一维立柱Solitaire和Duotaire
One-Dimensional Peg Solitaire, and Duotaire
摘要：
我们解决的问题，一维钉接龙。特别是，我们表明，一组配置，可以减少到一个单一的挂钩形式的正规语言，并存在一个线性时间算法减少任何配置的最小数量的挂钩。然后我们来看看拉维库马尔提出的公平的两人游戏，其中两名玩家轮流做出挂钩动作，哪个玩家没有动作就输了。我们计算了一些简单的尼姆值，并讨论了当游戏分离成一个小游戏的析取和。在一系列的跳跃可以在一个单一的移动的版本中，我们表明，无论是P-位置，也不是N-位置（即前一个或下一个玩家的胜利）是由一个定期或上下文无关的语言描述。
英文摘要：
We solve the problem of one-dimensional Peg Solitaire. In particular, we show that the set of configurations that can be reduced to a single peg forms a regular language, and that a linear-time algorithm exists for reducing any configuration to the minimum number of pegs. We then look at the impartial two-player game, proposed by Ravikumar, where two players take turns making peg moves, and whichever player is left without a move loses. We calculate some simple nim-values and discuss when the game separates into a disjunctive sum of smaller games. In the version where a series of hops can be made in a single move, we show that neither the P-positions nor the N-positions (i.e. wins for the previous or next player) are described by a regular or context-free language.
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。
