New Methods to Find Optimal Non-Disjoint Bi-Decompositions

This paper presents new efficient methods to find “optimal bi-decomposition” forms of logic functions. An “optimal bi-decomposition” form of f(X) is f = α(g1(X ), g2(X )) where the total number of variables in X and X is the smallest among all bi-decomposition forms of f . We consider two methods; one’s decomposition form is (g1 · g2) and the other’s is (g1⊕g2). The proposed methods can find one of the existing “optimal” decomposition forms efficiently based on the Branch-and-Bound algorithm. These methods can decompose incompletely specified functions. Preliminary experimental results show that the proposed methods can construct networks with fewer levels than conventional methods.