Efficient Boolean division and substitution

Boolean division, and hence Boolean substitution, produces better result than algebraic division and substitution. However, due to the lack of an efficient Boolean division algorithm, Boolean substitution has rarely been used. We present an efficient Boolean division and substitution algorithm. Our technique is based on the philosophy of redundancy addition and removal. By adding multiple wires/gates in a specialized way, we tailor the philosophy onto the Boolean division and substitution problem. From the viewpoint of traditional division/substitution, our algorithm can perform substitution not only in sum-of-product form for but also in product-of-sum form. Our algorithm can also naturally take all types of don't cares into consideration. As far as substitution is concerned, we also discuss the case where we are allowed to decompose not only the dividend but also the divisor. Experiments are presented and the result is promising.