The Realization of Symmetric Switching Functions with Linear-Input Logical Elements

The problem of synthesizing switching networks out of linear-input (threshold) elements is studied for the class of symmetric switching functions. Tight bounds are derived for the number of elements required in a minimal realization, and a method of synthesis is presented which yields economical networks. Minimal networks result for all symmetric functions of no more than about twelve variables, and for several other cases. In particular, it is shown how the parity function of any number n of variables can be realized with about log2(n) elements.