Reed-Muller Like Canonic Forms for Multivalued Functions

In this correspondence we show the existence of a Reed-Muller like expansion for multivalued functions. We establish that any m-variable, N-valued function [mi]f(xm,xm-1,...x1[/mi]) can be expressed as [mi]Co+ C1x1+ *--+ + CN^m_1xm^N-1xm-1^N-1x1^N-1[/mi]. A matrix method for determining the coefficients of these expansions is presented. The problem of finding minimal expression for a given function is discussed. Finally, we present a new technique for realizing multiple output functions.