A new linear constraint transformation approach for Petri nets with uncontrollable transitions

This work focuses on the problem of providing a linear algebraic characterization of the admissible marking set relative to a Petri net with uncontrollable transitions, subject to a linear constraint. More specifically, given a linear constraint that limits the number of tokens in one place, an algorithm is proposed to provide 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.