The Ins and Outs of Petri Net Composition

Composition is a key issue in Petri net modelling. It is a topic that has been studied for a long time, and that finds practical application in many Petri net frameworks and tools. Multiple approaches to composition exist, based on place or transition refinement, place superposition, transition synchronization, or sub-net substitution to cite a few. In this paper we revisit the peculiarities and technicalities (the ins and outs) of net composition based on the labelling of the net elements. We shall express general composition of nets through a combinatorial operator, that, instantiated with different policies, and completed with operators for parallel composition, label rewriting and restriction, allows us to define different forms of place-based and transition-based compositions. The use of this composition framework for model construction is also examined. For composition based on multisets of labels, we also provide an algorithm for the construction of the composed net that uses a modified version of the Farkas algorithm for the computation of semiflows.