Skip to main content
Springer Nature Link
Log in

Real-timed concurrent refineable behaviours

  • Session 9B
  • Conference paper
  • First Online:
Formal Techniques in Real-Time and Fault-Tolerant Systems (FTRTFT 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 571))

Abstract

The purpose of this paper is to present a real-timed concurrency theory incorporating true concurrency and event refinement. The theory is based on the occurrences of actions; each occurrence or event has a start and a finish. Causality is modelled by assigning a strict partial order to these starts and finishes, while timing is modelled by giving them reals.

The theory is presented in some detail. All of the traditional notions found in concurrency theories (such as conflict, confusion, liveness, fairness and so on) are seen to be expressible. Four notions of causality arise naturally from the model, leading to notions of securing. Three of the notions give rise to underlying event structures, demonstrating that our model generalises Winskel's.

Various causality-preserving bisimulations are introduced as notions of equivalence of timed causal structures. The nonatomicity of occurrences means that events can be refined into structures and, dually, substructures can be abstracted into single events. The equivalences presented are shown to be congruences of event refinement.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

Bibliography

  1. U. Abraham, S. Ben-David, and M. Magidor, On global time and inter-process communication, in Semantics for Concurrency (M. Kwiatkowska, M. Shields, and R. Thomas, Eds.), (1990), Springer-Verlag Workshops in Computing, Leicester.

    Google Scholar 

  2. L. Aceto, Action — refinement in process algebras, Ph.D. thesis, Department of Computer Science, University of Sussex, 1991, available as Technical Report Number 3/91.

    Google Scholar 

  3. M. Bednarczyk, Categories of asynchronous systems, Ph.D. thesis, Department of Computer Science, University of Sussex, 1987.

    Google Scholar 

  4. G. Boudol, I. Castellani, M. Hennessy, and A. Kiehn, Observing localities, Technical Report 4/91, Department of Computer Science, University of Sussex, 1991.

    Google Scholar 

  5. I. Castellani and M. Hennessy, Distributed bisimulations, Journal of the ACM, Volume 10 (1989), pp. 887–911.

    Google Scholar 

  6. P. Darondeau and P. Degano, Event structures, causal trees, and refinements, in Mathematical Foundations of Computer Science (B. Rovan, Ed.), (1990), Springer-Verlag LNCS 452.

    Google Scholar 

  7. J. Davies, Specification and proof in real-time systems, D.Phil. thesis, Oxford University Computing Laboratory, available as technical report Number 93, 1991.

    Google Scholar 

  8. J. Davies and S. Schneider, An introduction to timed CSP, Technical Report Number 75, Oxford University Computing Laboratory, 1989.

    Google Scholar 

  9. C. Fidge and M. Pilling, Specification languages for real-time software, Technical Report 156, Key Centre for Software Technology, Department of Computer Science, University of Queensland, 1990.

    Google Scholar 

  10. J. Gischer, The equational theory of pomsets, Theoretical Computer Science, Volume 61 (1989), Pp. 199–224.

    Google Scholar 

  11. M. Hennessy and T. Regan, A temporal process algebra, Technical Report 2/90, Department of Computer Science, University of Sussex, 1990.

    Google Scholar 

  12. C. Hoare, Communicating sequential processes, International series on computer science, Prentice-Hall, 1985.

    Google Scholar 

  13. W. Janssen, M. Poel, and J. Zwiers, Action systems and action refinement in the development of parallel systems, in the Proceedings of Concur, (1991), Springer-Verlag LNCS 527.

    Google Scholar 

  14. A. Jeffrey, Timed process algebra ≠ time × process algebra, Technical Report 79, Programming Methodology Group, Chalmers University, 1991.

    Google Scholar 

  15. M. Joseph and A. Goswami, Relating computation and time, Technical Report RR 138, Department of Computer Science, University of Warwick, 1985.

    Google Scholar 

  16. S. Kasangian and A. Labella, On continuous real time agents, in Mathematical Foundations of Programming Semantics, (1991), Springer-Verlag LNCS 469.

    Google Scholar 

  17. L. Lamport, On interprocess communication. part I: Basic formalism, Distributed Computing, Volume 1 (1986), Pp. 77–85.

    Google Scholar 

  18. D. Murphy, Time, causality, and concurrency, Ph.D. thesis, Department of Mathematics, University of Surrey, 1989, available as Technical Report CSC 90/R32, Department of Computing Science, University of Glasgow.

    Google Scholar 

  19. -, The physics of observation; a perspective for concurrency theorists, Bulletin of the EATCS, Volume 44 (1991), Pp. 192–200.

