Coloured Petri Nets Extended with Place Capacities, Test Arcs and Inhibitor Arcs

Abstract

In this paper we show how to extend Coloured Petri Nets (CP-nets), with three new modelling primitives-place capacities, test arcs and inhibitor arcs. The new modelling primitives are introduced to improve the possibilities of creating models that are on the one hand compact and comprehensive and on the other hand easy to develop, understand and analyse. A number of different place capacity and inhibitor concepts have been suggested earlier, e.g., integer and multi-set capacities and zero-testing and threshold inhibitors. These concepts can all be described as special cases of the more general place capacity and inhibitor concepts defined in this paper. We give an informal description of the new concepts and show how the concepts can be formally defined and integrated in the Petri net framework-keeping the basic properties of CP-nets. In contrast to a number of the previously suggested extensions to CP-nets the new modelling primitives preserve the concurrency properties of CP-nets. We show how CP-nets with place capacities, test arcs and inhibitor arcs can be transformed into behaviourally equivalent CP-nets without these primitives. From this we conclude that the basic properties of CP-nets are preserved and that the theory developed for CP-nets can be applied to the extended CP-nets. This means that, e.g., the generalisations of analysis methods of CP-nets to cover the new modelling primitives are straightforward.The reader is assumed to be familiar with the notion of CP-nets.

The Algebraic Structure of Petri Nets

“…Zero-safe nets, introduced by Bruni and Montanari [17,18], extend Petri nets with a simple mechanism to model transactions, i.e., two or more transitions that must always occur without any other transition occurring in between. Contextual nets [22,65,45] (see also [21,91,6,5]) are nets with 'read-arcs' used to 'read' without consuming, so allowing multiple, non-exclusive, concurrent uses of the same resource (token) and, therefore, the modeling of shared resources. Bruni and Sassone in [19] extend the categorical process semantics approach surveyed here satisfactorily to contextual nets, building on previous work by Gadducci and Montanari [33].…”

“…The decomposition approach is also followed by [71], while the semantics for the π-calculus (cf. [64]) presented in [20] is based on nets with inhibitory arcs (see, e.g., [22,45]), a powerful extension of PT nets. A related line of research, as already mentioned, takes inspiration from the work on process algebras and set out to design and study net algebras.…”

Checking Bounded Reachability in Asynchronous Systems by Symbolic Event Tracing

“…Our variant is called Colored Contextual Unweighted Petri Nets, or "nets" for short. The word contextual means that nets can contain test arcs [5], allowing compact modeling of non-destructive read operations. By unweighted we mean that each arc is associated with a single token instead of a multiset of tokens as in Colored Petri Nets.…”

Formal requirements modelling with executable use cases and coloured Petri nets

“…If two or more transitions are not in conflict in a given marking, they can be considered as truly concurrent and may be fired in any arbitrary order resulting in the same global state. This property is known as the diamond rule [5]. For formalisms where tokens have values (such as CPN), the diamond rule holds at the level of binding elements [17].…”