Disjunctive normal formula based supervisory control policy for general Petri nets

A Petri net (PN) is said to be live if it is possible to re any transition, although not immediately, from every reachable marking. A liveness enforcing supervisory policy (LESP) determines which controllable transition is to be prevented from ring at a marking, to ensure the supervised Petri net (PN) is live. A LESP is said to be minimally restrictive if the following property is true { if a minimally restrictive LESP prevents the ring of a transition at a marking, then all other LESPs should do the same. We restrict our attention to a class of general Petri nets (PN) structures, where the existence of an LESP for an instance initialized at a marking, implies the existence of an LESP when the same instance is initialized with a larger initial marking. We show that the minimally restrictive LESP for an instance N from this class is characterized by a collection of boolean formulae f tc(N)gtc2Tc , where Tc is the set of controllable transitions in the PN. The literals in tc(N) are true if and only if the token-load of speci c places meet a threshold. Consequently, appropriately placed threshold-sensors, which detect if the token-load of a place is greater than or equal to a predetermined threshold, provide su cient information to implement the minimally restrictive LESP