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.

翻译：Hive是一款在桌面上使用六边形棋子进行的抽象策略游戏。该游戏于2001年首次发布，至今仍在休闲玩家和竞技玩家中广受欢迎。本文证明，在适当推广的游戏版本中，判断任意局面下特定玩家是否存在必胜策略的计算问题是PSPACE难的。为此，我们通过从广义地理学的一个变体（称为公式游戏地理学）进行归约来证明这一结论。