Sufficient conditions for the marked graph realisability of labelled transition systems

Abstract

This paper describes two results within the context of Petri net synthesis from labelled transition systems. We consider a set of structural properties of transition systems, and we show that, given such properties, it is possible to re-engineer a Petri net realisation into one which lies inside the set of marked graphs, a well-understood and useful class of Petri nets.The first result originates from Petri net based workflow specifications, where it is desirable that k customers can share a system without mutual interferences. In a Petri net representation of a workflow, the presence of k customers can be modelled by an initial k-marking, in which the number of tokens on each place is a multiple of k. For any initial k-marking with k≥2, we show that other desirable assumptions such as reversibility and persistence suffice to guarantee marked graph realisability. For the case that k=1, we show that the existence of certain cycles, along with other properties such as reversibility and persistence, again suffices to guarantee marked graph realisability.