Fast algorithm for minimizing Reed-Muller expansions of systems of incompletely specified MVL functions

Abstract

A problem of the optimal implementation of multi-valued logic (MVL) functions on the basis of multivalued EXOR gates is considered. In this paper, we are concerned with the question of representing systems of MVL functions by minimum Reed-Muller expansions. A specific class of such representations, called superoptimal, is regarded. For the superoptimal solutions the number of different conjunctions in the sought-for system of polynomials equals to the number of linear independent output variables (on the area of definition). The proposed method enables to find a superoptimal solution for a given system of weakly specified MVL functions, if such a solution exists. It is based on the theory of linear vector spaces.