Detecting Symmetric Variables in Boolean Functions using Generalized Reel-Muller Forms

We present a new method for detecting groups of symmetric variables in completely specified Boolean functions. The canonical Generalized Reed-Muller forms are used as a powerful analysis tool. To reduce the search space a set of signatures which identify quickly sets of potentially symmetric variables has been developed. Detecting symmetries of any number of inputs is done simultaneously. Totally symmetric functions can be detected very quickly. The traditional definitions of symmetry have been extended to include more types allowing the grouping of input variables into more classes. Experiments have been performed on MCNC benchmark circuits and the results are very encouraging. >