HEURISTIC MINIMIZATION OF MULTIPLE-VALUED RELATIONS

A multiple-valued relation is a relation between inputs and outputs in which the input variables can assume more than two discrete values. Multiple-valued relations arise quite naturally in many contexts. Using characteristic functions to represent relations, we can handle the problem of minimizing multiple-valued relations as a generalization of the conventional minimization problem of regular logic functions. Our approach is based on a state-of-the-art paradigm for the two level minimization of functions. We clarify some special properties of relations, in contrast to functions, which must be carefully considered in realizing a high quality procedure for solving the minimization problem. An efficient heuristic method to find an optimal sum-of-products representation for a multiple-valued relation is proposed and implemented in the program GYOCRO. It uses multiple-valued decision diagrams (MDD's) to represent the characteristic functions for the relations. Experimental results are presented and compared with previous exact and heuristic Boolean relation minimizers to demonstrate the effectiveness of the proposed method.