On encoding and enumerating threshold functions

Abstract

In this paper, we deal with encoding and enumerating threshold functions defined on n-dimensional binary inputs. The paper specifies situations in which the unique characterization of functions from a given class is preserved by usage of an appropriate set of discrete moments. Moreover, sometimes such a characterization (coding) is optimal with respect to the number of necessary bit rate per coded function. By estimating the number of possible values of the discrete moments used, several upper bounds (for different classes of threshold functions) are derived, some of which are better than those previously known.