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Matematicheskie Trudy, 2009, Volume 12, Number 1, Pages 130–143 (Mi mt177)  

On the complexity of recognizing a set of vectors by a neuron

Yu. S. Okulovskii, V. Yu. Popov

Department of Mathematics and Mechanics (Chair of Algebra and Discrete Mathematics) Ural State University, Ekaterinburg, Russia
References:
Abstract: We consider the problems connected with the computational abilities of a neuron. The orderings of finite subsets of real vectors associated with neural computing are studied. We construct a lattice of such orderings and study some its properties. The interrelation between the orders on the sets and the neuron implementation of functions defined on these sets is derived. We prove the NP-hardness of “The Shortest Vector” problem and represent the relationship of the problem with neural computing.
Key words: neural networks, discrete functions, computational capability, computational complexity.
Received: 29.08.2008
English version:
Siberian Advances in Mathematics, 2010, Volume 20, Issue 4, Pages 293–300
DOI: https://doi.org/10.3103/S1055134410040048
Bibliographic databases:
UDC: 519.7
Language: Russian
Citation: Yu. S. Okulovskii, V. Yu. Popov, “On the complexity of recognizing a set of vectors by a neuron”, Mat. Tr., 12:1 (2009), 130–143; Siberian Adv. Math., 20:4 (2010), 293–300
Citation in format AMSBIB
\Bibitem{OkuPop09}
\by Yu.~S.~Okulovskii, V.~Yu.~Popov
\paper On the complexity of recognizing a~set of vectors by a~neuron
\jour Mat. Tr.
\yr 2009
\vol 12
\issue 1
\pages 130--143
\mathnet{http://mi.mathnet.ru/mt177}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2569650}
\transl
\jour Siberian Adv. Math.
\yr 2010
\vol 20
\issue 4
\pages 293--300
\crossref{https://doi.org/10.3103/S1055134410040048}
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    Математические труды Siberian Advances in Mathematics
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