Structural properties of petri nets

Abstract

Several necessary conditions for structural liveness and a necessary and sufficient condition for structural boundedness are given. These conditions can be verified by using techniques of linear algebra and could be used for proving liveness and boundedness depending on a given marking. Structural boundedness and liveness are related to the existence of deadlocks traps absorbers and generators of a special type in a PN. A necessary condition for a PN to be structurally bounded and live is that it be both invariant and consistent. Thus invariance and consistency, which imply also the strong connexity of the graphic representation, are necessary conditions for evitating pathological situations such as structural unboundedness and structural unliveness.