Problems of Information Transmission

, Volume 55, Issue 2, pp 152–173 | Cite as

Geometry of Translations on a Boolean Cube

  • M. N. VyalyiEmail author
  • V. K. LeontievEmail author
Large Systems


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.

Key words

Minkowski addition Boolean cube monoid generating elements primitive elements sequence of multiples 


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Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.Dorodnitsyn Computing Center of the Russian Academy of SciencesMoscowRussia
  2. 2.Moscow Institute of Physics and Technology (State University)MoscowRussia
  3. 3.National Research University-Higher School of EconomicsMoscowRussia

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