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Diskr. Mat., 2015, Volume 27, Issue 3, Pages 108–122 (Mi dm1338)  

Mean and variance of the number of subfunctions of random Boolean function which are close to the affine functions set} \runningtitle{Mean and variance of the number of subfunctions of random Boolean function

A. A. Serov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: For random equiprobable Boolean functions we investigate the distribution of the number of subfunctions which have a given number of variables and are close to the set of affine Boolean functions. It is shown, for example, that for Boolean functions of $n$ variables the mean number of subfunctions having $ s \geqslant 3+ \log_2 n $ variables and the Hamming distance to the set of affine functions smaller than $ 2 ^ {s-2} $ tends to $ 0 $ as $ n \rightarrow \infty $.

Keywords: random Boolean function, subfunction, affine Boolean functions, Hamming distance

DOI: https://doi.org/10.4213/dm1338

Full text: PDF file (475 kB)
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English version:
Discrete Mathematics and Applications, 2017, 27:1, 23–34

Bibliographic databases:

Document Type: Article
UDC: 519.212.2+519.213.2
Received: 17.02.2015

Citation: A. A. Serov, “Mean and variance of the number of subfunctions of random Boolean function which are close to the affine functions set} \runningtitle{Mean and variance of the number of subfunctions of random Boolean function”, Diskr. Mat., 27:3 (2015), 108–122; Discrete Math. Appl., 27:1 (2017), 23–34

Citation in format AMSBIB
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\pages 108--122
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\jour Discrete Math. Appl.
\yr 2017
\vol 27
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\pages 23--34
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