Petri Nets, Configuration Structures and Higher Dimensional Automata

  • Rob J. van Glabbeek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1664)


In this talk, translations between several models of concurrent systems are reviewed c.q. proposed. The models considered capture causality, branching time, and their interplay, and these features are preserved by the translations. To the extent that the models are intertranslatable, this yields support for the point of view that they are all different representations of the same phenomena. The translations can then be applied to reformulate any issue that arises in the context of one model into one expressed in another model, which might be more suitable for analysing that issue. To the extent that the models are not inter-translatable, my investigations are aimed at classifying them w.r.t. their expressiveness in modelling phenomena in concurrency. The results are summarised in the figure at the end of this paper.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E. Badouel (1996): Splitting of actions, higher-dimensional automata, and net synthesis. Technical Report RR-3490, Inria, France.Google Scholar
  2. 2.
    M. Bednarczyk (1987): Categories of asynchronous systems. PhD thesis, Computer Science, University of Sussex, Brighton.Google Scholar
  3. 3.
    G. Boudol (1990): Flow event structures and flow nets. In I. Guessarian, editor: Semantics of Systems of Concurrent Processes, Proceedings LITP Spring School on Theoretical Computer Science, La Roche Posay, France, LNCS 469, Springer, pp. 62–95.Google Scholar
  4. 4.
    G. L. Cattani and V. Sassone (1996): Higher dimensional transition systems. In Proceedings 11th Annual IEEE Symposium on Logic in Computer Science (LICS 96), New Brunswick, USA, IEEE Computer Society Press, pp. 55–62.CrossRefGoogle Scholar
  5. 5.
    M. Droste (1992): Concurrent automata and domains. International Journal of Foundations of Computer Science 3(4), pp. 389–418.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    A. Ehrenfeucht and G. Rozenberg (1990): Partial 2-structures. Acta Informatica 27(4), pp. 315–368.MATHMathSciNetGoogle Scholar
  7. 7.
    R. J. VAN Glabbeek (1988): An operational non-interleaved process graph semantics of CCSP (abstract). In E.-R. Olderog, U. Goltz and R. J. van Glabbeek, editors: Combining compositionality and concurrency, summary of a GMD-workshop, Königswinter, March 1988, Arbeitspapiere der GMD 320, pp. 18–19.Google Scholar
  8. 8.
    R. J. VAN Glabbeek (1991): Bisimulations for higher dimensional automata. Email message, July 7,’ 91. Available at
  9. 9.
    R. J. VAN Glabbeek and U. Goltz (1990): Refinement of actions in causality based models. In J. W. de Bakker, W. P. de Roever and G. Rozenberg, editors: Proceedings REX Workshop on Stepwise Refinement of Distributed Systems: Models, Formalism, Correctness, Mook, The Netherlands, May/June 1989, LNCS 430, Springer, pp. 267–300.Google Scholar
  10. 10.
    R. J. VAN Glabbeek and G. D. Plotkin (1995): Configuration structures (extended abstract). In D. Kozen, editor: Proceedings 10th Annual IEEE Symposium on Logic in Computer Science (LICS 95), San Diego, USA, IEEE Computer Society Press, pp. 199–209.Google Scholar
  11. 11.
    E. Goubault and T. Jensen (1992): Homology of higher dimensional automata. In W. R. Cleaveland, editor: Proceedings CONCUR 92, Stony Brook, NY, USA, LNCS 630, Springer, pp. 254–268.CrossRefGoogle Scholar
  12. 12.
    J. Gunawardena (1992): Causal automata. Theoretical Computer Science 101, pp. 265–288.MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    V. Gupta and V. R. Pratt (1993): Gates accept concurrent behavior. In Proc. 34th Ann. IEEE Symp. on Foundations of Comp. Sci., pp. 62–71. More material on Chu spaces can be found at
  14. 14.
    P. W. Hoogers, H. C. M. Kleijn and P. S. Thiagarajan (1993): Local event structures and Petri nets. In E. Best, editor: Proceedings CONCUR 93, Hildesheim, Germany, LNCS 715, Springer, pp. 462–476.Google Scholar
  15. 15.
    J. Meseguer, U. Montanari and V. Sassone (1992): On the semantics of Petri nets. In W. R. Cleaveland, editor: Proceedings CONCUR 92, Stony Brook, NY, USA, LNCS 630, Springer, pp. 286–301.CrossRefGoogle Scholar
  16. 16.
    M. Mukund (1992): Petri nets and step transition systems. International Journal of Foundations of Computer Science 3(4), pp. 443–478.MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    M. Nielsen, G. D. Plotkin and G. Winskel (1981): Petri nets, event structures and domains, part I. Theoretical Computer Science 13(1), pp. 85–108.MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    M. Nielsen, G. Rozenberg and P. S. Thiagarajan (1992): Elementary transition systems. Theoretical Computer Science 96, pp. 3–33.MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    G. M. Pinna and A. Poigné (1995): On the nature of events: another perspective in concurrency. Theoretical Computer Science 138(2), pp. 425–454.MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    V. R. Pratt (1991): Modeling concurrency with geometry. In Proc. 18th Ann. ACM Symposium on Principles of Programming Languages, pp. 311–322.Google Scholar
  21. 21.
    A. Rabinovich and B. A. Trakhtenbrot (1988): Behavior structures and nets. Fundamenta Informaticae 11(4), pp. 357–404.MATHMathSciNetGoogle Scholar
  22. 22.
    D. Scott (1970): Outline of a mathematical theory of computation. In Proceedings of the 4 th Annual Princeton Conference on Information Sciences and Systems, pp. 169–176.Google Scholar
  23. 23.
    M. W. Shields (1985): Concurrent machines. The Computer Journal 28(5), pp. 449–465.MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    E. W. Stark (1989): Concurrent transition systems. Theoretical Computer Science 64, pp. 221–269.MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    G. Winskel (1987): Event structures. In W. Brauer, W. Reisig and G. Rozenberg, editors: Petri Nets: Applications and Relationships to Other Models of Concurrency, Advances in Petri Nets 1986, Part II; Proceedings of an Advanced Course, Bad Honnef, September 1986, LNCS 255, Springer, pp. 325–392.Google Scholar
  26. 26.
    G. Winskel and M. Nielsen (1995): Models for concurrency. In S. Abramsky, D. M. Gabbay and T. S. E. Maibaum, editors: Handbook of Logic in Computer Science, volume 4: Semantic Modelling, chapter 1. Oxford University Press.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Rob J. van Glabbeek
    • 1
  1. 1.Computer Science DepartmentStanford UniversityStanfordUSA

Personalised recommendations