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Matematicheskie Zametki, 1971, Volume 9, Issue 1, Pages 35–40 (Mi mzm9639)  
This article is cited in 46 scientific papers (total in 48 papers)

Complexity of the realization of a linear function in the class of $\Pi$-circuits

V. M. Khrapchenko

Applied Mathematics Institute, Academy of Sciences of the USSR
Full-text PDF (665 kB) Citations (48)
Abstract: It is proved that the linear function $g_n(x_1,\dots,x_n)=x_1+\dots+x_n\mod2$ is realized in the class of $\Pi$-circuits with complexity $L_\pi(g_n)\geqslant n^2$. Combination of this result with S. V. Yablonskii's upper bound yields $L_\pi(g_n)\genfrac{}{}{0pt}{}{\smile}{\frown} n^2$.
Received: 23.04.1970
English version:
Mathematical Notes, 1971, Volume 9, Issue 1, Pages 21–23
DOI: https://doi.org/10.1007/BF01405045
Bibliographic databases:
Document Type: Article
UDC: 51.01.16
Language: Russian
Citation: V. M. Khrapchenko, “Complexity of the realization of a linear function in the class of $\Pi$-circuits”, Mat. Zametki, 9:1 (1971), 35–40; Math. Notes, 9:1 (1971), 21–23
Citation in format AMSBIB
\Bibitem{Khr71}
\by V.~M.~Khrapchenko
\paper Complexity of the realization of a linear function in the class of $\Pi$-circuits
\jour Mat. Zametki
\yr 1971
\vol 9
\issue 1
\pages 35--40
\mathnet{http://mi.mathnet.ru/mzm9639}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=290872}
\zmath{https://zbmath.org/?q=an:0222.94044|0206.29004}
\transl
\jour Math. Notes
\yr 1971
\vol 9
\issue 1
\pages 21--23
\crossref{https://doi.org/10.1007/BF01405045}
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    • This publication is cited in the following 48 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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