Transformation of Switching Functions to Completely Symmetric Switching Functions

Abstract—A number of techniques exist for realizing completely symmetric switching functions.1 Completely symmetric switching functions are particularly simple and economical to realize using contact-type gating elements. This paper shows that any switching function can be transformed to a completely symmetric switching function in which some of the arguments are redundant. (Obviously, if a given function is already completely symmetric no transformation is necessary.) The partial symmetry information inherent in a given function plays an important role in the transformation. Efficient machine-oriented methods exist for detecting the partial symmetries present in a switching function.