OPTIMUM AND HEURISTIC ALGORITHMS FOR AN APPROACH TO FINITE STATE MACHINE DECOMPOSITION

Techniques have been proposed in the past for various types of finite state machine (FSM) decomposition that use the number of states or edges in the decomposed circuits as the cost function to be optimized. Such measures are not reflective of the true logic complexity of the decomposed circuits. In addition, previous methods have been mainly heuristic in nature and offer limited guarantees as to the quality of the decomposition. In this paper, optimum and heuristic algorithms for the general decomposition of FSM's such that the sum total of the number of product terms in the one-hot coded and logic minimized submachines is minimum or minimal, are presented. This cost function is much more reflective of the area of an optimally state-assigned and minimized submachine than the number of states/edges in the submachine. The problem of optimum two-way FSM decomposition is formulated as one of symbolic output partitioning and it is shown that this is an easier problem than optimum state assignment. A procedure of constrained prime implicant generation and covering is described that represents an optimum FSM decomposition algorithm, under the specified cost function. It is shown that by means of this formulation, arbitrary decomposition topologies can be targeted by suitably modifying the encodeability constraints during the covering. Exact procedures are not viable for large problem instances because of limitations imposed by currently available computing resources. To overcome these limitations, a novel iterative optimization strategy of symbolic implicant expansion and reduction, modified from two-level Boolean minimizers, that represents a heuristic algorithm based on our exact procedure, is presented. Reduction and expansion are performed on functions with symbolic, rather than binary-valued outputs. The heuristic procedure can be used for problems of any size. Preliminary experimental results have been presented that illustrate both the efficacy of the proposed algorithms and the validity of the selected cost function.