Deciding Conjugacy in Thompson's Group F in Linear Time

Nabil Hossain, Robert W. McGrail, James M. Belk, Francesco Matucci
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引用次数: 2

Abstract

We present an efficient implementation of the solution to the conjugacy problem in Thompson's group F, a certain infinite group whose elements are piecewise-linear homeomorphisms of the unit interval. This algorithm checks for conjugacy by constructing and comparing directed graphs called strand diagrams. We provide a comprehensive description of our solution algorithm, including the data structure that stores strand diagrams and methods to simplify them. We prove that our algorithm theoretically achieves a linear time bound in the size of the input, and we present a quadratic time working solution.
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线性时间下汤普森群F的共轭性判定
给出了一类无限群(其元素为单位区间的分段线性同胚)中共轭问题解的一个有效实现。该算法通过构造和比较被称为链图的有向图来检查共轭性。我们提供了我们的解决算法的全面描述,包括存储链图的数据结构和简化它们的方法。我们从理论上证明了我们的算法在输入的大小上达到了一个线性的时间界限,并给出了一个二次的时间工作解。
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