational logic
linear time-branching time spectrum
parallel composition
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Abstract This survey reviews some of the most recent achievements in the saga of the axiomatisation of parallel composition, along with some classic results. We focus on the recursion, relabelling and restriction free fragment of CCS and we discuss the solutions to three problems that were open for many years. The first problem concerns the status of Bergstra and Klop's auxiliary operators left merge and communication merge in the finite axiomatisation of parallel composition modulo bisimiliarity: We argue that, under some natural assumptions, the addition of a single auxiliary binary operator to CCS does not yield a finite axiomatisation of bisimilarity. Then we delineate the boundary between finite and non-finite axiomatisability of the congruences in van Glabbeek's linear time-branching time spectrum over CCS. Finally, we present a novel result to the effect that rooted weak bisimilarity has no finite complete axiomatisation over CCS.
AbstractList This survey reviews some of the most recent achievements in the saga of the axiomatisation of parallel composition, along with some classic results. We focus on the recursion, relabelling and restriction free fragment of CCS and we discuss the solutions to three problems that were open for many years. The first problem concerns the status of Bergstra and Klop's auxiliary operators left merge and communication merge in the finite axiomatisation of parallel composition modulo bisimiliarity: We argue that, under some natural assumptions, the addition of a single auxiliary binary operator to CCS does not yield a finite axiomatisation of bisimilarity. Then we delineate the boundary between finite and non-finite axiomatisability of the congruences in van Glabbeek's linear time-branching time spectrum over CCS. Finally, we present a novel result to the effect that rooted weak bisimilarity has no finite complete axiomatisation over CCS.
Author Aceto, Luca
Anastasiadi, Elli
Ingolfsdottir, Anna
Luttik, Bas
Castiglioni, Valentina
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  givenname: Bas
  surname: Luttik
  fullname: Luttik, Bas
  email: s.p.luttik@tue.nl
  organization: Eindhoven University of Technology,Eindhoven,The Netherlands
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Snippet This survey reviews some of the most recent achievements in the saga of the axiomatisation of parallel composition, along with some classic results. We focus...
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SubjectTerms Algebra
bisimilarity
CCS
Computer science
Equational logic
linear time-branching time spectrum
parallel composition
Title In search of lost time: Axiomatising parallel composition in process algebras
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