Functional Decomposition for Completely Specified Single-Output Functions

Abstract

Functional decomposition as a technique to find realizations for Boolean functions was already introduced in the late fifties and early sixties by Ashenhurst (Ashenhurst, 1959), Curtis (Curtis, 1961), Roth and Karp (Roth and Karp, 1962; Karp, 1963). In recent years functional decomposition has attracted a lot of renewed interest due to several reasons:

• The increased capacities of today’s computers as well as the development of new methods have made the method applicable to larger—scale problems.

• Functional decomposition is especially well suited for the synthesis of lookup-table based fpgas architectures. During the last few years fpgas (see Section 1.4) have become increasingly important.

• robdds provide a data structure which is a compact representation for most Boolean functions occurring in practical applications. Algorithms for functional decomposition have been developed, which work directly based on robdds, so that the decomposition algorithm works based on compact representations and not on function tables as in previous approaches.