RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Diskr. Mat.: Year: Volume: Issue: Page: Find

 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

Full text: PDF file (133 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 519.7

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}