THEORY OF ADJUSTABLE SWITCHING NETWORKS.

Abstract : The two major parts of this report cover the theory of adjustable switching networks: Threshold Logic and Reliability of Switching Networks. Threshold Logic presents the initial stages of our work on the test-synthesis problem: For given switching functions, to determine whether or not they are threshold functions (test), and if they are, to obtain realizations (synthesis). Included here is a careful discussion of the preliminaries of test-synthesis: checking of unateness and positivization; checking of 2-monotonicity, ordering of arguments, and writing of the canonical form; and derivation of the complement and the reduced representations. Also included is a discussion of the basic system of linear equalities for test synthesis and their reduction. One of two dual solution theorems, upon which our proposed test-synthesis procedure is based, is stated and proved. Finally, more recent work on the test synthesis problem is summarized. We plan to write a comprehensive paper on test-synthesis which includes the material presented here (as its first part) and, in addition, a complete discussion of the results obtained more recently. Reliability of Switching Networks provides partial results on the various problems under investigation. (Author)