On the ill-timed but well-caused

  • Luca Aceto
  • David Murphy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 715)


There has been considerable controversy in concurrency theory between the ‘interleaving’ and ‘true concurrency’ schools. The former school advocates associating a transition system with a process which captures concurrent execution via the interleaving of occurrences: the latter adopts more complex semantic structures to avoid reducing concurrency to interleaving.

In this paper we show that the two approaches are not irreconcilable. We define a timed process algebra where occurrences are associated with intervals of time, and give it a transition system semantics. This semantics has many of the advantages of the interleaving approach; the algebra admits an expansion theorem, and bisimulation semantics can be used as usual. Our transition systems, however, incorporate timing information, and this enables us to express concurrency: merely adding timing appropriately generalises transition systems to asynchronous transition systems, showing that time gives a link between true concurrency and interleaving. Moreover, we can provide a complete axiomatisation of bisimulation for our algebra; a result that is often problematic in a timed setting.

Another advantage of incorporating timing information into the calculus is that it allows a particularly simple definition of action refinement; this we present.


Transition System Operational Semantic Label Transition System Process Algebra Local Clock 
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.
    L. Aceto, Relating distributed, temporal and causal observations of simple processes, Fundamenta Informaticae, Volume 17 (1992), Number 4, Pp. 369–397.Google Scholar
  2. 2.
    L. Aceto, D. Murphy, Timing and Causality in Process Algebra. In preparation.Google Scholar
  3. 3.
    L. Aceto and M. Hennessy, Towards action-refinement in process algebra, Information and Computation, Volume 103, Number 2 (1993).Google Scholar
  4. 4.
    T. Axford, Concurrent Programming: Fundamental Techniques for Real-Time and Parallel Software Design, Wiley, 1989Google Scholar
  5. 5.
    J. Baeten and J.A. Bergstra, Real time process algebra, Formal Aspects of Computing, Volume 3 (1991), Number 2, Pp. 142–188.CrossRefGoogle Scholar
  6. 6.
    J. Baeten and W. Weijland, Process algebra, Cambridge Tracts in Theoretical Computer Science, Volume 18, Cambridge University Press, 1990.Google Scholar
  7. 7.
    M. Bednarczyk, Categories of asynchronous systems, Ph.D. thesis, Department of Computer Science, University of Sussex, 1987, available as Technical Report Number 3/87.Google Scholar
  8. 8.
    G. Boudol, I. Castellani, M. Hennessy, and A. Kiehn, A theory of processes with locality, Technical Report 13/91, Department of Computer Science, University of Sussex, 1991.Google Scholar
  9. 9.
    P. Darondeau and P. Degano. Caused trees, in Automata, Languages and Programming (B. Rovan, Ed.), Volume 372, Springer-Verlag LNCS, 1989.Google Scholar
  10. 10.
    J. Davies and S. Schneider, An introduction to timed CSP, Technical Report Number 75, Oxford University Computer Laboratory, 1989.Google Scholar
  11. 11.
    G. Ferrari, R. Gorrieri, and U. Montanari, Parametric Jaws for concurrency, manuscript, Dipartimento di Informatica, Universitá di Pisa, 1992.Google Scholar
  12. 12.
    R. van Glabbeek, Comparative concurrency semantics and refinement of actions, Ph.D. thesis, Vrije Universiteit te Amsterdam, 1990.Google Scholar
  13. 13.
    J. Godskesen and K. Larsen, Real-time calculi and expansion theorems, in Proceedings of the 1st North American Process Algebra Workshop, 1992.Google Scholar
  14. 14.
    R. Gorrieri, Refinement, atomicity and transactions for process description languages, Ph.D. thesis, Dipartimento di Informatica, Università di Pisa, 1991, available as Technical Report TD 2/91.Google Scholar
  15. 15.
    R. Gorrieri and M. Roccetti, Towards performance evaluation in process algebra. To appear in the proceedings of AMAST 1993.Google Scholar
  16. 16.
    M. Hennessy, Axiomatising Finite Concurrent Processes, SIAM Journal of Computing, Volume 17, Number 5, 1988.Google Scholar
  17. 17.
    M. Hennessy and T. Regan, A temporal process algebra, Technical Report 2/90, Department of Computer Science, University of Sussex, 1990.Google Scholar
  18. 18.
    C. Hoare, Communicating sequential processes, International series on computer science, Prentice-Hall, 1985.Google Scholar
  19. 19.
    M. Joseph and A. Goswami, Relating computation and time, Technical Report RR 138, Department of Computer Science, University of Warwick, 1985.Google Scholar
  20. 20.
    L. Lamport, On interprocess communication. Part I: Basic formalism, Distributed Computing, Volume 1 (1986), Pp. 77–85.CrossRefGoogle Scholar
  21. 21.
    A. Mazurkiewicz, Traces, histories, graphs: Instances of a process monoid, in Mathematical Foundations of Computer Science, Volume 176, Springer-Verlag LNCS, 1984.Google Scholar
  22. 22.
    R. Milner, Communication and concurrency, International series on computer science, Prentice Hall International, 1989.Google Scholar
  23. 23.
    F. Moller and C. Tofts, A temporal calculus of communicating systems, in the Proceedings of Concur, Volume 459, Springer-Verlag LNCS, pp. 401–415, 1990.Google Scholar
  24. 24.
    D. Murphy, Intervals and actions in a timed process algebra, Technical Report Arbeitspapiere der GMD 680, Gesellschaft für Mathematik und Dataverarbeitung, St. Augustin, 1992, presented at MFPS '92 and submitted to Theoretical Computer Science.Google Scholar
  25. 25.
    X. Nicollin and J. Sifakis, The algebra of timed processes ATP: Theory and application, Technical Report RT-C26, Laboratoire de Génie Informatique de Grenoble, 1990.Google Scholar
  26. 26.
    G. Plotkin, A structurai approach to operational semantics, Technical Report DAIMI-FN-19, Computer Science Department, Århus University, 1981.Google Scholar
  27. 27.
    S. Schneider, An operational semantics for timed CSP, manuscript, Programming Research Group, Oxford University. To appear in Information and Computation.Google Scholar
  28. 28.
    V. Sassone, M. Nielsen and G. Winskel, A classification of models for concurrency, this volume.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Luca Aceto
    • 1
    • 2
  • David Murphy
    • 1
    • 2
  1. 1.School of Cognitive and Computing ScienceUniversity of SussexBrightonEngland
  2. 2.Department of Computer ScienceUniversity of BirminghamBirminghamEngland

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