CCMay 19

Hive is PSPACE-Hard

arXiv:2506.0349262.3
AI Analysis

For game theorists and complexity researchers, this shows that Hive belongs to a class of computationally hard games, though the result is for a generalized version rather than the standard game.

The paper proves that determining the winner in a generalized version of the board game Hive is PSPACE-hard, establishing its computational complexity.

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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