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Diskretnaya Matematika, 2000, Volume 12, Issue 1, Pages 135–144
DOI: https://doi.org/10.4213/dm313
(Mi dm313)
 

This article is cited in 4 scientific papers (total in 4 papers)

On the complexity of the realization of a linear function by formulas in finite Boolean bases

D. Yu. Cherukhin
Full-text PDF (854 kB) Citations (4)
References:
Abstract: We completely describe the set of bases over which the complexity of realization of the function $x_1\oplus\ldots\oplus x_n$ is of order $n$. For all bases not belonging to this set, we obtain the lower bound for the complexity of realization of the function $x_1\oplus\ldots\oplus x_n$, which is of the form $n^c$, where $c>1$ and $c$ does not depend on $n$. Basing on this bound for complexity, we give a more simple proof of existence of an infinite (descending) sequence of Boolean bases.
The research was supported by the Russian Foundation for Basic Research, grant 99–01–01175, and also by FTP ‘Integration’, grant 473.
Received: 16.11.1999
Bibliographic databases:
UDC: 519.6
Language: Russian
Citation: D. Yu. Cherukhin, “On the complexity of the realization of a linear function by formulas in finite Boolean bases”, Diskr. Mat., 12:1 (2000), 135–144; Discrete Math. Appl., 10:2 (2000), 147–157
Citation in format AMSBIB
\Bibitem{Che00}
\by D.~Yu.~Cherukhin
\paper On the complexity of the realization of a linear function by formulas in finite Boolean bases
\jour Diskr. Mat.
\yr 2000
\vol 12
\issue 1
\pages 135--144
\mathnet{http://mi.mathnet.ru/dm313}
\crossref{https://doi.org/10.4213/dm313}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1778772}
\zmath{https://zbmath.org/?q=an:0965.03075}
\transl
\jour Discrete Math. Appl.
\yr 2000
\vol 10
\issue 2
\pages 147--157
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  • https://www.mathnet.ru/eng/dm313
  • https://doi.org/10.4213/dm313
  • https://www.mathnet.ru/eng/dm/v12/i1/p135
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Дискретная математика
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    Abstract page:483
    Full-text PDF :203
    References:38
    First page:1
     
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