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 $k^i$ ($i=0,\,1,\,2\,\ldots$) 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.