In a recent work of ours (A. Nazeem et al., "Designing compact and maximally permissive deadlock avoidance policies for complex resource allocation systems through classification theory: The linear case," IEEE Trans. Autom. Control, vol. 56, 2011), we have proposed the reformulation of the synthesis of the maximally permissive deadlock avoidance policy for certain classes of complex resource allocation systems (RAS) as the design of a linear compact classifier effecting the dichotomy of the underlying reachable state space into its safe and unsafe subspaces. In thiswork, we extend the results of A. Nazeem et al. for the case that the sought dichotomy cannot be represented by a linear classifier. We propose new classification schemes for this more complex case and establish formally their completeness, i.e., their ability to provide an effective classifier for every instance of the considered RAS class. We also provide effective and computationally efficient procedures for the synthesis of the sought classifiers. Finally, the effectiveness and the efficacy of our approaches are demonstrated and assessed through a series of computational experiments.