Generalized Conditions for Liveness Enforcement and Deadlock Prevention in Petri Nets

This paper presents new results concerned with liveness, liveness of a subset of transitions and deadlock in Petri nets. Liveness is seen as a particular case of what we call T -liveness: all transitions in the set T are live. The first results characterize the relation between supervisors enforcing liveness and T -liveness with supervisors preventing deadlock. Then we introduce a class of Petri net subnets allowing us to extend two well known results. Specifically we generalize the result relating deadlock to siphons to a necessary and sufficient condition, and we extend the recent generalization of Commoner’s Theorem for asymmetric choice Petri nets. We conclude by considering how the theoretical results of this paper can be used for deadlock prevention, least restrictive deadlock prevention and least restrictive T -liveness enforcement.