Optimal deadlock avoidance for complex resource allocation systems through classification theory

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Most of the past research on the problem of deadlock avoidance for sequential complex resource allocation systems (RAS) has acknowledged the fact that the maximally permissive deadlock avoidance policy (DAP) possesses super-polynomial complexity for most RAS classes, and it has resorted to solutions that trade off maximal permissiveness for computational tractability. In this work, we seek the effective implementation of the maximally permissive DAP for a broad spectrum of RAS, by distinguishing between the off-line and the on-line computation that is required for the specification of this policy, and developing a representation of the derived result that will require minimal on-line computation. The particular representation that we adopt is that of a compact classifier that will effect the underlying dichotomy of the reachable state space into safe and unsafe subspaces. Through a series of reductions of the posed classification problem, we are also able to attain extensive reductions in the computational complexity of the off-line task of the construction of the sought classifier. A series of computational experiments demonstrate the efficacy of the proposed approach and establish its ability to provide tractable implementations of the maximally permissive DAP for problem instances significantly beyond the capacity of any other approach currently available in the literature.