Maximal Class of Weakly Live Ordinary Petri Nets Without Emptiable Siphons

It is known that a net is deadlock free, not necessarily live, if no siphons can become empty. The key structure in making some transitions not live is called virtual first-order structure (VFOS). A net with (without) VFOS is called a virtual net (V net) [nonvirtual net (NV net)]. The V net is a maximal class of nets that may be weakly live and not live, if no siphons can become empty. Any net in the NV nets is live if and only if no siphons can become empty. In this paper, it is shown that asymmetric choice nets, synchronized choice nets, and extended synchronized choice nets belong to the NV nets.