Searching for complete functions over E(3) with small radii

Abstract

Recent advances in laser and fiber optic technology have made it feasible to build optical processors which are based upon value systems larger than E(2)={0,1}. The problem of designing a transistor which can be used as the basis for the circuits of such a processor involves a detailed study of functions which are either complete or complete with constants over E(3) and E(4). The radii of all complete functions over E(3) have been calculated but the sequential methods used cannot be applied over E(4). The authors use the known results for E(3) to develop genetic algorithm techniques to "grow" functions over E(3) with small radii. The paper ends with a discussion of the modifications needed to move the techniques developed for E(3) to a massively parallel environment so that complete functions over E(4) with small radii may be developed.<>