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Problemy Peredachi Informatsii, 2019, Volume 55, Issue 2, Pages 58–81
DOI: https://doi.org/10.1134/S0555292319020049 (Mi ppi2290) 		 
Large Systems

Geometry of translations on a Boolean cube

M. N. Vyalyiabc, V. K. Leontievb

a Moscow Institute of Physics and Technology (State University), Moscow, Russia
b Dorodnitsyn Computing Center of the Russian Academy of Sciences, Moscow, Russia
c National Research University-Higher School of Economics, Moscow, Russia
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DOI: https://doi.org/10.1134/S0555292319020049
Abstract: The operation of Minkowski addition of geometric figures has a discrete analog, addition of subsets of a Boolean cube viewed as a vector space over the two-element field. Subsets of the Boolean cube (or multivariable Boolean functions) form a monoid with respect to this operation. This monoid is of interest in classical discrete analysis as well as in a number of problems related to information theory. We consider several complexity aspects of this monoid, namely structural, algorithmic, and algebraic.
Keywords: Minkowski addition, Boolean cube, monoid, generating elements, primitive elements, sequence of multiples.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 0063-2016-0003
Russian Foundation for Basic Research 17-01-00300_а
Ministry of Education and Science of the Russian Federation
The research of the first author was carried out under the State Assignment, theme no. 0063-2016-0003, and under the 5-100 Russian Academic Excellence Project; it was also supported in part by the Russian Foundation for Basic Research, project no. 17-01-00300. The research of the second author was carried out under the State Assignment, theme no. 0063-2016-0003, and was also supported in part by the Russian Foundation for Basic Research, project no. 17-01-00300.
Received: 24.02.2019
Revised: 26.04.2019
Accepted: 21.05.2019
English version:
Problems of Information Transmission, 2019, Volume 55, Issue 2, Pages 152–173
DOI: https://doi.org/10.1134/S0032946019020042
Bibliographic databases:
Document Type: Article
UDC: 621.391.1 : 519.7
Language: Russian
Citation: M. N. Vyalyi, V. K. Leontiev, “Geometry of translations on a Boolean cube”, Probl. Peredachi Inf., 55:2 (2019), 58–81; Problems Inform. Transmission, 55:2 (2019), 152–173
Citation in format AMSBIB
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\paper Geometry of translations on a Boolean cube
\jour Probl. Peredachi Inf.
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\pages 58--81
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\jour Problems Inform. Transmission
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\pages 152--173
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    		Проблемы передачи информации Problems of Information Transmission
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