On some properties of vector functionsof Boolean algebra
Diskretnaya Matematika, Tome 30 (2018) no. 1, pp. 114-128.

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

The functional system of Boolean vector functions with naturally defined superposition operation is studied. Sufficient conditions for membership of a number of important vector functions in closed classes are given.
Keywords: vector functions of Boolean algebra, superposition.
@article{DM_2018_30_1_a7,
     author = {V. A. Taimanov},
     title = {On some properties of vector functionsof {Boolean} algebra},
     journal = {Diskretnaya Matematika},
     pages = {114--128},
     publisher = {mathdoc},
     volume = {30},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2018_30_1_a7/}
}
TY  - JOUR
AU  - V. A. Taimanov
TI  - On some properties of vector functionsof Boolean algebra
JO  - Diskretnaya Matematika
PY  - 2018
SP  - 114
EP  - 128
VL  - 30
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2018_30_1_a7/
LA  - ru
ID  - DM_2018_30_1_a7
ER  - 
%0 Journal Article
%A V. A. Taimanov
%T On some properties of vector functionsof Boolean algebra
%J Diskretnaya Matematika
%D 2018
%P 114-128
%V 30
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2018_30_1_a7/
%G ru
%F DM_2018_30_1_a7
V. A. Taimanov. On some properties of vector functionsof Boolean algebra. Diskretnaya Matematika, Tome 30 (2018) no. 1, pp. 114-128. http://geodesic.mathdoc.fr/item/DM_2018_30_1_a7/

[1] Yablonskii S.V., Vvedenie v diskretnuyu matematiku, Nauka, Moskva, 2003, 484 pp. | MR

[2] Malcev I., “Graduated products of Post algebras”, Note on multiple-valued logic, 18:13 (1995), 1–4

[3] Malcev I., “Coordinated products of iterative algebras”, Proceedings VIII International Conference on logic and Computer Science, Novi Sad, Yugoslavia, 1997, 1–2 | MR

[4] Marchenkov S. S., On the completeness in the System $P_3 \times P_3$, 2:6 (1992), 587–606 | MR

[5] Marchenkov S. S., “On the Slupecki classes in the systems $P_k \times \ldots \times P_l$”, Discrete Math. Appl., 3:2 (1993), 147–160 | DOI | MR | MR

[6] Marchenkov S. S., “Precomplete classes in the Cartesian products of $P_2$ and $P_2$”, Discrete Math. Appl., 4:4 (1994), 209–228 | MR

[7] Romov B.A., “Algoritm resheniya problemy polnoty v klasse vektornykh funktsionalnykh sistem”, Matematicheskie modeli slozhnykh sistem, IK AN USSR, Kiev, 1973, 151–155

[8] Romov B.A., “O reshetke podalgebr pryamykh proizvedenii algebr Posta konechnoi stepeni”, Matematicheskie modeli slozhnykh sistem., IK AN USSR, Kiev, 1973, 156–168

[9] Romov B.A., “O polnote na kvadrate funktsii algebry logiki i v sistemakh $P_k \times P_l$”, Kibernetika, 4 (1987), 9–14 | MR

[10] Romov B.A., “Ob odnoi serii maksimalnykh podalgebr pryamykh proizvedenii algebr konechnoznachnykh logik”, Kibernetika, 3 (1989), 11–16 | MR

[11] Romov B.A., “O funktsionalnoi polnote v sisteme $P_2 \times P_k$”, Kibernetika, 1 (1991), 1–8 | MR

[12] Romov B.A., “The completness problem on the product of algebras of finite-valued logic”, ISMVL, Boston, USA, 1994, 184–186

[13] Taimanov V.A., “O dekartovykh stepenyakh $P_2$”, Dokl. AN SSSR, 270:6 (1983), 1327–1330 | MR

[14] Taimanov V.A., “O bazisakh zamknutykh klassov v $P_k \times P_m$”, Tezisy dokladov VIII Vsesoyuznoi konferentsii “Problemy teoreticheskoi kibernetiki”, Irkutsk, 1985, 188–189

[15] Taimanov V.A., “O bazisakh zamknutykh klassov vektor-funktsii mnogoznachnoi logiki.”, Diskretnaya matematika, 28:2 (2016), 127–132 | DOI | MR

[16] Yablonskii S.V., Gavrilov G.P., Kudryavtsev V.B., Funktsii algebry logiki i klassy Posta, Nauka, Moskva, 1966, 120 pp. | MR

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

[18] Post E.L., Two-valued iterative systems of mathematical logic, Princeton Univ. Press, Princeton, 1941, 122 pp. | MR