AOXMIN-MV: A Heuristic Algorithm for AND-OR-XOR Minimization

Three-level logic is shown to have a potential for reduction of the area over twolevel implementations, as well as for a gain in speed over multi-level implementations. In this paper we present an heuristic algorithm, AOXMIN-MV, targeting a three-level logic expression which is an XOR of two sum-of-products. For some practical functions, such an AND-OR-XOR expression may have up to 27 times less product-terms compared to the classical sum-of-products form. Several algorithms for finding minimal AND-OR-XOR expressions were presented, but they all are time-consuming for large functions. The algorithm presented here solves this problem by (1) introducing an estimation metric, checking whether the input function is likely to have a compact AND-OR-XOR expression; (2) employing a new strategy for decomposing the input function into two sum-of-products; (3) treating the output part of a multiple-output function as a single multiple-valued variable. The experimental results show that these modification yield a faster and more efficient algorithm. Furthermore, it gives a solution to a more general problem of minimization of multiple-valued input binary-valued output logic functions.