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Classes of functions closed with respect to a special superposition operation

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Abstract

Functions of the k-valued logic with k = 2m, m > 1 are studied in the paper. Such functions are encoded in the binary numeric system and a special operation of binary superposition is defined. R is shown that the set of classes containing only the functions taking not more than two values and closed under the operations of binary superposition and adding of fictitious variables is countable.

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References

  1. Yu. I. Yanov and A. A. Muchnik, “Existence of k-Valued Closed Classes Having no Finite Bases,” Doklady Akad. Nauk SSSR 127(1), 44 (1959).

    MATH  Google Scholar 

  2. A. V. Kuznetsov, “Tools for Detection of Non-derivability and Non-expressibility,” in Logical Derivation (Nauka, Moscow, 1979), pp. 5–33.

    Google Scholar 

  3. V. D. Solov’ev, “Closed Classes in k-Valued Logic With the operation of Branching over Predicates,” Disrket. Matem. 2(4), 18 (1990).

    MATH  Google Scholar 

  4. Nguyen Van Hoa, “Families of Closed Classes of k-Valued Logic Preserved by All Automorphisms,” Disrket. Matem. 5(4), 87 (1993).

    MATH  Google Scholar 

  5. S. S. Marchenkov, “S-Classification of Functions of Multivalued Logic,” Disrket. Matem. 9(3), 125 (1997).

    Google Scholar 

  6. O. S. Tarasova, “Classes of Functions of Three-Valued Logic Closed with Respect to Operations of Superposition and Permutation,” Matem. Voprosy Kibern. 13, 59 (2004).

    MATH  MathSciNet  Google Scholar 

  7. Ya. V. Akulov, “Completeness of Systems of Functions for Classes of Extended Superposition,” Vestn. Mosk. Univ., Matem. Mekhan., No. 1, 36 (2011).

    Google Scholar 

  8. S. V. Yablonskii, Introduction to Discrete Mathematics (Vysshaya Shkola, Moscow, 2003) [in Russian].

    Google Scholar 

  9. D. Lau, Function Algebras on Finite Sets (Springer, N.Y., 2006).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    D. K. Podol’ko

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  1. D. K. Podol’ko
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Additional information

Original Russian Text © D. K. Podol’ko, 2013, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2013, Vol. 68, No. 6, pp. 54–57.

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Podol’ko, D.K. Classes of functions closed with respect to a special superposition operation. Moscow Univ. Math. Bull. 68, 303–306 (2013). https://doi.org/10.3103/S0027132213060090

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  • DOI: https://doi.org/10.3103/S0027132213060090

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