The Individual and Collective Token Interpretations of Petri Nets

  • Robert Jan van Glabbeek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3653)

Abstract

Starting from the opinion that the standard firing rule of Petri nets embodies the collective token interpretation of nets rather than their individual token interpretation, I propose a new firing rule that embodies the latter. Also variants of both firing rules for the self-sequential interpretation of nets are studied. Using these rules, I express the four computational interpretations of Petri nets by semantic mappings from nets to labelled step transition systems, the latter being event-oriented representations of higher dimensional automata. This paper totally orders the expressive power of the four interpretations, measured in terms of the classes of labelled step transition systems up to isomorphism of reachable parts that can be denoted by nets under each of the interpretations. Furthermore, I extend the unfolding construction of place/transition nets into occurrence net to nets that may have transitions without incoming arcs.

References

  1. 1.
    Badouel, E.: Splitting of actions, higher-dimensional automata, and net synthesis. Technical Report RR-3490, Inria, France (1996) Google Scholar
  2. 2.
    Best, E., Devillers, R.: Sequential and concurrent behavior in Petri net theory. Theoretical Computer Science 55(1), 87–136 (1987)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Best, E., Devillers, R., Kiehn, A., Pomello, L.: Concurrent bisimulations in Petri nets. Acta Informatica 28, 231–264 (1991)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Engelfriet, J.: Branching processes of petri nets. Acta Informatica 28(6), 575–591 (1991)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    van Glabbeek, R.J.: On the expressiveness of higher dimensional automata (extended abstract). In: Proc. 11th International Workshop on Expressiveness in Concurrency, EXPRESS 2004. Electronic Notes in Theoretical Computer Science, vol. 128(2), pp. 5–34 (2005), Available at http://boole.stanford.edu/pub/hda-ea.pdf
  6. 6.
    van Glabbeek, R.J., Plotkin, G.D.: Configuration structures (extended abstract). In: Kozen, D. (ed.) Proceedings 10th Annual IEEE Symposium on Logic in Computer Science, LICS 1995, San Diego, USA, pp. 199–209. IEEE Computer Society Press, Los Alamitos (1995), Available at http://boole.stanford.edu/pub/conf.ps.gz
  7. 7.
    Goltz, U., Reisig, W.: The non-sequential behaviour of Petri nets. Information and Computation 57, 125–147 (1983)MATHMathSciNetGoogle Scholar
  8. 8.
    Meseguer, J., Montanari, U., Sassone, V.: On the semantics of place/transition Petri nets. Mathematical Structures in Computer Science 7, 359–397 (1997)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Mukund, M.: Petri nets and step transition systems. International Journal of Foundations of Computer Science 3(4), 443–478 (1992)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Pratt, V.R.: Modeling concurrency with geometry. In: Proc. 18th Ann. ACM Symposium on Principles of Programming Languages, pp. 311–322 (1991)Google Scholar
  11. 11.
    Winskel, G.: Event structures. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) Petri Nets: Applications and Relationships to Other Models of Concurrency, Advances in Petri Nets 1986, Part II, Proceedings of an Advanced Course, Bad Honnef. LNCS, vol. 255, pp. 325–392. Springer, Heidelberg (1987)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Robert Jan van Glabbeek
    • 1
  1. 1.National ICT Australia, and School of Computer Science and EngineeringThe University of New South Wales 

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