Geodesic
On Some Closed Classes of Self-dual Partial Many-valued Functions
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 2, pp. 16-24
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Let $S$ be a class of fully defined functions of any number of variables that are defined and take values in the set $E_k=\{0,1,\dots,k-1\}$ and are self-dual under given permutation on $E_k$. Let $S^*$ be the set of all partially defined $k$-valued functions that can be extended to functions from $S$. In this paper all closed classes (under superposition) that contain $S$ and are contained in $S^*$ are described for the case when permutation is the product of non-intersecting cycles of the same length.
Keywords: $k$-valued function, partially defined function, closed class, self-dual function. 
@article{UZKU_2009_151_2_a2,
     author = {V. B. Alekseev},
     title = {On {Some} {Closed} {Classes} of {Self-dual} {Partial} {Many-valued} {Functions}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {16--24},
     year = {2009},
     volume = {151},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2009_151_2_a2/}
}
TY  - JOUR
AU  - V. B. Alekseev
TI  - On Some Closed Classes of Self-dual Partial Many-valued Functions
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2009
SP  - 16
EP  - 24
VL  - 151
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/UZKU_2009_151_2_a2/
LA  - ru
ID  - UZKU_2009_151_2_a2
ER  - 
%0 Journal Article
%A V. B. Alekseev
%T On Some Closed Classes of Self-dual Partial Many-valued Functions
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2009
%P 16-24
%V 151
%N 2
%U http://geodesic.mathdoc.fr/item/UZKU_2009_151_2_a2/
%G ru
%F UZKU_2009_151_2_a2
V. B. Alekseev. On Some Closed Classes of Self-dual Partial Many-valued Functions. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 2, pp. 16-24. http://geodesic.mathdoc.fr/item/UZKU_2009_151_2_a2/

[1] Freivald R. V., “Kriterii polnoty dlya chastichnykh funktsii algebry logiki i mnogoznachnoi logiki”, Dokl. AN SSSR, 167 (1966), 1249–1250 | MR

[2] Romov B. A., “O maksimalnykh podalgebrakh algebry chastichnykh funktsii mnogoznachnoi logiki”, Kibernetika, 1980, no. 1, 28–35 | MR

[3] Lo Zhu Kai, “The completeness theory of partial many-valued logic functions”, Acta Math. Sinica, 27 (1984), 676–683 (Chinese) ; Lo Chzhukai, “Teoriya polnoty dlya chastichnykh funktsii mnogoznachnoi logiki”, Kibernet. sb., 25, Mir, M., 1988, 142–161 | MR | Zbl

[4] Alekseev V. B., Voronenko A. A., “O nekotorykh zamknutykh klassakh v chastichnoi dvuznachnoi logike”, Diskr. matem., 6:4 (1994), 58–79 | MR | Zbl

[5] Lau D., Function Algebras on Finite Sets. A basic course on many-valued logic and clone theory, Springer, 2006, 668 pp. | MR

[6] Alekseev V. B., “O nekotorykh zamknutykh klassakh chastichnykh mnogoznachnykh samodvoistvennykh funktsii”, Problemy teoreticheskoi kibernetiki, Tez. dokl. 15 mezhdunar. konf., ed. Yu. I. Zhuravlev, Otechestvo, Kazan, 2008, 5

[7] Haddad L., Lau D., Rosenberg I. G., “Intervals of partial clones containing maximal clones”, J. Automata, Language and Combinatorics, 11:4 (2006), 399–421 | MR | Zbl

[8] Yablonskii S. V., “Funktsionalnye postroeniya v $k$-znachnoi logike”, Trudy MIAN im. V. A. Steklova, 51, 1958, 5–142 | MR | Zbl