A universal principle of self-correction
Sbornik. Mathematics, Tome 55 (1986) no. 1, pp. 145-169 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper presents a new theory of self-correction in circuits, one which differs from earlier methods by being completely based upon properties of Boolean functions, thus guaranteeing the universality of the methods which have already been developed. The principal result is the construction of a self-correcting, information-nonredundant Boolean function expansion, which admits an analogue in any nontrivial control system and permits the construction of asymptotically nonredundant self-correcting circuits. The Boolean functions include a broad spectrum of special classes. Bibliography: 19 titles.
@article{SM_1986_55_1_a9,
     author = {A. E. Andreev},
     title = {A~universal principle of self-correction},
     journal = {Sbornik. Mathematics},
     pages = {145--169},
     year = {1986},
     volume = {55},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1986_55_1_a9/}
}
TY  - JOUR
AU  - A. E. Andreev
TI  - A universal principle of self-correction
JO  - Sbornik. Mathematics
PY  - 1986
SP  - 145
EP  - 169
VL  - 55
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1986_55_1_a9/
LA  - en
ID  - SM_1986_55_1_a9
ER  - 
%0 Journal Article
%A A. E. Andreev
%T A universal principle of self-correction
%J Sbornik. Mathematics
%D 1986
%P 145-169
%V 55
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1986_55_1_a9/
%G en
%F SM_1986_55_1_a9
A. E. Andreev. A universal principle of self-correction. Sbornik. Mathematics, Tome 55 (1986) no. 1, pp. 145-169. http://geodesic.mathdoc.fr/item/SM_1986_55_1_a9/

[1] Kirienko G. I., “O samokorrektiruyuschikhsya skhemakh iz funktsionalnykh elementov”, Problemy kibernetiki, 12 (1964), 29–37 | MR

[2] Kirienko G. I., “Sintez samokorrektiruyuschikhsya skhem iz funktsionalnykh elementov dlya sluchaya rastuschego chisla oshibok v skheme”, Diskretnyi analiz, 16, 1970, 38–43 | MR | Zbl

[3] Lupanov O. B., “O slozhnosti realizatsii funktsii algebry logiki formulami”, Problemy kibernetiki, 3 (1960), 61–80 | MR | Zbl

[4] Lupanov O. B., “O sinteze nekotorykh klassov upravlyayuschikh sistem”, Problemy kibernetiki, 10 (1963), 63–97 | MR | Zbl

[5] Madatyan Kh. A., “O sinteze skhem korrektiruyuschikh razmykaniya kontaktov”, DAN, 159:2 (1964), 290–293

[6] Nechiporuk E. I., “O topologicheskikh printsipakh samokorrektirovaniya”, DAN, 179:4 (1968), 786–789

[7] Nechiporuk E. I., “O korrektirovanii obryvov v ventilnykh i kontaktnykh skhemakh”, Kibernetika, 1968, no. 5, 40–48

[8] Nechiporuk E. I., “O topologicheskikh printsipakh samokorrektirovaniya”, Problemy kibernetiki, 21 (1969), 5–102 | Zbl

[9] Nechiporuk E. I., “O topologicheskikh printsipakh samokorrektirovaniya”, Problemy kibernetiki, 26 (1973), 19–26 | Zbl

[10] Ortyukov S. I., “Ob otsenkakh funktsii Shennona dlya skhem iz nenadezhnykh funktsionalnykh elementov”, Problemy kibernetiki, 40 (1983), 269

[11] Potapov Yu. G., Yablonskii S. V., “O sinteze samokorrektiruyuschikhsya kontaktnykh skhem”, DAN, 134:3 (1960), 544–547 | MR | Zbl

[12] Redkin N. P., “O samokorrektirovanii kontaktnykh skhem”, Problemy kibernetiki, 33 (1978), 119–138 | MR | Zbl

[13] Redkin N. P., “O samokorrektirovanii kontaktnykh skhem”, Problemy kibernetiki, 36 (1979), 195–208 | MR | Zbl

[14] Ulig D., “Samokorrektiruyuschiesya kontaktnye skhemy, ispravlyayuschie bolshoe chislo oshibok”, DAN, 241:6 (1978), 1273–1276 | MR

[15] Ulig D., “O sinteze samokorrektiruyuschikhsya skhem iz funktsionalnykh elementov s malym chislom nenadezhnykh elementov”, Matem. zametki, 15:6 (1974), 937–944 | MR

[16] Khrapchenko V. M., “Realizatsiya simmetricheskikh funktsii formulami”, Matem. zametki, 11:1 (1972), 109–120 | Zbl

[17] Yablonskii S. V., “Ob algoritmicheskikh trudnostyakh sinteza minimalnykh kontaktnykh skhem”, Problemy kibernetiki, 2 (1959), 75–121

[18] Diskretnaya matematika i matematicheskie voprosy kibernetiki, Nauka, M., 1974

[19] Andreev L. E., “O sinteze samokorrektiruyuschikhsya upravlyayuschikh sistem”, DAN, 277:3 (1984), 521–525 | MR | Zbl