A Structure Causality Relation for Liveness Characterisation in Petri Nets

Characterising liveness using a structure based approach is a key issue in theory of petri nets. in this paper, we introduce a structure causality relation from which a topological characterisation of liveness in petri nets is defined. this characterisation relies on a controllability property of siphons and allows to determine the borders of the largest abstract class of petri nets for which equivalence between liveness and deadlock-freeness holds. hence, interesting subclasses of p/t systems, for which membership can be easily determined, are presented. moreover, this paper resumes, from a new point of view, similar results related to this issue and, provides a unified interpretation of the causes of the non-equivalence between liveness and deadlock-freeness.