On Applicability of Deadlock Prevention Policies with Uncontrollable and Unobservable Transitions

In deadlock prevention, much work has been done under the assumption that all the transitions are controllable and observable. This paper develops a method to decide whether a deadlock prevention policy is applicable to a plant with uncontrollable and unobservable transitions. By solving a set of linear programming problems, a set of critical controllable transitions and a set of critical observable transitions are obtained. A sufficient and necessary condition is developed, under which a deadlock prevention policy is still applicable when there exist uncontrollable and unobservable transitions. It is concluded that a deadlock prevention policy is applicable if and only if the transitions in the set of critical controllable transitions are controllable and the transitions in the set of critical observable transitions are observable.