Geodesic
Classes of functions of multi-valued logic closed with respect to superposition and inversion operations
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2017), pp. 3-6 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The closure under composition and inversion operations is considered on the set of functions of the $k$-valued logic. A full description of such closed classes is obtained. 
@article{VMUMM_2017_2_a0,
     author = {D. E. Starodubtsev},
     title = {Classes of functions of multi-valued logic closed with respect to superposition and inversion operations},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {3--6},
     year = {2017},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2017_2_a0/}
}
TY  - JOUR
AU  - D. E. Starodubtsev
TI  - Classes of functions of multi-valued logic closed with respect to superposition and inversion operations
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2017
SP  - 3
EP  - 6
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2017_2_a0/
LA  - ru
ID  - VMUMM_2017_2_a0
ER  - 
%0 Journal Article
%A D. E. Starodubtsev
%T Classes of functions of multi-valued logic closed with respect to superposition and inversion operations
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2017
%P 3-6
%N 2
%U http://geodesic.mathdoc.fr/item/VMUMM_2017_2_a0/
%G ru
%F VMUMM_2017_2_a0
D. E. Starodubtsev. Classes of functions of multi-valued logic closed with respect to superposition and inversion operations. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2017), pp. 3-6. http://geodesic.mathdoc.fr/item/VMUMM_2017_2_a0/

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

[2] Lau D., Function algebras on finite sets: a basic course on many-valued logic and clone theory, Springer, Berlin, 2006 | MR | Zbl

[3] Post E.L., “Introduction to a general theory of elementary propositions”, Amer. J. Math., 43:3 (1921), 163–185 | DOI | MR | Zbl

[4] Post E.L., The two-valued iterative systems of mathematical logic, Ann. Math. Stud., 1941 | MR | Zbl

[5] 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

[6] Rosenberg I.G., “La structure des functions de plusieurs variables sur un ensemble fini”, C. r. Acad. sci. Paris, 260 (1965), 3817–3819 | MR | Zbl

[7] Yablonskii S.V., Gavrilov G.P., Nabebin A.A., Predpolnye klassy v mnogoznachnykh logikakh, Izd-vo MEI, M., 1997 | MR

[8] Mikhailovich A.V., “O zamknutykh klassakh funktsii mnogoznachnoi logiki, porozhdennykh simmetricheskimi funktsiyami”, Matematicheskie voprosy kibernetiki, 18, Fizmatlit, M., 2013, 123–212

[9] Ugolnikov A.B., “O nekotorykh zadachakh v oblasti mnogoznachnykh logik”, Mat-ly X Mezhdunar. seminara “Diskretnaya matematika i ee prilozheniya” (Moskva, MGU, 1–6 fevralya 2010 g.), ed. O. M. Kasim-Zade, Izd-vo TsPI pri mekh.-mat. f-te MGU, M., 2010, 18–34

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

[11] Tarasova O.S., “Klassy funktsii trekhznachnoi logiki, zamknutye otnositelno operatsii superpozitsii i perestanovok”, Matematicheskie voprosy kibernetiki, 13, Fizmatlit, M., 2004, 59–112