Boolean coordination problems for product discrete event systems

A general coordination problem is formulated for discrete event systems with concurrent operation modeled by the synchronous product of controllable generators. This problem requires that the invariance of a Boolean predicate on the state set be maintained by appropriate choice of control actions. Necessary and sufficient conditions for the existence of a coordinator which guarantees that the supervised system satisfies the Boolean predicate are presented. The computational tractability of two commonly encountered representations for coordination constraints specified by Boolean predicates (conjunctions of elementary disjunctions and hyperplanes) are investigated. It is shown that restricted instances of these problems can be solved in a time bounded by a polynomial in the input size