Timed high-level nets

Petri nets have been widely used for modeling and analyzing concurrent systems. Several reasons contribute to their success: the simplicity of the model, the immediate graphical representation, the easy modeling of asynchronous aspects, the possibility of reasoning about important properties such as reachability, liveness, boundedness. However, the original model fails in representing two important features: complex functional aspects, such as conditions which rule the flow of control, and time. Due to that, two different classes of extensions of Petri nets have been proposed: high-level nets and timed Petri nets. High-level nets allow the representation of functional aspects in full details, but do not provide a means for representing time; on the other hand, timed Petri nets have been thought for time representation, but they do not provide a means for representing detailed functional aspects. Thus, these two important aspects cannot be mastered together. In particular, it is difficult to express relationships between time and functional aspects. This paper investigates the relationships between high-level nets and timed Petri nets, thus extending a first set of results published in a previous paper, where a unifying Petri net based model for time representation has been proposed. It first recalls how time can be represented in a Petri net extension called ER nets, and assesses its generality. It then investigates the relationships of ER nets with the best known high-level nets. In particular it shows the overall equivalence of ER nets, Colored Petri nets and Predicate/Transition nets, and extends the mechanism for time representation introduced in ER nets to both Colored Petri nets and Predicate/Transition nets. It also shows that these models cannot be simplified without significantly constraining the timing aspects that can be modeled.