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Almost overlap-free words and the word problem for the free Burnside semigroup satisfying x^2=x^3

By A. N. Plyushchenko and A. M. Shur


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.Comment: 33 pages, submitted to Internat. J. of Algebra and Compu

Topics: Computer Science - Formal Languages and Automata Theory, Mathematics - Group Theory
Year: 2011
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