Orthogonal Expansion Applied to the Design of Threshold-element Networks

To gain insight into the problem of desigining threshold-element networks and providing mathematical background for design procedures, a study of functions of linearly transformed (modulo-2) input variables is presented. Circuitry for realizing linearly decomposed functions consists of two parts: linear and nonlinear. The linear circuitry design is straightforward. Orthogonal expansion demonstrates that the nonlinear cic cuitry can always be realized by a single threshold element. Functions of n variables which are linearly separable by n transformed variables for separability are more easily handled by a combination of compacting and implication. This method is efficient, but does not always lead to a single-element nonlinear circuit. A procedure is developed for assigning values to unspecified minterms based on the ease with which the completely specified function can be compacted. (Author).