Hive is PSPACE-Hard

Daniël Andel; Benjamin Rin

doi:10.4230/lipics.fun.2026.3

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arXiv · 2506.03492

Hive is PSPACE-Hard

Daniël Andel·Benjamin Rin

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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 a variant of Generalized Geography we call Formula Game Geography.

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Daniël Andel, Benjamin Rin. 2025-06-04. Hive is PSPACE-Hard. https://doi.org/10.4230/lipics.fun.2026.3

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