Geodesic
Orders of Discriminator Classes in Multivalued Logic
Matematičeskie zametki, Tome 86 (2009) no. 4, pp. 550-556.

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

For $k\ge2$, discriminator classes, that is, closed classes of functions of $k$-valued logic containing the ternary discriminator $p$, are considered. It is proved that any discriminator class has order at most $\max(3,k)$; moreover, the order of any discriminator class containing all homogeneous functions does not exceed $\max(3,k-1)$, and the order of a discriminator class containing all even functions does not exceed $\max(3,k-2)$. All of these three bounds are attainable.
Keywords: function of multivalued logic, discriminator class of functions, ternary discriminator, structure homogeneous functions, homogeneous functions, even functions. 
@article{MZM_2009_86_4_a7,
     author = {S. S. Marchenkov},
     title = {Orders of {Discriminator} {Classes} in {Multivalued} {Logic}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {550--556},
     publisher = {mathdoc},
     volume = {86},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_4_a7/}
}
TY  - JOUR
AU  - S. S. Marchenkov
TI  - Orders of Discriminator Classes in Multivalued Logic
JO  - Matematičeskie zametki
PY  - 2009
SP  - 550
EP  - 556
VL  - 86
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2009_86_4_a7/
LA  - ru
ID  - MZM_2009_86_4_a7
ER  - 
%0 Journal Article
%A S. S. Marchenkov
%T Orders of Discriminator Classes in Multivalued Logic
%J Matematičeskie zametki
%D 2009
%P 550-556
%V 86
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2009_86_4_a7/
%G ru
%F MZM_2009_86_4_a7
S. S. Marchenkov. Orders of Discriminator Classes in Multivalued Logic. Matematičeskie zametki, Tome 86 (2009) no. 4, pp. 550-556. http://geodesic.mathdoc.fr/item/MZM_2009_86_4_a7/

[1] K. A. Baker, A. F. Pixley, “Polynomial interpolation and the Chinese remainder theorem for algebraic systems”, Math. Z., 143:2 (1975), 165–174 | MR | Zbl

[2] S. S. Marchenkov, Funktsionalnye sistemy s operatsiei superpozitsii, Fizmatlit, M., 2004 | MR | Zbl

[3] S. S. Marchenkov, “O ravnomernom id-razlozhenii bulevykh funktsii”, Diskret. matem., 2:3 (1990), 29–41 | MR | Zbl

[4] S. S. Marchenkov, “O stepeni ravnomernogo id-razlozheniya zamknutykh klassov v $P_k$”, Diskret. matem., 3:4 (1991), 128–142 | MR | Zbl

[5] S. V. Yablonskii, Vvedenie v diskretnuyu matematiku, Nauka, M., 1986 | MR | Zbl

[6] E. Marczewski, “Homogeneous operations and homogeneous algebras”, Fund. Math., 56:1 (1964), 81–103 | MR | Zbl

[7] S. S. Marchenkov, “O klassifikatsii algebr so znakoperemennoi gruppoi avtomorfizmov”, Dokl. AN SSSR, 265:3 (1982), 533–536 | MR | Zbl

[8] S. S. Marchenkov, “Klassifikatsiya algebr so znakoperemennoi gruppoi avtomorfizmov”, Matematicheskie voprosy kibernetiki, Vyp. 2, Nauka, M., 1989, 100–122 | MR | Zbl

[9] S. S. Marchenkov, Zamknutye klassy bulevykh funktsii, Fizmatlit, M., 2000 | MR | Zbl

[10] B. Ganter, J. Płonka, H. Werner, “Homogeneous algebras are simple”, Fund. Math., 79:3 (1973), 217–220 | MR | Zbl

[11] S. S. Marchenkov, “O zamknutykh klassakh samodvoistvennykh funktsii mnogoznachnoi logiki”, Problemy kibernetiki, Vyp. 36, Nauka, M., 1979, 5–22 | MR | Zbl

[12] S. S. Marchenkov, “Odnorodnye algebry”, Problemy kibernetiki, Vyp. 39, Nauka, M., 1982, 85–106 | MR | Zbl

[13] S. S. Marchenkov, Ya. Demetrovich, L. Khannak, “O zamknutykh klassakh samodvoistvennykh funktsii v $P_3$”, Metody diskretnogo analiza v reshenii kombinatornykh zadach, Vyp. 34, In-t matem. SO AN SSSR, Novosibirsk, 1980, 38–73 | MR | Zbl