Characterization of Quaternary Threshold Functions in the Vilenkin-Chrestenson Basis

Abstract

This paper deals with the characterization of threshold functions defined on n-dimensional quaternary inputs using the representation of a function in the Vilenkin-Chrestenson basis. It is shown that such a function is uniquely characterized by (2n + 2)-dimensional vector of parameters, that correspond to the Vilenkin-Chrestenson spectrum. (2n + 1) of them correspond to the spectral coefficients of the function and the remaining one correspond to the zero-moment spectral coefficient of the character of the function. We apply the same reasoning to the class of ternary threshold functions as an alternative way to derive their spectral characterization.