Action Abstraction in Timed Process Algebra

The Case for an Untimed Silent Step
  • Michel A. Reniers
  • Muck van Weerdenburg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4767)


This paper discusses action abstraction in timed process algebras. It is observed that the leading approaches to action abstraction in timed process algebra all maintain the timing of actions, even if these actions are abstracted from.

This paper presents a novel approach to action abstraction in timed process algebras. Characteristic for this approach is that in abstracting from an action, also its timing is abstracted from. We define an abstraction operator and a timed variant of rooted branching bisimilarity and establish that this notion is an equivalence relation and a congruence.


Operational Semantic Process Algebra Deduction Rule Information Processing Letter Closed Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Bergstra, J., Klop, J.: Process algebra for synchronous communication. Information and Control 60(1/3), 109–137 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    van Glabbeek, R., Weijland, W.: Branching time and abstraction in bisimulation semantics (extended abstract). In: Ritter, G. (ed.) Information Processing 1989, pp. 613–618. North-Holland, Amsterdam (1989)Google Scholar
  3. 3.
    van Glabbeek, R., Weijland, W.: Branching time and abstraction in bisimulation semantics. Journal of the ACM 43(3), 555–600 (1996)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Klusener, A.: Models and Axioms for a Fragment of Real Time Process Algebra. PhD thesis, Eindhoven University of Technology (1993)Google Scholar
  5. 5.
    Baeten, J., Bergstra, J.: Discrete time process algebra with abstraction. In: Reichel, H. (ed.) FCT 1995. LNCS, vol. 965, pp. 1–15. Springer, Heidelberg (1995)Google Scholar
  6. 6.
    van der Zwaag, M.B.: The cones and foci proof technique for timed transition systems. Information Processing Letters 80(1), 33–40 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Moller, F., Tofts, C.: Behavioural abstraction in TCCS. In: Kuich, W. (ed.) Automata, Languages and Programming. LNCS, vol. 623, pp. 559–570. Springer, Heidelberg (1992)Google Scholar
  8. 8.
    Chen, L.: A model for real-time process algebras (extended abstract). In: Borzyszkowski, A.M., Sokolowski, S. (eds.) MFCS 1993. LNCS, vol. 711, pp. 372–381. Springer, Heidelberg (1993)Google Scholar
  9. 9.
    Quemada, J., de Frutos, D., Azcorra, A.: TIC: A TImed calculus. Formal Aspects of Computing 5(3), 224–252 (1993)zbMATHCrossRefGoogle Scholar
  10. 10.
    Ho-Stuart, C., Zedan, H., Fang, M.: Congruent weak bisimulation with dense real-time. Information Processing Letters 46(2), 55–61 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Baeten, J.C.M., Middelburg, C.A.: Process Algebra with Timing. EATCS Monographs. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  12. 12.
    Reniers, M., Groote, J., van der Zwaag, M., van Wamel, J.: Completeness of timed μCRL. Fundamenta Informaticae 50(3-4), 361–402 (2002)zbMATHMathSciNetGoogle Scholar
  13. 13.
    Baeten, J., Basten, T., Reniers, M.: Process algebra: Equational theories of communicating processes (2007)Google Scholar
  14. 14.
    Groote, J.: The syntax and semantics of timed μCRL. Technical Report SEN-R9709, CWI, Amsterdam (1997)Google Scholar
  15. 15.
    Aceto, L., Fokkink, W., Verhoef, C.: Structural operational semantics. In: Bergstra, J., Ponse, A., Smolka, S. (eds.) Handbook of Process Algebra, pp. 197–292. Elsevier, Amsterdam (2001)Google Scholar
  16. 16.
    Fokkink, W.: Clock, Trees and Stars in Process Theory. PhD thesis, University of Amsterdam (1994)Google Scholar
  17. 17.
    Fokkink, W.: An axiomatization for regular processes in timed branching bisimulation. Fundamenta Informaticae 32, 329–340 (1997)zbMATHMathSciNetGoogle Scholar
  18. 18.
    Baeten, J., Bergstra, J., Reniers, M.: Discrete time process algebra with silent step. In: Plotkin, G., Stirling, C., Tofte, M. (eds.) Proof, Language, and Interaction: Essays in Honour of Robin Milner. Foundations of Computing Series, pp. 535–569. MIT Press, Cambridge (2000)Google Scholar
  19. 19.
    Fokkink, W., Pang, J., Wijs, A.: Is timed branching bisimilarity an equivalence indeed? In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 258–272. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  20. 20.
    Baeten, J., Middelburg, C., Reniers, M.: A new equivalence for processes with timing: With an application to protocol verification. Technical Report CSR 02-10, Eindhoven University of Technology, Department of Computer Science (2002)Google Scholar
  21. 21.
    Basten, T.: Branching bisimilarity is an equivalence indeed! Information Processing Letters 58(3), 141–147 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Reniers, M., van Weerdenburg, M.: Action abstraction in timed process algebra: The case for an untimed silent step. Technical Report CSR 06-32, Eindhoven University of Technology, Department of Computer Science (2006)Google Scholar
  23. 23.
    Luttik, S.: Choice Quantification in Process Algebra. PhD thesis, University of Amsterdam (April 2002)Google Scholar
  24. 24.
    Baeten, J., Mousavi, M., Reniers, M.: Timing the untimed: Terminating successfully while being conservative. In: Middeldorp, A., van Oostrom, V., van Raamsdonk, F., de Vrijer, R. (eds.) Processes, Terms and Cycles: Steps on the Road to Infinity. LNCS, vol. 3838, pp. 251–279. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  25. 25.
    Baeten, J., Reniers, M.: Duplication of constants in process algebra. Journal of Logic and Algebraic Programming 70(2), 151–171 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Park, D.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) Theoretical Computer Science. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (1981)CrossRefGoogle Scholar
  27. 27.
    Hennessy, M., Milner, R.: Algebraic laws for nondeterminism and concurrency. Journal of the ACM 32, 137–161 (1985)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Michel A. Reniers
    • 1
  • Muck van Weerdenburg
    • 1
  1. 1.Technical University Eindhoven (TU/e), P.O. Box 513, NL-5600 MB EindhovenThe Netherlands

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