Computational Hardness of Multidimensional Subtraction Games

  • Vladimir Gurvich
  • Mikhail VyalyiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12159)


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.


Subtraction games Cellular automata Computational hardness 



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


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsMoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyMoscowRussia
  3. 3.Dorodnicyn Computing Centre, FRC CSC RASMoscowRussia
  4. 4.Rutgers UniversityNew BrunswickUSA

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