Detection of symmetries in combinatorial functions by spectral means

The detection of symmetries in switching functions is proposed using Rademacher-Walsh spectral techniques rather than Boolean-based methods. It is shown that the spectral domain can provide an immediate guidance to which symmetries may be present in any given function by a single necessary but not sufficient numerical test. Sufficiency may be proved by further simple checks. The power of the method enables a comprehensive range of symmetries to be defined, of which complete symmetry in all input variables is merely a special case. The possible use of symmetries in the efficient synthesis of given functions is briefly indicated.