Document Open Access Logo

Hive Is PSPACE-Hard

Authors Daniël I. Andel, Benjamin G. Rin

PDF

File

Thumbnail PDF
PDF
LIPIcs.FUN.2026.3.pdf
  • Filesize: 1.21 MB
  • 20 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Computational complexity
  • Combinatorial games
  • Hive
  • PSPACE-hardness
  • Formula Game
  • Generalized Geography

Metrics

Abstract

Hive is an abstract strategy game played on a table with hexagonal pieces. First published in 2001, it was and continues to be highly popular among both casual and competitive players. In this paper, we show that for a suitably generalized version of the game, the computational problem of determining whether a given player in an arbitrary position has a winning strategy is PSPACE-hard. We do this by reduction from Formula Game, which is first reduced to an intermediate problem we call Formula Game Geography, after which the latter is reduced to our decision problem.

Cite As Get BibTex

Daniël I. Andel and Benjamin G. Rin. Hive Is PSPACE-Hard. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.FUN.2026.3

Author Details

Daniël I. Andel
  • Utrecht University, The Netherlands
Benjamin G. Rin
  • Utrecht University, The Netherlands

Acknowledgements

We would like to thank Rosalie Iemhoff and Robert Barish for their helpful conversations and comments. We also wish to thank the anonymous referees for their valuable feedback.

References

  1. Daniël Andel. On the complexity of Hive. Bachelor’s thesis, Utrecht University, 2020. Google Scholar
  2. Aviezri S. Fraenkel and David Lichtenstein. Computing a perfect strategy for n × n chess requires time exponential in n. J. Comb. Theory, Ser. A, 31(2):199-214, 1981. URL: https://doi.org/10.1016/0097-3165(81)90016-9.
  3. Robert Hearn. Amazons, Konane, and Cross Purposes are PSPACE-complete. Games of No Chance 3, 56, March 2009. URL: https://doi.org/10.1017/CBO9780511807251.015.
  4. Robert A. Hearn and Erik D. Demaine. Games, puzzles and computation. A K Peters, 2009. Google Scholar
  5. David Lichtenstein and Michael Sipser. Go is polynomial-space hard. Journal of the ACM, 27(2):393-401, April 1980. URL: https://doi.org/10.1145/322186.322201.
  6. Stefan Reisch. Gobang ist PSPACE-vollständig. Acta Informatica, 13:59-66, 1980. URL: https://doi.org/10.1007/BF00288536.
  7. Stefan Reisch. Hex ist PSPACE-vollständig. Acta Informatica, 15:167-191, 1981. URL: https://doi.org/10.1007/BF00288964.
  8. Benjamin G. Rin and Atze Schipper. Arimaa is PSPACE-Hard. In Andrei Z. Broder and Tami Tamir, editors, 12th International Conference on Fun with Algorithms, FUN 2024, June 4-8, 2024, Island of La Maddalena, Sardinia, Italy, volume 291 of LIPIcs, pages 27:1-27:24. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. URL: https://doi.org/10.4230/LIPIcs.FUN.2024.27.
  9. J. M. Robson. N by N checkers is Exptime complete. SIAM Journal on Computing, 13(2):252-267, 1984. URL: https://doi.org/10.1137/0213018.
  10. Michael Sipser. Introduction to the Theory of Computation. CENGAGE Learning, 3 edition, 2013. International ed. Google Scholar
  11. James A. Storer. On the complexity of chess. Journal of Computer and System Sciences, 27(1):77-100, 1983. URL: https://doi.org/10.1016/0022-0000(83)90030-2.
  12. Giovanni Viglietta. Lemmings is PSPACE-complete. Theor. Comput. Sci., 586:120-134, 2015. URL: https://doi.org/10.1016/J.TCS.2015.01.055.
  13. John Yianni. Hive: a game buzzing with possibilities. https://www.gen42.com/wp-content/uploads/Hive-rules.pdf, 2010. Accessed: 2026-03-03.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact