A heuristic algorithm to design AND-OR-EXOR three-level networks

An AND-OR-EXOR network, where the output EXOR gate has only two inputs, is one of the simplest three-level architecture. This network realizes an EXOR of two sum-of-products expressions (EX-SOP). In this paper, we show an algorithm to simplify EX-SOPs for multiple-output functions. Our objective is to minimize the number of distinct products in the sum-of-products expressions of EX-SOPs. The algorithm uses a divide-and-conquer strategy. It recursively applies the Shannon decomposition on a function with more than five variables. The algorithm obtains EX-SOPs for the five-variable functions by using an exact minimization program, then combines those EX-SOPs to generate EX-SOPs for the functions with more variables. We present experimental results for a set of benchmark functions, and show that EX-SOPs require many fewer products and literals than sum-of-products expressions. This is evidence that AND-OR-EXOR is a powerful architecture to realize many practical logic functions