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Diskretn. Anal. Issled. Oper., 2018, Volume 25, Number 3, Pages 36–94 (Mi da902)  

Complexity of the realization of a linear Boolean function in the class of $\pi$-schemes

K. L. Rychkov

Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia

Abstract: Using Khrapchenko's method, we obtain the exact lower bound of 40 for the complexity in the class of $\pi$-schemes of a linear Boolean function depending substantially on 6 variables. We give a simplified proof of several lower bounds for the complexity of linear Boolean functions which are previously obtained on the basis of the same method. Bibliogr. 18.

Keywords: Boolean function, $\pi$-scheme, lower complexity bound.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations I.1.1, 0314-2016-0001
The author was supported by the Program of Basic Scientific Research of the Siberian Branch of the Russian Academy of Sciences No. I.1.1 (project no. 0314-2016-0001).


DOI: https://doi.org/10.17377/daio.2018.25.589

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English version:
Journal of Applied and Industrial Mathematics, 2018, 12:3, 540–576

Document Type: Article
UDC: 519.714
Received: 18.09.2017
Revised: 10.05.2018

Citation: K. L. Rychkov, “Complexity of the realization of a linear Boolean function in the class of $\pi$-schemes”, Diskretn. Anal. Issled. Oper., 25:3 (2018), 36–94; J. Appl. Industr. Math., 12:3 (2018), 540–576

Citation in format AMSBIB
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\by K.~L.~Rychkov
\paper Complexity of the realization of a~linear Boolean function in the class of $\pi$-schemes
\jour Diskretn. Anal. Issled. Oper.
\yr 2018
\vol 25
\issue 3
\pages 36--94
\mathnet{http://mi.mathnet.ru/da902}
\crossref{https://doi.org/10.17377/daio.2018.25.589}
\transl
\jour J. Appl. Industr. Math.
\yr 2018
\vol 12
\issue 3
\pages 540--576
\crossref{https://doi.org/10.1134/S1990478918030146}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85052123067}


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