A Method for Testing and Realization of Threshold Functions

A standard method for testing and realizing a threshold function is to solve a set of linear inequalities in which the unknowns are the n weights to be assigned to the n variables. In this paper a simple method of solving this set of inequalities is presented. Instead of using the weights themselves as the unknowns, a set of n new unknowns, the incremental weights Δa₁, Δa₂, . . ., Δa_n-1, together with the lowest weight a_n, is used. This change of unknowns results in a simpler set of inequalities which, in turn, furnishes direct information on 1-realizability¹ of the function and on the assignment of weights for realization, often without the necessity for trial and adjustment.