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Unifying Petri Net Semantics with Token Flows

  • Gabriel Juhás
  • Robert Lorenz
  • Jörg Desel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5606)

Abstract

In this paper we advocate a unifying technique for description of Petri net semantics. Semantics, i.e. a possible behaviour, is basically a set of node-labelled and arc-labelled directed acyclic graphs, called token flows, where the graphs are distinguished up to isomorphism. The nodes of a token flow represent occurrences of transitions of the underlying net, so they are labelled by transitions. Arcs are labelled by multisets of places. Namelly, an arc between an occurrence x of a transition a and an occurrence y of a transition b is labelled by a multiset of places, saying how many tokens produced by the occurrence x of the transition a is consumed by the occurrence y of the transition b. The variants of Petri net behaviour are given by different interpretation of arcs and different structure of token flows, resulting in different sets of labelled directed acyclic graphs accepted by the net. We show that the most prominent semantics of Petri nets, namely processes of Goltz and Reisig, partial languages of Petri nets introduced by Grabowski, rewriting terms of Meseguer and Montanari, step sequences as well as classical occurrence (firing) sequences correspond to different subsets of token flows. Finally, we discuss several results achieved using token flows during the last four years, including polynomial test for the acceptance of a partial word by a Petri net, synthesis of Petri nets from partial languages and token flow unfolding.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Gabriel Juhás
    • 1
  • Robert Lorenz
    • 2
  • Jörg Desel
    • 3
  1. 1.Faculty of Electrical Engineering and Information TechnologySlovak University of TechnologyBratislavaSlovakia
  2. 2.Department of Computer ScienceUniversity of AugsburgGermany
  3. 3.Department of Applied Computer ScienceCatholic University of Eichstätt-IngolstadtGermany

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