An Algorithm for Threshold Element Analysis

A majority or threshold element is a device with a finite number of inputs and a single output. The output, Fn is a Boolean function of the n binary valued variables (x1, x2, ..., xn) applied to the inputs. The analysis of a threshold element is the determination of the output Boolean function, Fn when the input variables and their multiplicities are specified. The multiplicity of an input variable xi is the number of inputs to which the variable is applied. The fundamental problem in analysis is the determination of Fn when the number of inputs is moderately large. An algorithm is given which permits a simple straightforward determination of Fn in reduced, disjunctive form.