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Diskretnaya Matematika, 2017, Volume 29, Issue 2, Pages 70–83
DOI: https://doi.org/10.4213/dm1419
(Mi dm1419)
 

This article is cited in 2 scientific papers (total in 2 papers)

A generalization of Shannon function

N. P. Red'kin

Lomonosov Moscow State University
Full-text PDF (480 kB) Citations (2)
References:
Abstract: When investigating the complexity of implementing Boolean functions, it is usually assumed that the basis in which the schemes are constructed and the measure of the complexity of the schemes are known. For them, the Shannon function is introduced, which associates with each Boolean function the least complexity of implementing this function in the considered basis. In this paper we propose a generalization of such a Shannon function in the form of an upper bound that is taken over all functionally complete bases. This generalization gives an idea of the complexity of implementing Boolean functions in the “worst” bases for them. The conceptual content of the proposed generalization is demonstrated by the example of a conjunction.
Keywords: Boolean function, Boolean circuit, complexity of a Boolean function, Shannon function.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00452
Received: 03.02.2017
English version:
Discrete Mathematics and Applications, 2018, Volume 28, Issue 5
DOI: https://doi.org/10.1515/dma-2018-0027
Bibliographic databases:
Document Type: Article
UDC: 519.95
Language: Russian
Citation: N. P. Red'kin, “A generalization of Shannon function”, Diskr. Mat., 29:2 (2017), 70–83
Citation in format AMSBIB
\Bibitem{Red17}
\by N.~P.~Red'kin
\paper A generalization of Shannon function
\jour Diskr. Mat.
\yr 2017
\vol 29
\issue 2
\pages 70--83
\mathnet{http://mi.mathnet.ru/dm1419}
\crossref{https://doi.org/10.4213/dm1419}
\elib{https://elibrary.ru/item.asp?id=29437296}
Linking options:
  • https://www.mathnet.ru/eng/dm1419
  • https://doi.org/10.4213/dm1419
  • https://www.mathnet.ru/eng/dm/v29/i2/p70
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Дискретная математика
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    Abstract page:381
    Full-text PDF :77
    References:65
    First page:38
     
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