THEORY OF AJUSTABLE SWITCHING NETWORKS. I: A. THRESHOLD LOGIC. B. RELIABILITY OF SWITCHING NETWORKS

Abstract : A discussion is presented of a doubly infinite chain of properties of threshold functions, the second limit of which characterizes such functions. The first two properties, which are the most useful as necessary conditions, are given special attention; they yield interpretations in algebraic expressions for the function and provide a natural ordering of the function's arguments. Relations between the families of properties are given, and their independence shown. Some other conjectured characterizations of threshold functions are shown invalid. The number of threshold functions, as a function of n, is given a relatively good upper bound. (Author)