Discrete Parameters in Petri Nets

Nicolas David (1) , Claude Jard (1) , Didier Lime (2) , Olivier Henri Roux (2)

1 LINA - Laboratoire d'Informatique de Nantes Atlantique
2 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes

With the aim of significantly increasing the modeling capability of Petri nets, we suggest that models involve parameters to represent the weights of arcs, or the number of tokens in places. We consider the property of coverability of markings. Two general questions arise: " Is there a parameter value for which the property is satisfied? " and " Does the property hold for all possible values of the parameters? ". We show that these issues are undecidable in the general case. Therefore, we also define subclasses of parameterised networks, depending on whether the parameters are used on places, input or output arcs of transitions. For some subclasses, we prove that certain problems become decidable, making these subclasses more usable in practice.

Mots clés: Petri net; Parameters; Coverability

Domaines: Informatique [cs]; Théorie et langage formel [cs.FL]

Nicolas David, Claude Jard, Didier Lime, Olivier Henri Roux. Discrete Parameters in Petri Nets. Application and Theory of Petri Nets and Concurrency, 36th International Conference, PETRI NETS 2015, Jun 2015, Bruxelles, Belgium. pp.137-156, ⟨10.1007/978-3-319-19488-2_7⟩. ⟨hal-01222021⟩