Simplification of switching functions expressed in Reed-Muller algebraic form

The simplification of switching functions expressed as modulo-2 sums of products is investigated. It is demonstrated that the apparently different approaches of general simplification and the location of the optimum canonical representation of a given function are ultimately equivalent providing the complete range of possible canonical forms is considered. An extended form of function vector is introduced and it is shown that the set of all possible vectors can be partitioned into equal-sized cosets each of which corresponds to different truth vector. Some properties of these cosets are given and a number of simplification procedures based on this extended function vector are outlined.