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Computational Hardness of Multidimensional Subtraction Games

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Computer Science – Theory and Applications (CSR 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12159))

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Abstract

We study the algorithmic complexity of solving subtraction games in a fixed dimension with a finite difference set. We prove that there exists a game in this class such that solving the game is \({\mathbf {EXP}}\)-complete and requires time \(2^{\varOmega (n)}\), where n is the input size. This bound is optimal up to a polynomial speed-up.

The results are based on the construction introduced by Larsson and Wästlund. It relates subtraction games and cellular automata.

The article was prepared within the framework of the HSE University Basic Research Program. The second author was supported in part by RFBR grant 20-01-00645 and the state assignment topic no. 0063-2016-0003.

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Acknowledgment

The authors are grateful to the anonymous referee for several helpful remarks improving both, the results and their presentation.

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Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow, Russia

    Vladimir Gurvich & Mikhail Vyalyi

  2. Moscow Institute of Physics and Technology, Moscow, Russia

    Mikhail Vyalyi

  3. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Mikhail Vyalyi

  4. Rutgers University, New Brunswick, NJ, 08901-8554, USA

    Vladimir Gurvich

Authors
  1. Vladimir Gurvich
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  2. Mikhail Vyalyi
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Corresponding author

Correspondence to Mikhail Vyalyi .

Editor information

Editors and Affiliations

  1. University of Trier, Trier, Germany

    Henning Fernau

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Gurvich, V., Vyalyi, M. (2020). Computational Hardness of Multidimensional Subtraction Games. In: Fernau, H. (eds) Computer Science – Theory and Applications. CSR 2020. Lecture Notes in Computer Science(), vol 12159. Springer, Cham. https://doi.org/10.1007/978-3-030-50026-9_17

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  • DOI: https://doi.org/10.1007/978-3-030-50026-9_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-50025-2

  • Online ISBN: 978-3-030-50026-9

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