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, F
n
is a Boolean function of the n binary valued variables (x
1
, x
2
, ..., x
n
) applied to the inputs. The analysis of a threshold element is the determination of the output Boolean function, F
n
when the input variables and their multiplicities are specified. The multiplicity of an input variable x
i
is the number of inputs to which the variable is applied. The fundamental problem in analysis is the determination of F
n
when the number of inputs is moderately large. An algorithm is given which permits a simple straightforward determination of F
n
in reduced, disjunctive form.