Formalization of Ternary Logic for Application to Digital Signal Processing

Abstract

In this article, an abelian group G = (−1,0,1) is considered. In addition, advantages of using this group for digital signal processing were demonstrated. The main of ones are a natural form of representation of negative numbers, as well as natural digital form of slowly changing signals. This group is isomorphic to multiplicative group formed by three cubic roots of unity. This isomorphism can be used in implementation of computer systems in which physical representation of logical variables is carried out through a phase of a signal. This multiplicative group may turn out a very promising for development of computer systems where information about value of a logical variable (whatever is meant by this term) is embedded in the phase of the oscillating signal. The oscillating signals are the most promising object for implementation of quantum, optical and nanocomputing systems, since the implementation of stable states (or stable currents) that correspond to classical approaches to the creation of computer technology is problematic here.