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(X¹ ),g₂(X²)) where the total number of variables in X¹ and X² 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