Abstract
The k-valued (in particular ternary) computing has been becoming more and more relevant during the last decade. The research and development of algorithms based on k-valued logic is very relevant in many fields of science and engineering. A fundamentally essential problem—the problem of full description of closed classes of three-valued logic functions—must be solved to make the implementation of such algorithms are possible. A continuum of closed classes on the superposition operation appeared in the transition to a multivalued logic (greater than two). We can’t construct a complete description in this case. In this paper, we consider the problem of verifying the finite generation of classes containing some subclass of functions of one variable. We also give a description of the over lattices of classes in \( P_k \) containing some precomplete class of unary functions. The finite generation of overlattices has been proved.
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This publication was prepared with the support of the Russian Foundation for Basic Research according to the research project No. 20-01-00575_A.
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Kalimulina, E.Y. (2023). Mutual Generation of the Choice and Majority Functions. In: Yilmaz, F., Queiruga-Dios, A., Martín Vaquero, J., Mierluş-Mazilu, I., Rasteiro, D., Gayoso Martínez, V. (eds) Mathematical Methods for Engineering Applications. ICMASE 2022. Springer Proceedings in Mathematics & Statistics, vol 414. Springer, Cham. https://doi.org/10.1007/978-3-031-21700-5_6
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