This particular monograph aims to present the state-of-the-art developments in the design of behaviorally and structurally optimal liveness-enforcing Petri net supervisors with computationally tractable approaches. The approaches published recently are included in this monograph, including the BDD-based computation and analysis of Petri nets, the theory of regions, the ecient computation of optimal supervisors, the design of the most permissive supervisors if no optimal one exists, the design of an optimal supervisors with the minimal number of control places, the design of behaviorally optimal and structurally simple supervisors, and the optimal supervisor design for forbidden state problems. The main novelties of the presented deadlock resolution are summarized below: 1. Presentation of a method to design a maximally permissive Petri net supervisor.