An optimization of AND-OR-EXOR three-level networks

Presents a design method for AND-OR-EXOR three-level networks, where a single two-input EXOR gate is used. The network realizes an exclusive-OR of two sum-of-products expressions (EX-SOP), where the two sum-of-products expressions (SOPs) cannot share products. The problem is to minimize the total number of products in the two SOPs. We introduced the μ-equivalence of logic functions to develop minimization algorithms for EX-SOPs with up to five variables. We minimized all the representative functions of NP-equivalence classes for up to five variables and found that five-variable functions require up to nine products in minimum EX-SOPs. For n-variable functions, minimum EX-SOPs require at most 9·2^n-5 (n⩾6) products. This upper bound is smaller than 2^n-1, the upper bound for conventional SOPs