Geodesic
A simple proof for the upper bound of the computational complexity of three monomials in three variables
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2019), pp. 3-8 
V. V. Kochergin. A simple proof for the upper bound of the computational complexity of three monomials in three variables. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2019), pp. 3-8. http://geodesic.mathdoc.fr/item/VMUMM_2019_2_a0/
@article{VMUMM_2019_2_a0,
     author = {V. V. Kochergin},
     title = {A simple proof for the upper bound of the computational complexity of three monomials in three variables},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {3--8},
     year = {2019},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_2_a0/}
}
TY  - JOUR
AU  - V. V. Kochergin
TI  - A simple proof for the upper bound of the computational complexity of three monomials in three variables
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2019
SP  - 3
EP  - 8
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2019_2_a0/
LA  - ru
ID  - VMUMM_2019_2_a0
ER  - 
%0 Journal Article
%A V. V. Kochergin
%T A simple proof for the upper bound of the computational complexity of three monomials in three variables
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2019
%P 3-8
%N 2
%U http://geodesic.mathdoc.fr/item/VMUMM_2019_2_a0/
%G ru
%F VMUMM_2019_2_a0

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

The problem of the minimal number of multiplication operations sufficient for the joint computing of three monomials in three variables is considered. For this problem, we propose a simple proof of the upper bound asymptotically equal to the lower bound. The known proof of a similar bound contains more than 60 pages.

[1] Knut D. E., Iskusstvo programmirovaniya dlya EVM, v. 2, 1-e izd., Mir, M., 1977

[2] Pippenger N., “On evaluation of powers and monomials”, SIAM J. Comput., 9:2 (1980), 230–250 | DOI | MR | Zbl

[3] Kochergin V. V., “O zadachakh Bellmana i Knuta i ikh obobscheniyakh”, Fund. i prikl. matem., 20:6 (2015), 159–189

[4] Kochergin V. V., “Ob asimptotike slozhnosti additivnykh vychislenii sistem tselochislennykh lineinykh form”, Diskretnyi analiz i issledovanie operatsii. Ser. 1, 13:2 (2006), 38–58 | Zbl

[5] Kochergin V. V., “O slozhnosti additivnykh vychislenii, ispolzuyuschikh tolko operatsii vychitaniya”, Tr. VIII Mezhdunar. konf. “Diskretnye modeli v teorii upravlyayuschikh sistem” (Moskva, 6–9 aprelya 2009 g.), MAKS Press, M., 2009, 174–179

[6] Kochergin V. V., “Ob odnom sootnoshenii dvukh mer slozhnosti vychisleniya sistem odnochlenov”, Vestn. Mosk. un-ta. Matem. Mekhan., 2009, no. 4, 8–13 | Zbl

[7] Kochergin V. V., “O slozhnosti vychisleniya sistemy iz trekh odnochlenov ot trekh peremennykh”, Matematicheskie voprosy kibernetiki, 15, Fizmatlit, M., 2006, 79–155

[8] Lupanov O. B., “O sinteze nekotorykh klassov upravlyayuschikh sistem”, Problemy kibernetiki, 10, Fizmatgiz, M., 1963, 63–97

[9] Brauer A., “On addition chains”, Bull. Amer. Math. Soc., 45 (1939), 736–739 | DOI | MR

[10] Kochergin V. V., “O slozhnosti vychisleniya sistem odnochlenov ot dvukh peremennykh”, Tr. VII Mezhdunar. konf. “Diskretnye modeli v teorii upravlyayuschikh sistem”, MAKS Press, M., 2006, 185–190