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Diskr. Mat., 2011, Volume 23, Issue 4, Pages 39–47 (Mi dm1160)  

Lower bounds for complexity of Boolean circuits of finite depth with arbitrary elements

D. Yu. Cherukhin


Abstract: We consider circuits of functional elements of a finite depth whose elements are arbitrary Boolean functions of any number of arguments. We suggest a method of finding nonlinear lower bounds for complexity applicable, in particular, to the operator of cyclic convolution. The obtained lower bounds for the circuits of depth $d\ge2$ are of the form $\Omega(n\lambda_{d-1}(n))$. In particular, for $d=2,3,4$ they are of the form $\Omega(n^{3/2})$, $\Omega(n\log n)$ and $\Omega(n\log\log n)$ respectively; for $d\ge5$ the function $\lambda_{d-1}(n)$ is a slowly increasing function. These lower bounds are the greatest known ones for all even $d$ and for $d=3$. For $d=2,3$, these estimates have been obtained in earlier studies of the author.

DOI: https://doi.org/10.4213/dm1160

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English version:
Discrete Mathematics and Applications, 2011, 21:4, 499–508

Bibliographic databases:

UDC: 519.7
Received: 25.02.2009

Citation: D. Yu. Cherukhin, “Lower bounds for complexity of Boolean circuits of finite depth with arbitrary elements”, Diskr. Mat., 23:4 (2011), 39–47; Discrete Math. Appl., 21:4 (2011), 499–508

Citation in format AMSBIB
\Bibitem{Che11}
\by D.~Yu.~Cherukhin
\paper Lower bounds for complexity of Boolean circuits of finite depth with arbitrary elements
\jour Diskr. Mat.
\yr 2011
\vol 23
\issue 4
\pages 39--47
\mathnet{http://mi.mathnet.ru/dm1160}
\crossref{https://doi.org/10.4213/dm1160}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2933098}
\elib{http://elibrary.ru/item.asp?id=20730403}
\transl
\jour Discrete Math. Appl.
\yr 2011
\vol 21
\issue 4
\pages 499--508
\crossref{https://doi.org/10.1515/DMA.2011.031}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-81555200990}


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