无限移动单人国际象棋的复杂性
Complexity of Solo Chess with Unlimited Moves
摘要：
我们分析了单人国际象棋难题，其中输入是一个$n \times n$板，其中包含一些相同颜色的标准国际象棋棋子，目标是进行一系列的捕获移动，以减少到一个单一的棋子。以前的工作分析了这个难题为一个单一的棋子类型时，每个棋子被限制为最多两个捕获移动（如在独奏国际象棋难题chess.com）。相比之下，我们研究的是每个棋子何时可以做出无限数量的捕捉动作。我们表明，任何单一的件类型可以解决在多项式时间的一般模型的件类型，而任何两个标准的国际象棋件类型是NP-完全的。我们还分析了限制（如在chess.com上），即一个片段类型是唯一的，必须是最后一个幸存的片段，表明在这种情况下，一些对片段类型变得易于处理，而其他类型仍然很难。
英文摘要：
We analyze Solo Chess puzzles, where the input is an $n \times n$ board containing some standard Chess pieces of the same color, and the goal is to make a sequence of capture moves to reduce down to a single piece. Prior work analyzes this puzzle for a single piece type when each piece is limited to make at most two capture moves (as in the Solo Chess puzzles on chess.com). By contrast, we study when each piece can make an unlimited number of capture moves. We show that any single piece type can be solved in polynomial time in a general model of piece types, while any two standard Chess piece types are NP-complete. We also analyze the restriction (as on chess.com) that one piece type is unique and must be the last surviving piece, showing that in this case some pairs of piece types become tractable while others remain hard.
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。
