Sequencing and Intermediate Acceptance: Axiomatisation and Decidability of Bisimilarity

Authors Astrid Belder, Bas Luttik, Jos Baeten

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Astrid Belder
  • Eindhoven University of Technology, Eindhoven, The Netherlands
Bas Luttik
  • Eindhoven University of Technology, Eindhoven, The Netherlands
Jos Baeten
  • CWI, Amsterdam, The Netherlands
  • University of Amsterdam, Amsterdam, The Netherlands


We thank the anonymous reviewers for their elaborate reviews.

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Astrid Belder, Bas Luttik, and Jos Baeten. Sequencing and Intermediate Acceptance: Axiomatisation and Decidability of Bisimilarity. In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 11:1-11:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


The Theory of Sequential Processes includes deadlock, successful termination, action prefixing, alternative and sequential composition. Intermediate acceptance, which is important for the integration of classical automata theory, can be expressed through a combination of alternative composition and successful termination. Recently, it was argued that complications arising from the interplay between intermediate acceptance and sequential composition can be eliminated by replacing sequential composition by sequencing. In this paper we study the equational theory of the recursion-free fragment of the resulting process theory modulo bisimilarity, proving that it is not finitely based, but does afford a ground-complete axiomatisation if a unary auxiliary operator is added. Furthermore, we prove that bisimilarity is decidable for processes definable by means of a finite guarded recursive specification over the process theory.

Subject Classification

ACM Subject Classification
  • Theory of computation → Process calculi
  • Sequencing
  • Sequential composition
  • Bisimilarity
  • Axiomatisation
  • Decidability


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