Finite Equational Bases in Process Algebra: Results and Open Questions

  • Luca Aceto
  • Wan Fokkink
  • Anna Ingolfsdottir
  • Bas Luttik
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3838)

Abstract

Van Glabbeek (1990) presented the linear time/branching time spectrum of behavioral equivalences for finitely branching, concrete, sequential processes. He studied these semantics in the setting of the basic process algebra BCCSP, and tried to give finite complete axiomatizations for them. Obtaining such axiomatizations in concurrency theory often turns out to be difficult, even in the setting of simple languages like BCCSP. This has raised a host of open questions that have been the subject of intensive research in recent years. Most of these questions have been settled over BCCSP, either positively by giving a finite complete axiomatization, or negatively by proving that such an axiomatization does not exist. Still some open questions remain. This paper reports on these results, and on the state-of-the-art in axiomatizations for richer process algebras with constructs like sequential and parallel composition.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Luca Aceto
    • 1
    • 4
  • Wan Fokkink
    • 2
    • 5
  • Anna Ingolfsdottir
    • 1
    • 4
  • Bas Luttik
    • 2
    • 3
  1. 1.BRICS (Basic Research in Computer Science), Centre of the Danish National Research Foundation, Department of Computer ScienceAalborg UniversityAalborg ØDenmark
  2. 2.Department of Software EngineeringCWIAmsterdamThe Netherlands
  3. 3.Department of Mathematics and Computer ScienceEindhoven Technical UniversityEindhovenThe Netherlands
  4. 4.Department of Computer ScienceReykjavík UniversityReykjavíkIceland
  5. 5.Department of Computer Science, Section Theoretical Computer ScienceVrije Universiteit AmsterdamAmsterdamThe Netherlands

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