A Novel Approach for Constraint Transformation in Petri Nets with Uncontrollable Transitions

The main contribution of this correspondence paper consists in a linear algebraic characterization of the admissible marking set relative to a Petri net with uncontrollable transitions, subject to a linear constraint. In more detail, given a linear constraint that limits the number of tokens in one place, an algorithm is proposed to compute an approximation of the admissible marking set in terms of a disjunction of transformed linear constraints. The optimality of the solution is guaranteed provided that certain conditions are satisfied during the intermediate steps of the iterative approach. In all the other cases, the set of markings described by the transformed constraints could be surely contained in the admissible marking set.