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A new class of a high-level Petri net for modelling logical OR efficiently: Coloured AND/OR Petri nets (CARPN)

In Petri nets (PN), because all the input places of a transition are connected to each other with Logical AND to enable the transition, Logical OR connections amongst its input places cannot be modelled. In the case there are k alternatives (Logical ORs) to perform a task, e.g. assembly of a product, k transitions are required for modelling these k alternatives in a PN model, each transition representing each alternative. This inflates the number of transitions in the PN when the number of alternatives increases. This paper introduces CARPN to model the same k alternatives with fewer transitions and places. The similarities between PN and CARPN are discussed, and based on these similarities formal analysis methods are introduced, as well as a new type of graphical representation. Because the elements of the incidence matrix of a CARPN are integers, the current techniques to obtain the invariants of PN can also be applied to CARPN. In the case of systems having similar structures, the reduction of the incidence matrix, keeping its elements integers, is also discussed.