Fast transforms for multiple-valued input binary output PLI logic

Abstract

Fast forward and inverse transforms for multiple-valued input binary output PLI logic are derived. New matrix functions are introduced which allow feasible transformation of arbitrary q-valued input binary output functions. This allows representation of the function in the algebra of GF(2), where q/spl ges/2. The representation of MVB functions in various functional bases having always fast algorithms is the foundation for the efficient synthesis of PLI expansions of MVB functions. The computational complexity of such algorithms is essentially reduced when compared to standard matrix multiplication and inversion based methods of the earlier work in PLI logic.