Geodesic
On closed classes of a~$k$-valued logics functions defined by a~single endomorphism
Diskretnyj analiz i issledovanie operacij, Tome 16 (2009) no. 6, pp. 52-67.

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

The closed classes in $P_k$ defined by a single endomorphism are investigated. It is proved that every such class is positive closed. In the case of nonidentical idempotent endomorphism the corresponding class is positive precomplete in $P_k$. For $k=2,3$ all positive precomplete classes in $P_k$ are defined by the same endomorphisms. All positive submaximal classes in $P_3$ are found. Bibl. 11.
Keywords: many-valued logic function, positive closed classes.
Mots-clés : endomorphism 
@article{DA_2009_16_6_a4,
     author = {S. S. Marchenkov},
     title = {On closed classes of a~$k$-valued logics functions defined by a~single endomorphism},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {52--67},
     publisher = {mathdoc},
     volume = {16},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2009_16_6_a4/}
}
TY  - JOUR
AU  - S. S. Marchenkov
TI  - On closed classes of a~$k$-valued logics functions defined by a~single endomorphism
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2009
SP  - 52
EP  - 67
VL  - 16
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2009_16_6_a4/
LA  - ru
ID  - DA_2009_16_6_a4
ER  - 
%0 Journal Article
%A S. S. Marchenkov
%T On closed classes of a~$k$-valued logics functions defined by a~single endomorphism
%J Diskretnyj analiz i issledovanie operacij
%D 2009
%P 52-67
%V 16
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2009_16_6_a4/
%G ru
%F DA_2009_16_6_a4
S. S. Marchenkov. On closed classes of a~$k$-valued logics functions defined by a~single endomorphism. Diskretnyj analiz i issledovanie operacij, Tome 16 (2009) no. 6, pp. 52-67. http://geodesic.mathdoc.fr/item/DA_2009_16_6_a4/

[1] 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

[2] Kon P., Universalnaya algebra, Mir, M., 1968, 351 pp. | MR

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

[4] Marchenkov S. S., “Ob odnorodnykh algebrakh”, Dokl. AN SSSR, 256:4 (1981), 787–790 | MR | Zbl

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

[6] Marchenkov S. S., “O vyrazimosti funktsii mnogoznachnoi logiki v nekotorykh logiko-funktsionalnykh yazykakh”, Diskret. matematika, 11:4 (1999), 110–126 | MR | Zbl

[7] Marchenkov S. S., “Klony, opredelyaemye znakoperemennymi monoidami”, Diskret. matematika, 14:2 (2002), 3–8 | MR | Zbl

[8] Marchenkov S. S., “Kriterii pozitivnoi polnoty v trëkhznachnoi logike”, Diskret. analiz i issled. operatsii. Ser. 1, 13:3 (2006), 27–39 | MR

[9] Marchenkov S. S., “Diskriminatornye pozitivno zamknutye klassy trëkhznachnoi logiki”, Diskret. analiz i issled. operatsii. Ser. 1, 14:3 (2007), 53–66 | MR

[10] Yablonskii S. V., Vvedenie v diskretnuyu matematiku, Nauka, M., 1986, 384 pp. | MR

[11] Machida H., Miyakawa M., Rosenberg I. G., “Relations between clones and full monoids”, Proc. 31 Int. Symp. on Multiple-Valued Logic (Warsaw, Poland, May 22–24, 2001), IEEE Computer Society Press, Warsaw, 2001, 279–284