A procedure called Hierarchically Accelerated Dynamic programming (HADP) is presented which, at the cost of a degree of suboptimality, can significantly accelerate dynamic programming algorithms (by up to several orders of magnitude) for discrete event systems modeled by finite-state machines (FSMs). The methodology is based upon the (possibly iterated) dynamical abstraction of a given FSM by state aggregation in order to generate a so-called partition machine hierarchy (Caines and Wei, 1995, 1998). Necessary and sufficient conditions for the RADP procedure to generate globally optimal solutions are given as well as bounds on the degree of suboptimality of the method. A group of examples called the Broken Manhattan Grid (BMG) problems is used to illustrate an implementation of RADP with two and three level hierarchies. Approaches to improving the performance of suboptimal HADP procedures by the use of the so-called semidual HADP method are outlined in the Appendix. A set of open problems is described concerning the construction and selection of the partition machine abstractions and the improvement of the estimation of RADP suboptimality.