Analysis and design principles of modern control systems based on multi-valued logic models

An analysis and an overview of modern applications based on three-valued logic have been presented in this paper. Small computing units based on three-valued logic is a better solution (in comparison with binary models) for several applications such as the telecommunications industry, where three-valued logic units may increase the data transmission rate by one and a half times. It is important to have a possibility to assembly any circuits from three-valued logic chips. An important fundamental problem of class completeness for three-valued logic functions must be solved to make such implementation possible. The class completeness for three-valued logic functions guarantees that any digital circuit may be assembled from the finite number of ternary chipsets. The closure operator on the set of three-valued functions has been considered in this paper. It is a strength of the substitution operator. The completeness problem for this operator has been proved. This fact allows to restore in the general case the sublattice of closed classes with respect to the classical operator of superpositions. It’s a principal theoretical result that can optimize the assembly process for new digital circuits for transmission and data processing problems.