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Finite Equational Bases in Process Algebra: Results and Open Questions

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Processes, Terms and Cycles: Steps on the Road to Infinity

Part of the book series: Lecture Notes in Computer Science ((LNTCS,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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Author information

Authors and Affiliations

  1. BRICS (Basic Research in Computer Science), Centre of the Danish National Research Foundation, Department of Computer Science, Aalborg University, Fr. Bajersvej 7B, 9220, Aalborg Ø, Denmark

    Luca Aceto & Anna Ingolfsdottir

  2. Department of Software Engineering, CWI, PO Box 94079, 1090 GB, Amsterdam, The Netherlands

    Wan Fokkink & Bas Luttik

  3. Department of Mathematics and Computer Science, Eindhoven Technical University, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Bas Luttik

  4. Department of Computer Science, Reykjavík University, Ofanleiti 2, 103, Reykjavík, Iceland

    Luca Aceto & Anna Ingolfsdottir

  5. Department of Computer Science, Section Theoretical Computer Science, Vrije Universiteit Amsterdam, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    Wan Fokkink

Authors
  1. Luca Aceto
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  2. Wan Fokkink
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  3. Anna Ingolfsdottir
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  4. Bas Luttik
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Editor information

Editors and Affiliations

  1. Institute of Computer Science, University of Innsbruck, Austria

    Aart Middeldorp

  2. Department of Philosophy, Utrecht University, Heidelberglaan 8, 3584 CS, Utrecht, The Netherlands

    Vincent van Oostrom

  3. Department of Theoretical Computer Science, Vrije Universiteit, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    Femke van Raamsdonk

  4. VU Vrije Universiteit Amsterdam,  

    Roel de Vrijer

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Aceto, L., Fokkink, W., Ingolfsdottir, A., Luttik, B. (2005). Finite Equational Bases in Process Algebra: Results and Open Questions. In: Middeldorp, A., van Oostrom, V., van Raamsdonk, F., de Vrijer, R. (eds) Processes, Terms and Cycles: Steps on the Road to Infinity. Lecture Notes in Computer Science, vol 3838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11601548_18

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  • DOI: https://doi.org/10.1007/11601548_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30911-6

  • Online ISBN: 978-3-540-32425-6

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