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Most of the past research on the problem of deadlock avoidance for sequential 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 sequential RAS, by distinguishing between the off-line and the on-line computation 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. The reported results establish that the proposed method can support the effective deployment of maximally permissive DAP for RAS with very large state spaces.