New Interpolation Algorithms for Multiple-Valued Reed-Muller Forms

This paper presents new algorithms for the sparse multivariate polynomial interpolation over finite fields, which can be used for optimizing Reed-Muller forms for MVL functions. Starting with a new quadratic time interpolation algorithm for Boolean functions, we develop a method that decomposes the problem into several smaller problems for the MVL case. We then show how each of these problems can be solved by a practical probabilistic algorithm. The approach is extended to fixed polarity RM forms, in which the complexity of the resulting forms becomes simpler and also the running time of the algorithm is reduced. 1 Introduction Binary Reed-Muller (RM) expansions [9], [10] can be generalized to nonbinary domains as field expansions, which are defined as a polynomial representation of switching functions over finite fields GF (q), with q = p m , for some prime p and integer m. For incompletely specified functions it is possible to minimize the cost of RM forms by assigning suitable v..