Correctness Verification of Generalized Algebraic Deadlock Avoidance Policies through Mathematical Programming

Generalized algebraic deadlock avoidance policies (DAPs) for sequential resource allocation systems (RAS) have recently been proposed as an interesting extension of the class of algebraic DAPs, that maintains the analytical representation and computational simplicity of the latter, while it guarantees completeness with respect to the maximally permissive DAP. The original work of S. Reveliotis, et al., (2007) that introduced these policies also provided a design methodology for them, but this methodology is limited by the fact that it necessitates the deployment of the entire state space of the considered RAS. Hence, this paper seeks the development of alternative computational tools that can support the synthesis of correct generalized algebraic DAPs while controlling the underlying computational complexity. From a conceptual standpoint, the presented results are motivated by and extend similar past results for the synthesis of correct algebraic DAPs. However, when viewed from a more technical standpoint, the presented developments are complicated by the fact that generalized algebraic DAPs do not admit a convenient representation in the Petri net (PN) modeling framework, that has been the primary vehicle for the aforementioned past developments, and therefore, the relevant analysis must be pursued in an alternative, automaton-based representation of the RAS behavior and the applied policy logic. We believe that this translation of the past results in this new representational framework is a significant contribution in itself, since it enables a more profound understanding of the past developments, and at the same time, it renders them more accessible to the practitioner.