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(x<inf>m</inf>,x<inf>m-1</inf>,...x<inf>1</inf>[/mi]) can be expressed as [mi]C<inf>o</inf>+ C<inf>1</inf>x<inf>1</inf>+ *--+ + C<inf>N</inf><sup>m</sup>_<inf>1</inf>x<inf>m</inf><sup>N-1</sup>x<inf>m-1</inf><sup>N-1</sup>x<inf>1</inf><sup>N-1</sup>[/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.

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