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的抽象策略游戏。自2001年首次发布以来，该游戏在休闲玩家和竞技玩家中一直广受欢迎。本文证明，对于该游戏的一个适当推广版本，判定任意棋局中给定玩家是否拥有必胜策略的计算问题是PSPACE难的。我们通过从一种称为公式游戏地理的广义地理变体进行归约来证明这一结论。