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 Diskr. Mat., 2008, Volume 20, Issue 1, Pages 120–130 (Mi dm995)

On complexity of realisation of a class of almost symmetric functions by formulas of depth 3

S. E. Cherukhina

Abstract: We consider the class of almost symmetric Boolean functions. For any function of this class, the values on all tiers except the second one coincide with the values of a monotone symmetric function with threshold 3. The values on the second tier are arbitrary. We study realisation of functions of this class by $&\vee&$- formulas over the basis $\{&,\vee\}$.
We obtain a sharp bound for the minimum complexity of the functions of this class (the function of minimum complexity is explicitly written out) and an asymptotic estimate of complexity of a monotone symmetric function with threshold 3 which is maximal in order of complexity in the class under consideration.

DOI: https://doi.org/10.4213/dm995

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English version:
Discrete Mathematics and Applications, 2008, 18:2, 131–142

Bibliographic databases:

UDC: 519.7

Citation: S. E. Cherukhina, “On complexity of realisation of a class of almost symmetric functions by formulas of depth 3”, Diskr. Mat., 20:1 (2008), 120–130; Discrete Math. Appl., 18:2 (2008), 131–142

Citation in format AMSBIB
\Bibitem{Che08} \by S.~E.~Cherukhina \paper On complexity of realisation of a~class of almost symmetric functions by formulas of depth~3 \jour Diskr. Mat. \yr 2008 \vol 20 \issue 1 \pages 120--130 \mathnet{http://mi.mathnet.ru/dm995} \crossref{https://doi.org/10.4213/dm995} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2420503} \zmath{https://zbmath.org/?q=an:1182.94065} \elib{http://elibrary.ru/item.asp?id=20730235} \transl \jour Discrete Math. Appl. \yr 2008 \vol 18 \issue 2 \pages 131--142 \crossref{https://doi.org/10.1515/DMA.2008.010} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-44449154929}