Abstract
Generalized resources are defined as multisets of Petri net vertices. Here places represent material resources (designated by tokens residing in these places). Transitions correspond to activity resources represented by transition firings. Two generalized resources are called similar if in any Petri net marking one resource can be replaced by another without changing the observable system’s behaviour (modulo bisimulation). In this paper we study some basic properties of generalized resource similarity and prove that, being undecidable, generalized resource similarity is finitely based, and thus can be finitely described. We show also, that similarity of generalized resources allows to express some substantial properties of systems modelled by Petri nets.
This research was partly supported by the Russian Foundation for Basic Research (Grant 03-01-00804) and by the Presidium of the Russian Academy of Science, program “Intellectual computer systems”, project 2.3.
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
Autant, C., Schnoebelen, P.: Place bisimulations in Petri nets. In: Jensen, K. (ed.) ICATPN 1992. LNCS, vol. 616, pp. 45–61. Springer, Heidelberg (1992)
Bashkin, V.A., Lomazova, I.A.: Reduction of Coloured Petri nets based on resource bisimulation. Joint Bulletin of NCC & IIS (Comp. Science) 13, 12–17 (2000) (Novosibirsk, Russia)
Bashkin, V.A., Lomazova, I.A.: Petri Nets and resource bisimulation. Fundamenta Informaticae 55(2), 101–114 (2003)
Bashkin, V.A., Lomazova, I.A.: Resource similarities in Petri net models of distributed systems. In: Malyshkin, V.E. (ed.) PaCT 2003. LNCS, vol. 2763, pp. 35–48. Springer, Heidelberg (2003)
Hirshfeld, Y.: Congruences in commutative semigroups. Research report ECS-LFCS-94-291, Department of Computer Science, University of Edinburgh (1994)
Jančar, P.: Decidability questions for bisimilarity of Petri nets and some related problems. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds.) STACS 1994. LNCS, vol. 775, pp. 581–592. Springer, Heidelberg (1994)
Redei, L.: The theory of finitely generated commutative semigroups. Oxford University Press, New York (1965)
Milner, R.: A Calculus of Communicating Systems. In: Milner, R. (ed.) A Calculus of Communication Systems. LNCS, vol. 92. Springer, Heidelberg (1980)
Shnoebelen, P., Sidorova, N.: Bisimulation and the reduction of Petri nets. In: Nielsen, M., Simpson, D. (eds.) ICATPN 2000. LNCS, vol. 1825, pp. 409–423. Springer, Heidelberg (2000)
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
Bashkin, V.A., Lomazova, I.A. (2005). Similarity of Generalized Resources in Petri Nets. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 2005. Lecture Notes in Computer Science, vol 3606. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11535294_3
Download citation
DOI: https://doi.org/10.1007/11535294_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28126-9
Online ISBN: 978-3-540-31826-2
eBook Packages: Computer ScienceComputer Science (R0)