An Algorithm for Transformation of an Arbitrary Switching Function to a Completely Symmetric Function

It is well known that any switching function may be transformed into a completely symmetric function when repetition of the input variables is allowed. We present an algorithm that may be applied to reduce the number of repeated variables when the transformation is performed. The method is based on an iterative construction of symmetric functions by admitting an increasing number of variables towards a completely symmetric function. The algorithm produces a near minimal number of the total number of inputs in the resultant symmetric function. This algorithm can also be used to determine all partially symmetric variable sets of a given function.