On the Axiomatizability of Priority

  • Luca Aceto
  • Taolue Chen
  • Wan Fokkink
  • Anna Ingolfsdottir
Conference paper

DOI: 10.1007/11787006_41

Volume 4052 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Aceto L., Chen T., Fokkink W., Ingolfsdottir A. (2006) On the Axiomatizability of Priority. In: Bugliesi M., Preneel B., Sassone V., Wegener I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4052. Springer, Berlin, Heidelberg

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Luca Aceto
    • 1
    • 2
  • Taolue Chen
    • 3
    • 5
  • Wan Fokkink
    • 3
    • 4
  • Anna Ingolfsdottir
    • 1
    • 2
  1. 1.School of Science and EngineeringReykjavík UniversityReykjavíkIceland
  2. 2.Department of Computer ScienceBRICS, Aalborg UniversityAalborg ØDenmark
  3. 3.CWI, Embedded Systems GroupAmsterdamThe Netherlands
  4. 4.Section Theoretical Computer ScienceVrije UniversiteitAmsterdamThe Netherlands
  5. 5.State Key Laboratory of Novel Software TechnologyNanjing UniversityNanjing, JiangsuP.R.China