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 Mat. Vopr. Kriptogr., 2016, Volume 7, Issue 3, Pages 61–72 (Mi mvk196)

The stability of sets of solutions for systems of equations with random distortions

V. G. Mikhailova, A. V. Volginb

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Moscow State University of Information Technologies, Radioengineering and Electronics, Moscow

Abstract: Let in a system of equations left sides be functions from $\{0,1,…,N-1\}$ to $\{0,1\}$ and in the other system all equations be obtained from the equations of the first one by random distortions of the truth tables of these functions. We find conditions on the probability laws of distortions under which the set of solutions of the second system includes all, some or no solutions of the first system.

Key words: set of solutions of system of equations, binomial distribution, Boolean functions.

DOI: https://doi.org/10.4213/mvk196

Full text: PDF file (136 kB)

Bibliographic databases:

UDC: 519.212.2
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Citation: V. G. Mikhailov, A. V. Volgin, “The stability of sets of solutions for systems of equations with random distortions”, Mat. Vopr. Kriptogr., 7:3 (2016), 61–72

Citation in format AMSBIB
\Bibitem{MikVol16} \by V.~G.~Mikhailov, A.~V.~Volgin \paper The stability of sets of solutions for systems of equations with random distortions \jour Mat. Vopr. Kriptogr. \yr 2016 \vol 7 \issue 3 \pages 61--72 \mathnet{http://mi.mathnet.ru/mvk196} \crossref{https://doi.org/10.4213/mvk196} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3588374} \elib{https://elibrary.ru/item.asp?id=28931395}