逆向和互助国际象棋问题的复杂性：即使合作国际象棋也很难
Complexity of Retrograde and Helpmate Chess Problems: Even Cooperative Chess is Hard
摘要：
我们证明了PSPACE-完全的两个经典类型的国际象棋问题时，推广到n × n板。“逆行”问题询问是否可能从自然起始位置到达位置，即，该位置是否“有效”、“合法”或“可达”。大多数现实世界中的逆行国际象棋问题要求这样一个序列的最后几步，我们分析的决策问题，在指数长移动序列的存在。一个“帮手”问题是问一个玩家是否有可能通过从给定位置开始的任何一系列移动而被将死。帮手问题本质上是国际象棋的一种合作形式，两个玩家一起工作以使特定玩家获胜;它也出现在常规国际象棋游戏中，其中耗尽时间（标志）的玩家只有在他们可能从当前位置被将死时才会输（即，问题有解决的办法）。我们的PSPACE硬度降低是从一个名为地铁洗牌益智游戏的变体。
英文摘要：
We prove PSPACE-completeness of two classic types of Chess problems when generalized to n-by-n boards. A "retrograde" problem asks whether it is possible for a position to be reached from a natural starting position, i.e., whether the position is "valid" or "legal" or "reachable". Most real-world retrograde Chess problems ask for the last few moves of such a sequence; we analyze the decision question which gets at the existence of an exponentially long move sequence. A "helpmate" problem asks whether it is possible for a player to become checkmated by any sequence of moves from a given position. A helpmate problem is essentially a cooperative form of Chess, where both players work together to cause a particular player to win; it also arises in regular Chess games, where a player who runs out of time (flags) loses only if they could ever possibly be checkmated from the current position (i.e., the helpmate problem has a solution). Our PSPACE-hardness reductions are from a variant of a puzzle game called Subway Shuffle.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
