Generation and Asymmetry of Self-Dual Threshold Functions

Abstract

Properties of self-dual threshold functions are discussed because of the importance of self-dual functions in threshold logic. Since any threshold function can be easily converted into or reduced from a positive self-dual threshold function, we will not lose generality in discussion by exploring the properties of positive self-dual threshold functions. First functions generated by additively or subtractively merging two variables of a positive self-dual threshold function are discussed. Expansions of a positive self-dual threshold function with respect to two variables are then shown, and the generation of functions based on them is discussed. The concepts of strongly asymmetrical self-dual threshold functions and its degree are introduced, and the relation of all self-dual threshold functions of fewer variables with strongly asymmetrical ones is shown. The above discussion enables the classification of threshold functions and the relation between threshold functions of n variables and those of more variables to be better seen. © 1965 IEEE. All rights reserved.