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Arimaa Is PSPACE-Hard

Authors Benjamin G. Rin , Atze Schipper

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ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Arimaa
  • complexity theory
  • PSPACE-hardness
  • board games
  • Generalized Geography

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Abstract

Arimaa is a strategy board game developed in 2003 by Omar Syed, designed to be hard for AI to win because of its large branching factor. In this paper, its theoretical complexity is considered. We prove that Arimaa (suitably generalized to an n × n board) is PSPACE-hard. This result is found by reducing a known PSPACE-hard variant of Generalized Geography to a variant of Arimaa that we call Arimaa^′, which in turn is then reduced to (n × n) Arimaa. Since the game is easily seen to be solvable in exponential time, it follows that its complexity lies somewhere between being PSPACE-complete and EXPTIME-complete.

Cite As Get BibTex

Benjamin G. Rin and Atze Schipper. Arimaa Is PSPACE-Hard. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 27:1-27:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.FUN.2024.27

Author Details

Benjamin G. Rin
  • Utrecht University, The Netherlands
Atze Schipper
  • Utrecht University, The Netherlands

Acknowledgements

We would like to thank Rosalie Iemhoff for her useful feedback and suggestions, as well as Colin Caret, Dominik Klein, Johannes Korbmacher, Jaap van Oosten, and all other attendees at The Utrecht Logic in Progress Series for their comments on a presentation of an early version of this paper. We also would like to thank the anonymous referees for their feedback.

References

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