Transformation of an Arbitrary Switching Function to a Totally Symmetric Function

It is known that any switching function can be written as a totally symmetric function with some of its variables being repetitive. In this note, the least upper bound for the number of variables of the transformed totally symmetric functions based on the partition on the set of variables induced by the partial symmetry of the given switching function is found, and a technique for obtaining a transformed totally symmetric function with the number of variables equal to the least upper bound is given.