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






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

Full text: PDF file (136 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 519.7
Received: 19.12.2005

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}


Linking options:
  • http://mi.mathnet.ru/eng/dm995
  • https://doi.org/10.4213/dm995
  • http://mi.mathnet.ru/eng/dm/v20/i1/p120

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Дискретная математика
    Number of views:
    This page:217
    Full text:84
    References:19
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020