新型点灯谜题的代数可解性

Connor Gregor, D. Ashlock, Allan R. Willms
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引用次数: 0

摘要

在本研究中,有限循环点灯状态群被重新解释为新颖的点灯谜题。谜题的规则被概述出来,并与点灯者群体的属性联系起来,讨论哪些谜题实例是可解决的。本文表明,通过使用代数,可以在不使用穷举搜索算法的情况下识别许多谜题实例为可解的。可解性取决于有限循环lamplighter群的子群和这些子群形成的余集的不规则生成集的创建。最后还讨论了点灯人难题的进一步可能的概括。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The algebraic solvability of the novel lamplighter puzzle
In this study, the group of finite cyclic lamplighter states is reinterpreted as the novel lamplighter puzzle. The rules of the puzzle are outlined and related back to properties of the lamplighter group with specific interest placed upon the discussion of which puzzle instances are solvable. The paper shows that, through the use of algebra, many puzzle instances can be identified as solvable without the use of an exhaustive search algorithm. Solvability depends upon the creation of irregular generating sets for subgroups of the finite cyclic lamplighter group and the cosets formed by these subgroups. Further possible generalizations of the lamplighter puzzle are also discussed in closing.
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