Generation of self-dual threshold functions and lower bounds of the number of threshold functions and a maximum weight

Abstract

This paper consists of the following: recursive methods of generating self-dual threshold functions, a class of self-dual threshold functions which have interesting properties, a lower bound of the number of threshold functions, and a lower bound of a maximum weight. Any threshold function can be reduced from a self-dual threshold function by assigning 1 or 0 to some variable. In this paper, discussion is limited to self-dual threshold functions but it does not lose generality.