Email this article Geometry of Translations on a Boolean Cube
- Authors: Vyalyi M.N.1,2,3, Leontiev V.K.1
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Affiliations:
- Dorodnitsyn Computing Center of the Russian Academy of Sciences
- Moscow Institute of Physics and Technology (State University)
- National Research University-Higher School of Economics
- Issue: Vol 55, No 2 (2019)
- Pages: 152-173
- Section: Large Systems
- URL: https://journal-vniispk.ru/0032-9460/article/view/166595
- DOI: https://doi.org/10.1134/S0032946019020042
- ID: 166595
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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.
About the authors
M. N. 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
Author for correspondence.
Email: vyalyi@gmail.com
Russian Federation, Moscow; Moscow; Moscow
V. K. Leontiev
Dorodnitsyn Computing Center of the Russian Academy of Sciences
Author for correspondence.
Email: vkleontiev@yandex.ru
Russian Federation, Moscow
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