    Google Scholar 

  20. -, Testing, betting and timed true concurrency, in the Proceedings of Concur, (1991), Springer-Verlag LNCS 527.

    Google Scholar 

  21. -, Timed process algebra, Petri nets, and event refinement, in Refinement (J. Morris, Ed.), (1991), Springer-Verlag Workshops in Computing.

    Google Scholar 

  22. E-R. Olderog, Nets, terms and formulas, Cambridge Tracts in Theoretical Computer Science, Volume 23, 1991.

    Google Scholar 

  23. A. Pnueli, Linear and branching structures in the semantics and logics of reactive systems, in Automata, Languages and Programming (W. Brauer, Ed.), (1986), Springer-Verlag LNCS 194.

    Google Scholar 

  24. V. Prasad, A calculus of broadcasting systems, in the Proceedings of TAPSOFT (CAAP) (S. Abramsky, Ed.), (1991), Springer-Verlag LNCS 494.

    Google Scholar 

  25. V. Pratt, The pomset model of parallel processes: Unifying the temporal and the spatial, in Proceedings of the CMU/SERC Workshop on Analysis of Concurrency, (1984), Springer-Verlag LNCS 197.

    Google Scholar 

  26. W. Reisig, Petri nets: An introduction, EATCS Monographs on theoretical computer science, Springer-Verlag, 1985.

    Google Scholar 

  27. A. Rensink, Elementary structures of non-atomic events, Technical Report 89-65, Faculteit der Informatica, Universiteit Twente, 1990.

    Google Scholar 

  28. M. Roncken and R. Gerth, A denotational semantics for synchronous and asynchronous behaviour with multiform time, in Semantics for Concurrency (M. Kwiatkowska, M. Shields, and R. Thomas, Eds.), (1990), Springer-Verlag Workshops in Computing, Leicester, 1990.

    Google Scholar 

  29. A. Schettini and J. Winkowsi, Towards an algebra for timed behaviours, Technical report, Institute of Computer Science, Polish Academy of Sciences, 1990, to appear in Theoretical Computer Science.

    Google Scholar 

  30. J. van Benthem, The logic of time, D. Reidel, 1983.

    Google Scholar 

  31. R. van Glabbeek and U. Goltz, Equivalence notions for concurrent systems and refinement of actions, in Mathematical Foundations of Computer Science, (1989), Springer-Verlag LNCS 379.

    Google Scholar 

  32. -, Refinement of actions in causality based models, in Stepwise Refinement of Distributed Systems (J. de Bakker, Ed.), (1990), Springer-Verlag LNCS 430, Proceedings of REX 1989.

    Google Scholar 

  33. R. van Glabbeek and F. Vaandrager, Petri net models for algebraic theories of concurrency, in the Proceedings of the PARLE conference (J. de Bakker, Nijman, and Treleaven, Eds.), (1987), Springer-Verlag LNCS 259.

    Google Scholar 

  34. W. Vogler, Bisimulation and action refinement, Technical Report 342/10/90A, Institut für Informatik, Technische Universität München, 1990.

    Google Scholar 

  35. G. Winskel, Synchronization trees, Theoretical Computer Science, Volume 34 (1985), Pp. 34–84.

    Google Scholar 

  36. -, Event structures, in Petri Nets: Central Models and Their Properties (W. Brauer, W. Reisig, and G. Rozenberg, Eds.), (1986), Springer-Verlag LNCS 254, Proceedings of Advances in Petri Nets.

    Google Scholar 

  37. -, An introduction to event structures, in Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency (J. de Bakker, W. de Roever, and G. Rozenberg, Eds.), (1989), Springer-Verlag LNCS 354, Proceedings of REX 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. GMD F2G2, Schloss Birlinghoven, Postfach 1240, 5205, Sankt Augustin, Germany

    David Murphy

  2. Department of Computational and Mathematical Sciences, University of Surrey, GU2 5XH, Guildford, England

    David Pitt

Authors
  1. David Murphy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David Pitt
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jan Vytopil

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Murphy, D., Pitt, D. (1991). Real-timed concurrent refineable behaviours. In: Vytopil, J. (eds) Formal Techniques in Real-Time and Fault-Tolerant Systems. FTRTFT 1992. Lecture Notes in Computer Science, vol 571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55092-5_29

Download citation

  • DOI: https://doi.org/10.1007/3-540-55092-5_29

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55092-1

  • Online ISBN: 978-3-540-46692-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics