Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2013, Number 2, Pages 17–23 (Mi vmumm388)  
This article is cited in 3 scientific papers (total in 3 papers)

Mathematics

Lower estimates of circuit complexity in the basis of antichain functions

O. V. Podolskaya

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (242 kB) Citations (3) English version article
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Abstract: The antichain function is a characteristic function of an antichain in the Boolean cube. The set of antichain functions is an infinite complete basis. We study the computational complexity of Boolean functions over an antichain functional basis. In this paper we prove an asymptotic lower bound of order $\sqrt{n}$ on the computational complexity of the linear function, the majority function, and almost all Boolean functions of $n$ variables.
Key words: antichain function, Boolean circuits, linear function, majority function.
Received: 15.06.2012
English version:
Moscow University Mathematics Bulletin, 2013, Volume 68, Issue 2, Pages 98–103
DOI: https://doi.org/10.3103/S0027132213020046
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: O. V. Podolskaya, “Lower estimates of circuit complexity in the basis of antichain functions”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2013, no. 2, 17–23; Moscow University Mathematics Bulletin, 68:2 (2013), 98–103
Citation in format AMSBIB
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\paper Lower estimates of circuit complexity in the basis of antichain functions
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2013
\issue 2
\pages 17--23
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\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=3114031}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2013
\vol 68
\issue 2
\pages 98--103
\crossref{https://doi.org/10.3103/S0027132213020046}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84878033695}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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