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Diskr. Mat., 2017, Volume 29, Issue 2, Pages 70–83 (Mi dm1419)  

This article is cited in 1 scientific paper (total in 1 paper)

A generalization of Shannon function

N. P. Red'kin

Lomonosov Moscow State University

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


DOI: https://doi.org/10.4213/dm1419

Full text: PDF file (480 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Discrete Mathematics and Applications, 2018, 28:5

Bibliographic databases:

UDC: 519.95
Received: 03.02.2017

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{http://elibrary.ru/item.asp?id=29437296}


Linking options:
  • http://mi.mathnet.ru/eng/dm1419
  • https://doi.org/10.4213/dm1419
  • http://mi.mathnet.ru/eng/dm/v29/i2/p70

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. P. Redkin, “Obobschennaya slozhnost lineinykh bulevykh funktsii”, Diskret. matem., 30:4 (2018), 88–95  mathnet  crossref  elib
  • Дискретная математика
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