Synthesis of Supervisors Enforcing Firing Vector Constraints in Petri Nets

This paper considers the problem of enforcing linear constraints containing marking terms, firing vector terms, and Parikh vector terms. Such constraints increase the expressivity power of the linear marking constraints. We show how this new type of constraints can be enforced in Petri nets. In the case of fully controllable and observable Petri nets, we give the construction of a supervisor enforcing such constraints. In the case of Petri nets with uncontrollable and/or unobservable transitions, we reduce the supervisor synthesis problem to enforcing linear marking constraints on a transformed Petri net.