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

| In this paper, we present 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 (SOP) cannot share products. The problem is to minimize the total number of product in the two SOPs. We introduced the -equivalence of logic functions to develop minimization algorithms for EXSOPs with up to ve variables. We minimized all the representative functions of NP-equivalence classes for up to ve variables and found that ve-variable functions require up to 9 products in minimum EX-SOPs. For n-variable functions, minimum EX-SOPs require at most 9 2n 5 (n 6) products. This upper bound is smaller than 2n , the upper bound for the conventional sum-of-products expressions. Index Terms | Three-level network, AND-EXOR, logic minimization, spectral method, NP-equivalence, -equivalence, coordinate representation, complexity.