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.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Badouel, E.: Splitting of actions, higher-dimensional automata, and net synthesis. Technical Report RR-3490, Inria, France (1996)
Best, E., Devillers, R.: Sequential and concurrent behavior in Petri net theory. Theoretical Computer Science 55(1), 87–136 (1987)
Best, E., Devillers, R., Kiehn, A., Pomello, L.: Concurrent bisimulations in Petri nets. Acta Informatica 28, 231–264 (1991)
Engelfriet, J.: Branching processes of petri nets. Acta Informatica 28(6), 575–591 (1991)
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
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
Goltz, U., Reisig, W.: The non-sequential behaviour of Petri nets. Information and Computation 57, 125–147 (1983)
Meseguer, J., Montanari, U., Sassone, V.: On the semantics of place/transition Petri nets. Mathematical Structures in Computer Science 7, 359–397 (1997)
Mukund, M.: Petri nets and step transition systems. International Journal of Foundations of Computer Science 3(4), 443–478 (1992)
Pratt, V.R.: Modeling concurrency with geometry. In: Proc. 18th Ann. ACM Symposium on Principles of Programming Languages, pp. 311–322 (1991)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
van Glabbeek, R.J. (2005). The Individual and Collective Token Interpretations of Petri Nets. In: Abadi, M., de Alfaro, L. (eds) CONCUR 2005 – Concurrency Theory. CONCUR 2005. Lecture Notes in Computer Science, vol 3653. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11539452_26
Download citation
DOI: https://doi.org/10.1007/11539452_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28309-6
Online ISBN: 978-3-540-31934-4
eBook Packages: Computer ScienceComputer Science (R0)