Geometry of Translations on a Boolean Cube


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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.

作者简介

M. Vyalyi

Dorodnitsyn Computing Center of the Russian Academy of Sciences; Moscow Institute of Physics and Technology (State University); National Research University-Higher School of Economics

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Email: vyalyi@gmail.com
俄罗斯联邦, Moscow; Moscow; Moscow

V. Leontiev

Dorodnitsyn Computing Center of the Russian Academy of Sciences

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Email: vkleontiev@yandex.ru
俄罗斯联邦, Moscow

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