Detection of Totally Symmetric Boolean Functions

A new method for detection and identification of totally symmetric Boolean functions is developed. Instead of using maps, charts, or truth tables, with permutations and complementations of variables, this method is based on the number of vertices contained in symmetric functions and the concept of distance between two vertices. Since the distance between any two vertices remains invariant under any number of permutations and complementations of the variables, this method lends itself equally conveniently to the detection of total symmetry of Boolean functions with respect to purely uncomplemented, purely complemented, or mixed variables. A procedure is presented, and an example is worked out to illustrate the application of the method.