满足x^2=x^3的自由Burnside半群的几乎无伪字和字问题
Almost overlap-free words and the word problem for the free Burnside semigroup satisfying x^2=x^3
摘要：
本文研究了满足x^2=x^3且有两个生成元的自由Burnside半群的字问题.这个半群的元素是等价词的类。解决单词问题的一个自然方法是为每个等价类选择一个唯一的“规范”代表。我们证明了无干扰词和所谓的几乎无干扰词（这个概念是无干扰词的概念的一些推广）可以作为相应的等价类的典型代表。我们证明了在给定的类中，如果有这样的字，可以有效地找到。因此，我们构造了一个线性时间算法，部分地解决了所考虑的半群的字问题。
英文摘要：
In this paper we investigate the word problem of the free Burnside semigroup satisfying x^2=x^3 and having two generators. Elements of this semigroup are classes of equivalent words. A natural way to solve the word problem is to select a unique "canonical" representative for each equivalence class. We prove that overlap-free words and so-called almost overlap-free words (this notion is some generalization of the notion of overlap-free words) can serve as canonical representatives for corresponding equivalence classes. We show that such a word in a given class, if any, can be efficiently found. As a result, we construct a linear-time algorithm that partially solves the word problem for the semigroup under consideration.
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