Characterization of Admissible Marking Sets in Petri Nets with Uncontrollable Transitions

This work studies the equivalent transformation from a legal marking set to its admissible marking set. First, the concepts of escaping-marking set and transforming marking set are defined, and two algorithms are provided to compute the transforming marking set and the admissible marking set. Second, the equivalent transformation of a disjunction of linear constraints expressed in terms of generalized mutual exclusion constraints (GMECs) with non-negative weights via uncontrollable transitions is established.