Some Classes of Live and Safe Petri Nets

We study a series of structural restrictions which gives rise to a set of classes of marked nets: S-systems, T-systems, free choice systems and asymmetric choice systems. This series of restrictions corresponds to a series of behavioural properties of marked nets first introduced by C.A.Petri — sequentially, determinacy and confusion-freeness.For each one of these restrictions, we address the question to what extent the behaviour of a marked net is determined by the structure of the underlying net. In particular, we study the characterisation of liveness and the characterisation of safeness in the presence of liveness. The paper presents strengthened, streamlined and elementary proofs of some important results.