On one continual set of $\beta$-closed classes of the multivalued logic functions
Prikladnaâ diskretnaâ matematika, no. 2 (2014), pp. 12-20.

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The paper studies $\beta$-closed classes of the multivalued logic functions, where the $\beta$-closure operator is defined on the basis of the functions encoding in the binary number system. A continual set of $\beta$-closed classes, which contain only functions taking no more than three values, is given and some of its properties are proved.
Keywords: multivalued logic functions, closed classes, $\beta$-closure.
Mots-clés : superposition
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D. K. Podolko. On one continual set of  $\beta$-closed classes of the multivalued logic functions. Prikladnaâ diskretnaâ matematika, no. 2 (2014), pp. 12-20. http://geodesic.mathdoc.fr/item/PDM_2014_2_a1/

[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 | Zbl

[2] Yablonskii S. V., Vvedenie v diskretnuyu matematiku, Vysshaya shkola, M., 2001, 384 pp. | MR

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

[4] Marchenkov S. S., “$S$-klassifikatsiya funktsii mnogoznachnoi logiki”, Diskretnaya matematika, 9:3 (1997), 125–152 | DOI | MR | Zbl

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

[6] Podolko D. K., “O klassakh funktsii, zamknutykh otnositelno spetsialnoi operatsii superpozitsii”, Vestnik Moskovskogo universiteta. Ser. 1. Matematika. Mekhanika, 2013, no. 6, 54–57

[7] Kon P., Universalnaya algebra, Mir, M., 1968, 352 pp. | MR

[8] Ugolnikov A. B., Klassy Posta, Ucheb. posobie, Izd-vo TsPI pri mekhaniko-matematicheskom fakultete MGU im. M. V. Lomonosova, M., 2008, 64 pp.

[9] Marchenkov S. S., “O zamknutykh klassakh samodvoistvennykh funktsii mnogoznachnoi logiki. II”, Problemy kibernetiki, 40, 1983, 261–266 | MR | Zbl