On the Minimal Synthesis of One Terminal-Pair Contact Networks

In this paper synthesis of one terminal-pair contact networks is discussed. Concepts of graph theory are used in an attempt to obtain a minimal realization of a given switching function. A tentative cut-set matrix is defined as a dual of the circuit matrix. The latter corresponds to the representation of the switching function as a sum of products, and the former, as a product of sums. It is shown that for a broad class of switching functions [which is a certain extension of the single contact (SC) functions], there exists a pair of dual, orthogonal matrices. Conditions are given under which the realization of one of these matrices turns out to be a minimal one.