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

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

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

Bibliographic databases:

UDC: 519.95

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} 

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