An algorithm for linear constraint transformation in Petri nets

Linear constraint transformation is an important technique to solve the forbidden state problem in Petri nets containing uncontrollable transitions. This work develops an algorithm to perform the transformation of a linear constraint in Petri nets with arbitrary structures. Particularly, two rules are given to specify the priority of transitions for transformation. Moreover, a condition is proposed, under which a complementary marking set appearing during transformation can be directly added to the final transformation result rather than being continuously transformed. Examples are finally presented to illustrate the application of the proposed algorithm.