Recursive Petri nets: Theory and application to discrete event systems

Authors:
Serge Haddad;Denis Poitrenaud
Affiliations:
Université Paris-Dauphine, Place du Maréchal De Lattre de Tassigny, 75775, Paris Cedex 16, France;Université Paris VI, Jussieu, 4, Place Jussieu, 75252, Paris Cedex 05, France
Venue:
Acta Informatica
Year:
2007

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Abstract

In order to design and analyse complex systems, modelers need formal models with two contradictory requirements: a high expressivity and the decidability of behavioural property checking. Here we present and develop the theory of such a model, the recursive Petri nets. First, we show that the mechanisms supported by recursive Petri nets enable to model patterns of discrete event systems related to the dynamic structure of processes. Furthermore, we prove that these patterns cannot be modelled by ordinary Petri nets. Then we study the decidability of some problems: reachability, finiteness and bisimulation. At last, we develop the concept of linear invariants for this kind of nets and we design efficient computations specifically tailored to take advantage of their structure.