Non-binary functional synthesis using ACO-based heuristic

Abstract

Multiple-valued logic (MVL) synthesis is a problem that has attracted increased interest in recent years. The MVL synthesis problem is more involved compared to its binary counterpart. The search space for finding optimal MVL functional synthesis is enormous. Conventional deterministic methods for MVL functional synthesis are prohibitively expensive, indicating an eminent need for the use of iterative heuristic-based synthesis techniques. In this paper, an ant colony optimization (ACO) based heuristic algorithm for synthesis of MVL functions is proposed. The algorithm mimics the ants' behaviour in the real world. Real ants are found to be able to select the shortest path between their nest and food sources in the existence of alternate paths, or even hurdles between the two. The proposed ACO algorithm uses some of the known real ant techniques in finding the shortest paths to the (near) optimal number of product terms that can cover the minterms of a given MVL function. The proposed algorithm is tested using 50 000 randomly generated 2-variable 4-valued functions. The results obtained using the proposed approach show that the proposed approach outperforms existing direct cover (DC) techniques in terms of the average number of product terms (implicants) required to synthesize a given MVL function.