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Diskretnaya Matematika, 2015, Volume 27, Issue 2, Pages 94–105
DOI: https://doi.org/10.4213/dm1327
(Mi dm1327)
 

This article is cited in 2 scientific papers (total in 2 papers)

Functions without short implicents.Part I: lower estimates of weights

Pavel V. Roldugin, Alexey V. Tarasov

Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)
Full-text PDF (482 kB) Citations (2)
References:
Abstract: The paper is concerned with $n$-place Boolean functions not admitting implicents of $k$ variables, $1\le k<n$. Estimates for the minimal possible weight $w\left( {n,\;k} \right)$ of such functions are obtained. It is shown that $w\left( {n,\;1} \right) = 2$, $n = 2,3,...$, and $w\left( {n,\;2} \right)\sim{\log _2}n$ as $n \to \infty$, and moreover, for $k > 2$ there exists ${n_0}$ such that $w\left( {n,\;k} \right) > {2^{k - 2}} \cdot {\log _2}n$ for all $n > {n_0}$.
Keywords: Boolean function, implicent, combinatorially complete matrix.
Received: 27.01.2015
English version:
Discrete Mathematics and Applications, 2016, Volume 26, Issue 1, Pages 41–50
DOI: https://doi.org/10.1515/dma-2016-0004
Bibliographic databases:
Document Type: Article
UDC: 519.571
Language: Russian
Citation: Pavel V. Roldugin, Alexey V. Tarasov, “Functions without short implicents.Part I: lower estimates of weights”, Diskr. Mat., 27:2 (2015), 94–105; Discrete Math. Appl., 26:1 (2016), 41–50
Citation in format AMSBIB
\Bibitem{RolTar15}
\by Pavel V. Roldugin, Alexey V. Tarasov
\paper Functions without short implicents.Part I: lower estimates of weights
\jour Diskr. Mat.
\yr 2015
\vol 27
\issue 2
\pages 94--105
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\crossref{https://doi.org/10.4213/dm1327}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3468393}
\elib{https://elibrary.ru/item.asp?id=24073695}
\transl
\jour Discrete Math. Appl.
\yr 2016
\vol 26
\issue 1
\pages 41--50
\crossref{https://doi.org/10.1515/dma-2016-0004}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000374106100004}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84958999582}
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  • https://www.mathnet.ru/eng/dm1327
  • https://doi.org/10.4213/dm1327
  • https://www.mathnet.ru/eng/dm/v27/i2/p94
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    Citing articles in Google Scholar: Russian citations, English citations
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    Дискретная математика
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