Geodesic
Galois theory for clones and superclones
Diskretnaya Matematika, Tome 27 (2015) no. 4, pp. 79-93.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study clones (closed sets of operations that contain projections) and superclones on finite sets. According to A. I. Mal'tsev a clone may be considered as an algebra. If we replace algebra universe with a set of multioperations and add the operation of simplest equation solvability then we will obtain an algebra called a superclone. The paper establishes Galois connection between clones and superclones.
Keywords: clone, superclone, operation, multioperation, superposition. 
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N. A. Peryazev; I. K. Sharankhaev. Galois theory for clones and superclones. Diskretnaya Matematika, Tome 27 (2015) no. 4, pp. 79-93. http://geodesic.mathdoc.fr/item/DM_2015_27_4_a6/

[1] Yablonskii S. V., “O superpozitsiyakh funktsii algebry logiki”, Matem. sb., 30 (1952), 329–348 | MR

[2] Yablonskii S. V., “Funktsionalnye postroeniya v $k$-znachnoi logike”, Trudy Matem. in-ta im. V.A.Steklova AN SSSR, 51 (1958), 5–142

[3] Maltsev A. I., “Iterativnye algebry i mnogoobraziya Posta”, Algebra i logika, 1966, no. 5, 3–9 | Zbl

[4] Kon P., Universalnaya algebra, MIR, M., 1968, 352 pp. | MR

[5] Lau D., Function algebras on finite sets. A basic course on many-valued logic and clone theory, Springer-Verlag, Berlin, 2006, 668 pp. | MR | Zbl

[6] Bodnarchuk V. G., Kaluzhnin L. A., Kotov V.N., Romov B. A., “Teoriya Galua dlya algebr Posta”, Kibernetika, 1969, no. 3, 1–10 ; no. 5, 1–9 | MR | Zbl

[7] Poscher R., Kaluznin L. A., Funktionen- und Relationenalgebren, Ein Kapitel der diskreten Mathematik, VEB DVW, Berlin, 1979, 237 pp. | MR

[8] Peryazev N. A., “Nedoopredelennye chastichnye bulevy funktsii”, Mater. XV Mezhdunar. konf. «Problemy teoreticheskoi kibernetiki», Kazan, 2008, 92

[9] Peryazev N. A., “Klony, ko-klony, giperklony i superklony”, Uchenye zapiski Kazanskogo gos. un-ta. Seriya: Fiziko-matem. nauki, 151:2 (2009), 120–125 | Zbl

[10] Peryazev N. A., “Multioperatsii i superklony”, Mezhdunar. konf. «Maltsevskie chteniya», Tezisy dokl, 2011, 84

[11] Peryazev N. A., “Teoriya Galua dlya klonov i superklonov”, Materialy XVI Mezhdunar. konf. «Problemy teoreticheskoi kibernetiki», 2011, 359–363

[12] Ore O., Teoriya grafov, Nauka, Moskva, 1980, 336 pp. | MR

[13] Kuznetsov A. V., “O sredstvakh dlya obnaruzheniya nevyvodimosti ili nevyrazimosti”, Logicheskii vyvod, Nauka, Moskva, 1979, 5–33