Several analytic procedures exist for transforming a partially symmetric switching function to a totally symmetric switching function by judiciously repeating certain variables. Presumably the best totally symmetric representation for a given function would be the one having the fewest variables. This note presents an iterative technique for finding the totally symmetric realization for a given function that has the absolute minimum number of variables.

It is shown that any ternary switching function can be transformed to a completely symmetric ternary switching function in which some of the variables are repeated. The partial symmetry information inherent in a given function plays a key role in this transformation.

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.