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Three metric domains of processes for bisimulation

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Mathematical Foundations of Programming Semantics (MFPS 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 802))

Abstract

A new metric domain of processes is presented. This domain is located in between two metric process domains introduced by De Bakker and Zucker. The new process domain characterizes the collection of image finite processes. This domain has as advantages over the other process domains that no complications arise in the definitions of operators like sequential composition and parallel composition, and that image finite language constructions like random assignment can be modelled in an elementary way. As in the other domains, bisimilarity and equality coincide in this domain.

The three domains are obtained as unique (up to isometry) solutions of equations in a category of 1-bounded complete metric spaces. In the case the action set is finite, the three domains are shown to be equal (up to isometry). For infinite action sets, e.g., equipollent to the set of natural or real numbers, the process domains are proved not to be isometric.

This work was partially supported by the Netherlands Nationale Faciliteit Informatica programme, project Research and Education in Concurrent Systems (REX).

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Authors and Affiliations

  1. Department of Software Technology, CWI, Kruislaan 413, 1098, SJ Amsterdam

    Franck van Breugel

  2. Department of Mathematics and Computer Science, Vrije Universiteit, De Boelelaan 1081a, 1081, HV Amsterdam

    Franck van Breugel

Authors
  1. Franck van Breugel
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Editor information

Stephen Brookes Michael Main Austin Melton Michael Mislove David Schmidt

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© 1994 Springer-Verlag Berlin Heidelberg

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van Breugel, F. (1994). Three metric domains of processes for bisimulation. In: Brookes, S., Main, M., Melton, A., Mislove, M., Schmidt, D. (eds) Mathematical Foundations of Programming Semantics. MFPS 1993. Lecture Notes in Computer Science, vol 802. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58027-1_5

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  • DOI: https://doi.org/10.1007/3-540-58027-1_5

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  • Print ISBN: 978-3-540-58027-0

  • Online ISBN: 978-3-540-48419-6

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