Decomposition of the supervisory control problem for Petri nets under preservation of maximal permissiveness

Decomposing the design of supervisory control laws for Petri nets is an efficient way to tackle its complexity. We consider legal sets which are the union of two sets. In general, this can make the control law obtained via decomposition too restrictive, i.e., it disables more transitions than necessary. Generalizing existing results, we give structural conditions under which the control law via decomposition is maximally permissive.