Generalized Conditions for Liveness Enforcement and Deadlock Prevention in Petri Nets

This paper presents new results concernedwith 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 extendt wo well known results. Specifically we generalize the result relating deadlock to siphons and the extension to asymmetric choice Petri nets of the Commoner's Theorem. 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.

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