Generalized Algebraic Deadlock Avoidance Policies for Sequential Resource Allocation Systems

Currently, one of the most actively researched approaches regarding the design of deadlock avoidance policies for sequential resource allocation systems is based on concepts and techniques provided by the, so called, theory of regions, that addresses the broader problem of synthesizing PN models with prespecified behaviors. However, one limitation of the theory of regions and its aforementioned derivatives is that they cannot be applied when the target behavior has a nonconvex representation in the underlying state space. In this note, we show how this problem can be circumvented by appropriately generalizing the employed class of the candidate policies.