Abstract
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.
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Translated from Avtomatika i Telemekhanika, No. 7, 2005, pp. 66–86.
Original Russian Text Copyright © 2005 by Fin’ko.
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Fin’ko, O.A. Modular Forms of Systems of k-valued Functions of the Algebra of Logic. Autom Remote Control 66, 1081–1100 (2005). https://doi.org/10.1007/s10513-005-0150-x
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DOI: https://doi.org/10.1007/s10513-005-0150-x