On Symmetric Functions with Redundant Variables–Weighted Functions

Any switching function may be transformed into a completely symmetric switching function with some of its variables repetitive. In this paper we shall discuss certain properties, easily detectable in decomposition charts, that may be applied to reduce the number of repeated variables when such a transformation is performed. An algorithm utilizing lookup tables based on these properties has been devised enabling us with relative ease to transform an arbitrary switching function of four variables into a completely symmetric switching function with the least number of variables. The algorithm may be generalized to n-variable switching functions provided that the corresponding lookup tables are made available.