Symmetric Ternary Switching Functions: Their Detection and Realization with Threshold Logic

A simple, systematic procedure for detecting symmetric ternary switching functions is developed. The detection procedure is essentially based on a derived counting theorem. Other important properties and close bounds on the number of ternary symmetric functions are developed. A design method is given whereby symmetric functions can be readily synthesized with switching networks which are economical, and, in certain instances, minimal in the number of ternary threshold devices required. The greatest lower bound on the number of devices required for a given symmetric function is developed.