Towards a Unified Method of Handling Medium Composition of Petri Nets

Abstract — Introducing modularity in order to analyze a net means finding methods to decompose it into subnets such that properties of the net can be deduced from properties of these subnets. The aim of this paper is to develop a unified approach for deriving some of the fundamental properties of the global net from the properties of its components for certain types of Petri nets such as Place/Transition nets, Colored Petri nets, FIFO nets and Colored FIFO nets. To this end, we define a class of Petri nets: Petri nets on trace monoids. We then show that the newly-defined class of nets offers an umbrella under which the aforementioned four classes of nets can be thought of as its subclasses. Finally, we define the concept of medium composition for Petri nets on trace monoids and discuss the liveness preservation by this composition operation. 1