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Fundamentalnaya i Prikladnaya Matematika, 2015, Volume 20, Issue 6, Pages 159–188 (Mi fpm1692)  

This article is cited in 6 scientific papers (total in 6 papers)

On Bellman's and Knuth's problems and their generalizations

V. V. Kochergin

Lomonosov Moscow State University, Bogoliubov Institute for Theoretical Problems of Microphysics
Full-text PDF (267 kB) Citations (6)
References:
Abstract: Various generalizations of the classical problem of the fastest raising to a power (or the so-called problem on addition chains) are studied in the asymptotic sense. Under weak restrictions, we demonstrate asymptotically tight solutions of the two best known generalizations, namely, Bellman's problem on the computational complexity (on the minimal number of multiplication operations) of a normed monomial of several variables and Knuth's problem on the computational complexity of a powers system of one variable. We also briefly review some results on the computational complexity for three problems, namely, the computation of $p$-element systems of normed monomials in $q$ variables, additive computations for systems of $p$ integer linear forms over $q$ variables, and the computation of $p$-element systems of the free Abelian group with $q$ generators.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00598_a
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 233, Issue 1, Pages 103–124
DOI: https://doi.org/10.1007/s10958-018-3928-4
Document Type: Article
UDC: 519.7
Language: Russian
Citation: V. V. Kochergin, “On Bellman's and Knuth's problems and their generalizations”, Fundam. Prikl. Mat., 20:6 (2015), 159–188; J. Math. Sci., 233:1 (2018), 103–124
Citation in format AMSBIB
\Bibitem{Koc15}
\by V.~V.~Kochergin
\paper On Bellman's and Knuth's problems and their generalizations
\jour Fundam. Prikl. Mat.
\yr 2015
\vol 20
\issue 6
\pages 159--188
\mathnet{http://mi.mathnet.ru/fpm1692}
\transl
\jour J. Math. Sci.
\yr 2018
\vol 233
\issue 1
\pages 103--124
\crossref{https://doi.org/10.1007/s10958-018-3928-4}
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  • https://www.mathnet.ru/eng/fpm/v20/i6/p159
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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