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Binary Solutions to Some Systems of Linear Equations

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Optimization Problems and Their Applications (OPTA 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 871))

Abstract

A point is called binary if its coordinates are equal to either zero or one. It is well known that it is hard to find a binary solution to the system of linear equations whose coefficients are integers with small absolute values. The aim of the article is to propose an effective probabilistic reduction from the system to the unique equation when there is a small difference between the number of binary solutions to the first equation and the number of binary solutions to the system. There exist nontrivial examples of linear equations with small positive coefficients having a small number of binary solutions in high dimensions.

This research has been supported by the Russian Science Foundation, Project No. 14–50–00150.

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Acknowledgements

The author would like to thank the anonymous reviewers for useful comments.

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Authors and Affiliations

  1. Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Bolshoy Karetny per. 19, build.1, Moscow, 127051, Russia

    Alexandr V. Seliverstov

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  1. Alexandr V. Seliverstov
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Correspondence to Alexandr V. Seliverstov .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, Omsk, Russia

    Anton Eremeev

  2. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  3. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

    Yury Kochetov

  4. Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos Pardalos

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Seliverstov, A.V. (2018). Binary Solutions to Some Systems of Linear Equations. In: Eremeev, A., Khachay, M., Kochetov, Y., Pardalos, P. (eds) Optimization Problems and Their Applications. OPTA 2018. Communications in Computer and Information Science, vol 871. Springer, Cham. https://doi.org/10.1007/978-3-319-93800-4_15

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  • DOI: https://doi.org/10.1007/978-3-319-93800-4_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-93799-1

  • Online ISBN: 978-3-319-93800-4

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