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Automata, Languages and Programming

Volume 4052 of the series Lecture Notes in Computer Science pp 480-491

On the Axiomatizability of Priority

  • Luca AcetoAffiliated withCarnegie Mellon UniversitySchool of Science and Engineering, Reykjavík UniversityDepartment of Computer Science, BRICS, Aalborg University
  • , Taolue ChenAffiliated withCarnegie Mellon UniversityCWI, Embedded Systems GroupState Key Laboratory of Novel Software Technology, Nanjing University
  • , Wan FokkinkAffiliated withCarnegie Mellon UniversityCWI, Embedded Systems GroupSection Theoretical Computer Science, Vrije Universiteit
  • , Anna IngolfsdottirAffiliated withCarnegie Mellon UniversitySchool of Science and Engineering, Reykjavík UniversityDepartment of Computer Science, BRICS, Aalborg University

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Abstract

This paper studies the equational theory of bisimulation equivalence over the process algebra BCCSP extended with the priority operator of Baeten, Bergstra and Klop. It is proven that, in the presence of an infinite set of actions, bisimulation equivalence has no finite, sound, ground-complete equational axiomatization over that language. This negative result applies even if the syntax is extended with an arbitrary collection of auxiliary operators, and motivates the study of axiomatizations using conditional equations. In the presence of an infinite set of actions, it is shown that, in general, bisimulation equivalence has no finite, sound, ground-complete axiomatization consisting of conditional equations over BCCSP. Sufficient conditions on the priority structure over actions are identified that lead to a finite, ground-complete axiomatization of bisimulation equivalence using conditional equations.