Modular forms of systems of k-valued functions of the algebra of logic

Methods of realization of the k-valued functions of the algebra of logic by the modular forms of arithmetic polynomials based on "weighing" by the numbers k(i) (i = 0, 1, 2, were considered. The modular polynomial and matrix (number-theoretic) transformations were examined and extended to the case of systems of k-valued functions. A new principle of designing the modular form of one arithmetic polynomial to realize systems of k-valued functions in terms of the Chinese remainder theorem was proposed. The results obtained provide advantages in terms of complexity of the analytical description and realization of the k-valued functions.