Skip to main content

Metric completion versus ideal completion

  • Conference paper
Structures in Concurrency Theory

Part of the book series: Workshops in Computing ((WORKSHOPS COMP.))

  • 50 Accesses

Abstract

Complete partial orders have been used for a long time for defining semantics of programming languages. In the context of concurrency de Bakker and Zucker [4] proposed a metric setting for handling concurrency, recursion and nontermination, which has proved to be very successful in many applications. Starting with a semantic domain D for ‘finite behaviour’ we investigate the relation between the ideal completion Idl(D) and the metric completion which are both suitable to model recursion and infinite behaviour. We also consider the properties of semantic operators.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. Baier, M.E. Majster-Cederbaum: Denotational semantics in the cpo and metric approach, Theoretical Computer Science, Vol. 135, 1994.

    Google Scholar 

  2. 2]C. Baier, M.E. Majster-Cederbaum: Construction of a cms on a given cpo, Techn. Report 11/94, Universität Mannheim, 1994.

    Google Scholar 

  3. C. Baier, M.E. Majster-Cederbaum: The connection between initial and unique solutions of domain equations in the partial order and metric approach, in print.

    Google Scholar 

  4. J.W. de Bakker, J.I.Zucker: Processes and the Denotational Semantics of Concurrency, Information and Control, Vol.54, No. 1 /2, pp 70–120, 1982.

    Google Scholar 

  5. G. Comyn, M. Dauchet: Metric approximations in ordered domains, Algebraic Methods in Semantics, Cambridge University Press, 1985.

    Google Scholar 

  6. G. Gierz, H. Hofmann, K. Keimel, J. Lawson, M. Mislove, D. Scott: A Compendium of Continuous Lattices, Springer-Verlag, 1980.

    Google Scholar 

  7. K. Kuratowski: Toplogy, Academic Press, 1966.

    Google Scholar 

  8. M.Z. Kwiatkowska: On three constructions of infinite traces, Techn. Report No. CSD-48, University of Leicester, 1991.

    Google Scholar 

  9. M. Majster-Cederbaum, F. Zetzsche: The comparison of a cpo-based with a cms-based semantics for CSP, Theoretical Computer Science, Vol. 124, 1994.

    Google Scholar 

  10. S. Matthews: The Cycle Contracting Mapping Theorem, Research Report 228, Department of Computer Science, University of Warwick, 1992.

    Google Scholar 

  11. 11]A. Mazurkiewicz: Basic notions of trace theory, in Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, Lecture Notes in Computer Science 354, 1989.

    Google Scholar 

  12. R. Milner: Communication and Concurrency, Prentice Hall, 1989.

    Google Scholar 

  13. M.B. Smyth: Quasi-uniformities: Reconciling Domains with Metric Spaces, Proc. of the Third Workshop on the Mathematical Foundations of Pragramming Language Semantics, Lecture Notes in Computer Science 298, 1988.

    Google Scholar 

  14. K. Weihrauch, U. Schreiber: Metric spaces defined by weighted algebraic cpo’s, Fundamentals of Computation Theory, FCT ‘79, Proceedings of the Conference on Algebraic, Arithmetric, and Categorial Methods in Computation Theory, Akademie-Verlag, 1979.

    Google Scholar 

  15. G. Winskel: Event Structure Semantics for CCS and Related Languages, Proc. ICALP 82, Lecture Notes in Computer Science 140, Springer-Verlag, pp 561–576, 1982.

    Google Scholar 

  16. G. Winskel: Synchronisation trees, Theoretical Computer Science, Vol. 34, 1984.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1995 British Computer Society

About this paper

Cite this paper

Majster-Cederbaum, M.E., Baier, C. (1995). Metric completion versus ideal completion. In: Desel, J. (eds) Structures in Concurrency Theory. Workshops in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3078-9_16

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-3078-9_16

  • Publisher Name: Springer, London

  • Print ISBN: 978-3-540-19982-3

  • Online ISBN: 978-1-4471-3078-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics