各种地理变量的计算复杂性
On the Computational Complexities of Various Geography Variants
摘要：
广义地理学是一个在有向图上进行的组合游戏。玩家轮流将一个代币从一个顶点移动到另一个顶点，将代币从一个顶点移开后删除该顶点。无法移动的玩家输。众所周知，在广义地理学中，从给定的位置决定哪个玩家应该获胜的计算复杂性是PSPACE完全的。我们介绍了几个规则的变种，广义地理，我们探讨了计算复杂性，确定赢家的位置，许多由此产生的游戏。在我们的研究结果是一个证明，确定在文献中称为无向游击队地理游戏的赢家是PSPACE完全的，即使被限制在一个二分图。
英文摘要：
Generalized Geography is a combinatorial game played on a directed graph. Players take turns moving a token from vertex to vertex, deleting a vertex after moving the token away from it. A player unable to move loses. It is well known that the computational complexity of determining which player should win from a given position of Generalized Geography is PSPACE-complete. We introduce several rule variants to Generalized Geography, and we explore the computational complexity of determining the winner of positions of many resulting games. Among our results is a proof that determining the winner of a game known in the literature as Undirected Partizan Geography is PSPACE-complete, even when restricted to being played on a bipartite graph.
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。
