On decomposing Boolean functions via extended cofactoring

We investigate restructuring techniques based on decomposition/factorization, with the objective to move critical signals toward the output while minimizing area. A specific application is synthesis for minimum switching activity (or high performance), with minimum area penalty, where decompositions with respect to specific critical variables are needed (the ones of highest switching activity for example). In this paper we describe new types of factorization that extend Shannon cofactoring and are based on projection functions that change the Hamming distance of the original minterms and on appropriate don´t care sets, to favor logic minimization of the component blocks. We define two new general forms of decomposition that are special cases of the pattern F = G(H(X),Y). The related implementations, called P-Circuits, show experimentally promising results in area with respect to Shannon cofactoring.