Geodesic
Improvement of the lower bound for the complexity of exponentiation
Prikladnaâ diskretnaâ matematika, no. 4 (2017), pp. 119-132

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

Let $l(x^n)$ be the minimal number of multiplications sufficient for computing $x^n$. In the paper, we improve the lower bound of $l(x^n)$. We establish that for all $\varepsilon >0$ the fraction of the numbers $k$, $k\le n$, satisfying the relation \begin{equation*} l(x^k)>\log_2n+\frac{\log_2n}{\log_2\log_2n}\left(1-(2+\varepsilon)\frac{\log_2\log_2\log_2n}{\log_2\log_2n}\right), \end{equation*} tends to 1 as $n\to\infty$.
Mots-clés : addition chains
Keywords: exponentiation, lower bounds of complexity. 
@article{PDM_2017_4_a9,
     author = {V. V. Kochergin and D. V. Kochergin},
     title = {Improvement of the lower bound for the complexity of  exponentiation},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {119--132},
     publisher = {mathdoc},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2017_4_a9/}
}
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V. V. Kochergin; D. V. Kochergin. Improvement of the lower bound for the complexity of  exponentiation. Prikladnaâ diskretnaâ matematika, no. 4 (2017), pp. 119-132. http://geodesic.mathdoc.fr/item/PDM_2017_4_a9/