The silent step in time

  • A. S. Klusener
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 630)


In untimed process algebras such as CCS and ACP the silent step enables abstraction from internal actions. Several formalizations of abstraction have been introduced, such as observational congruence, delay bisimulation and branching bisimulation. However, in real time process algebras, such as ACPρ, the silent step has not yet received much attention, so far. Therefore, we formalize these semantics regarding the silent step into real time process algebra. We study the characterizing laws, which correspond closely to the untimed laws, and we investigate which of the semantics is appropriate in the context of ACPρ.

1985 Mathematics Subject Classification


1982 CR Categories

D.3.1 F.3.1 J.7 

Key Words & Phrases

Real Time Process Algebra ACP Abstraction 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BB91]
    J.C.M. Baeten and J.A. Bergstra. Real time process algebra. Journal of Formal Aspects of Computing Science, 3(2):142–188, 1991.MATHMathSciNetCrossRefGoogle Scholar
  2. [BG87]
    J.C.M. Baeten and R.J. van Glabbeek. Another look at abstraction in process algebra. In Proceedings 14 th ICALP, Karlsruhe, LNCS 267, pages 84–94. Springer-Verlag, 1987.Google Scholar
  3. [BW90]
    J.C.M. Baeten and W.P. Weijland. Process algebra. Cambridge Tracts in Theoretical Computer Science 18. Cambridge University Press, 1990.Google Scholar
  4. [Fok91]
    W.J. Fokkink. Normal forms in real time process algebra. Report CS-R9149, CWI, Amsterdam, 1991.Google Scholar
  5. [GW91]
    R.J. van Glabbeek and W.P. Weijland. Branching time and abstraction in bisimulation semantics. Report CS-R9120, CWI, Amsterdam, 1991. An extended abstract of an earlier version has appeared in Information Processing 89, North-Holland, 1989.Google Scholar
  6. [HM80]
    M. Hennessy and R. Milner. On observing nondeterminism and concurrency. In Proceedings 7 th ICALP, LNCS 85, pages 299–309. Springer-Verlag, 1980. This is a preliminary version of Algebraic laws for nondeterminism and concurrency. JACM 32(1), pp. 137–161, 1985.Google Scholar
  7. [Hoa85]
    C.A.R. Hoare. Communicating Sequential Processes. Prentice Hall International, 1985.Google Scholar
  8. [Jef91]
    A. Jeffrey. Discrete timed CSP. Technical Report Memo 78, Chalmers University, Goteborg, 1991.Google Scholar
  9. [Klu91a]
    A.S. Klusener. Completeness in real time process algebra. Report CS-R9106, CWI, Amsterdam, 1991. An extended abstract appeared in Proceedings CONCUR 91, Amsterdam, LNCS 527, pages 376–392. Springer-Verlag, 1991.Google Scholar
  10. [Klu91b]
    A.S. Klusener. Abstraction in real time process algebra. Report CS-R9144, CWI, Amsterdam, 1991. An extended abstract appeared in Proceedings of the REX workshop “Real-Time: Theory in Practice”, LNCS 600, Springer-Verlag, 1991.Google Scholar
  11. [Klu92]
    A.S. Klusener. The silent step in time. To appear, CWI, Amsterdam, 1992.Google Scholar
  12. [Mil80]
    R. Milner. A Calculus of Communicating Systems, LNCS 92. Springer-Verlag, 1980.Google Scholar
  13. [Mil81]
    R. Milner. Modal characterisation of observable machine behaviour. In Proceedings CAAP 81, LNCS 112, pages 25–34. Springer-Verlag, 1981.Google Scholar
  14. [Mil83]
    R. Milner. Calculi for synchrony and asynchrony. Theoretical Computer Science, 25:267–310, 1983.MATHMathSciNetCrossRefGoogle Scholar
  15. [Mil89]
    R. Milner. Communication and concurrency. Prentice Hall International, 1989.Google Scholar
  16. [MT90]
    F. Moller and C. Tofts. A temporal calculus of communicating systems. In Proceedings CONCUR 90, Amsterdam, LNCS 458, pages 401–415. Springer-Verlag, 1990.Google Scholar
  17. [MT92]
    F. Moller and C. Tofts. Behavioural abstraction in TCCS. To appear in Proceedings ICALP 92, Vienna, LNCS, Springer-Verlag, 1992.Google Scholar
  18. [Plo81]
    G.D. Plotkin. A structural approach to operational semantics. Report DAIMI FN-19, Computer Science Department, Aarhus University, 1981.Google Scholar
  19. [VL92]
    F.W. Vaandrager and N.A. Lynch. Action transducers and timed automata. 1992. This Volume.Google Scholar
  20. [Wan90]
    Y. Wang. A Calculus of Real Time Systems. PhD thesis, Chalmers University of Technology, Göteborg, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • A. S. Klusener
    • 1
  1. 1.Dept. of Softw. Techn.CWIAB AmsterdamThe Netherlands

Personalised recommendations