On the Resource Equivalences in Petri Nets with Invisible Transitions

Two resources (submarkings) are called similar if in any marking any one of them can be replaced by another one without affecting the net’s behaviour (modulo marking bisimulation). It is known that resource similarity is undecidable for general labelled Petri nets. In this paper we study the properties of resource similarity and resource bisimulation (a subset of complete similarity relation, closed under transition firing) in Petri nets with invisible transitions (where some transitions may be unlabelled and hence invisible for external observer). It is shown that for a proper subclass — p-saturated nets — the weak transfer property of resource bisimulation can be effectively checked.