A Graph Theoretic Approach to Switching Function Minimization

Abstract

In this paper we pursue the graph theoretic approach to the switching function minimization problem which is still important in view of today's technological innovations such as programmable logic arrays. We use switching functions graphs (SFG) for studying the structure of switching functions and the minimization problem. The graph theoretic interpretation of the classical minimization problem leads to an alternative and powerful approach to logic design that is suitable for computer implementations. The approach is particularly useful in the analysis and design of suboptimum algorithms for minimization of arbitrarily complex switching functions arising in practice for which exact algorithms are known to be computationally intractable. A few graph theoretic algorithms leading to minimization of switching functions are presented and examples indicating the power of our approach, and algorithms are worked out. Further work needed in the area is indicated.