Classes of functions closed with respect to a special superposition operation
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2013), pp. 54-57 Cet article a éte moissonné depuis la source Math-Net.Ru

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Functions of the $k$-valued logic with $k=2^m$, $m>1$ are studied in the paper. Such functions are encoded in the binary number system and a special operation of binary superposition is defined. It 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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D. K. Podol'ko. Classes of functions closed with respect to a special superposition operation. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2013), pp. 54-57. http://geodesic.mathdoc.fr/item/VMUMM_2013_6_a10/

[1] Yanov Yu.I., Muchnik A.A., “O suschestvovanii $k$-znachnykh zamknutykh klassov, ne imeyuschikh konechnogo bazisa”, Dokl. AN SSSR, 127:1 (1959), 44–46

[2] Kuznetsov A.V., “O sredstvakh dlya obnaruzheniya nevyvodimosti i nevyrazimosti”, Logicheskii vyvod, Nauka, M., 1979, 5–33

[3] Solovev V.D., “Zamknutye klassy v $k$-znachnoi logike s operatsiei razvetvleniya po predikatam”, Diskret. matem., 2:4 (1990), 18–25 | MR

[4] Nguen Van Khoa., “O semeistvakh zamknutykh klassov $k$-znachnoi logiki, sokhranyaemykh vsemi avtomorfizmami”, Diskret. matem., 5:4 (1993), 87–108 | MR

[5] Marchenkov S.S., “$S$-klassifikatsiya funktsii mnogoznachnoi logiki”, Diskret. matem., 9:3 (1997), 125–152 | DOI | MR

[6] Tarasova O.S., “Klassy funktsii $k$-znachnoi logiki, zamknutye otnositelno operatsii superpozitsii i perestanovok”, Matematicheskie voprosy kibernetiki, 13, Fizmatlit, M., 2004, 59–112

[7] Akulov Ya.V., “O polnote sistem funktsii dlya klassov rasshirennoi superpozitsii”, Vestn. Mosk. un-ta. Matem. Mekhan., 2011, no. 1, 36–41

[8] Yablonskii S.V., Vvedenie v diskretnuyu matematiku, Vysshaya shkola, M., 2001 | MR

[9] Lau D., Function algebras on finite sets, Springer, N.Y., 2006 | MR