Orders of growth of Shannon functions for circuit complexity over infinite bases
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2013), pp. 55-57 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is shown that any function of one real variable being composition of rational functions with real coefficients, logarithms, and exponents and having an order of growth between $n$ and $2^{O(n^{1/2})}$ is an order of growth of the Shannon function for the circuit complexity over a certain infinite basis.
@article{VMUMM_2013_3_a8,
     author = {O. M. Kasim-zade},
     title = {Orders of growth of {Shannon} functions for circuit complexity over infinite bases},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {55--57},
     year = {2013},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2013_3_a8/}
}
TY  - JOUR
AU  - O. M. Kasim-zade
TI  - Orders of growth of Shannon functions for circuit complexity over infinite bases
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2013
SP  - 55
EP  - 57
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2013_3_a8/
LA  - ru
ID  - VMUMM_2013_3_a8
ER  - 
%0 Journal Article
%A O. M. Kasim-zade
%T Orders of growth of Shannon functions for circuit complexity over infinite bases
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2013
%P 55-57
%N 3
%U http://geodesic.mathdoc.fr/item/VMUMM_2013_3_a8/
%G ru
%F VMUMM_2013_3_a8
O. M. Kasim-zade. Orders of growth of Shannon functions for circuit complexity over infinite bases. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2013), pp. 55-57. http://geodesic.mathdoc.fr/item/VMUMM_2013_3_a8/

[1] Lupanov O.B., Asimptoticheskie otsenki slozhnosti upravlyayuschikh sistem, Izd-vo MGU, M., 1984

[2] Hardy G.H., Orders of Infinity, Cambridge Univ. Press, Cambridge, 1910

[3] Burbaki N., Teoriya funktsii deistvitelnogo peremennogo, Nauka, M., 1965 | MR

[4] Muller D.E., “Complexity in electronic switching circuits”, IRE Trans. Electron. Comput., EC-5:1 (1956), 15–19 | DOI

[5] Lupanov O.B., “Ob odnom metode sinteza skhem”, Izv. vuzov. Radiofizika, 1:1 (1958), 120–140

[6] Gilbert E.N., “Lattice theoretic properties of frontal switching functions”, J. Math. and Phys., 33:1 (1954), 57–67 ; Gilbert E.N., “Teoretiko-strukturnye svoistva zamykayuschikh pereklyuchatelnykh funktsii”, Kibernet. sb., 1, IL, M., 1960, 175–188 | DOI | MR

[7] Markov A.A., “Ob inversionnoi slozhnosti sistem funktsii”, Dokl. AN SSSR, 116:6 (1957), 917–919

[8] Nechiporuk E.I., “O slozhnosti skhem v nekotorykh bazisakh, soderzhaschikh netrivialnye elementy s nulevymi vesami”, Problemy kibernetiki, 8, Fizmatgiz, M., 1962, 123–160 | MR

[9] Nechiporuk E.I., “O sinteze skhem iz porogovykh elementov”, Problemy kibernetiki, 11, Nauka, M., 1964, 49–62 | MR

[10] Lupanov O.B., “O sinteze skhem iz porogovykh elementov”, Problemy kibernetiki, 26, Nauka, M., 1973, 109–140

[11] Kasim-Zade O.M., “O slozhnosti realizatsii bulevykh funktsii skhemami v odnom beskonechnom bazise”, Diskretnyi analiz i issledovanie operatsii, 2:1 (1995), 7–20 | MR

[12] Kasim-Zade O.M., “Obschaya verkhnyaya otsenka slozhnosti skhem v proizvolnom beskonechnom polnom bazise”, Vestn. Mosk. un-ta. Matem. Mekhan., 1997, no. 4, 59–61

[13] Karpova N.A., “O nekotorykh svoistvakh funktsii Shennona”, Matem. zametki, 8:5 (1970), 663–674