Automated Synthesis of Deadlock Prevention Supervisors Using Petri Nets

Given an arbitrary Petri net structure, which may have uncontrollable and unobservable transitions, the deadlock prevention procedure presented here determines a set of linear inequalities on the marking of a Petri net. When the Petri net is supervised so that its markings satisfy these inequalities, the supervised net is proved to be deadlock-free for all initial markings that satisfy the supervision constraints. Deadlock-freedom implies that there will always be at least one transition that is enabled in the closed loop (supervised) system. The method is not guaranteed to insure liveness, as it can be applied to systems that cannot be made live under any circumstances. However, it is shown that when the method does insure liveness, it is at least as permissive as any other liveness-insuring supervisor. Moreover, it is shown that the method is not too restrictive even for Petri nets in which not all transitions can be made live. The procedure allows automated synthesis of the supervisors. Based on this method we formulate and prove two extended methods with guaranteed termination and a method for maximally permissive deadlock prevention.