ALMOST OVERLAP-FREE WORDS AND THE WORD PROBLEM FOR THE FREE BURNSIDE SEMIGROUP SATISFYING x2 = x3
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چکیده
منابع مشابه
Almost overlap-free words and the word problem for the free Burnside semigroup satisfying x2=x3
In this paper we investigate the word problem of the free Burnside semigroup satisfying x2 = x3 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 socalled almost overlap-free words (this notion is some gene...
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15 صفحه اولOverlap-Free Words and Generalizations
The study of combinatorics on words dates back at least to the beginning of the 20 century and the work of Axel Thue. Thue was the first to give an example of an infinite word over a three letter alphabet that contains no squares (identical adjacent blocks) xx. This result was eventually used to solve some longstanding open problems in algebra and has remarkable connections to other areas of ma...
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Shallit and Wang studied deterministic automatic complexity of words. They showed that the automatic Hausdorff dimension I(t) of the infinite Thue word satisfies 1/3 6 I(t) 6 1/2. We improve that result by showing that I(t) = 1/2. We prove that the nondeterministic automatic complexity AN (x) of a word x of length n is bounded by b(n) := bn/2c+ 1. This enables us to define the complexity defici...
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A word on a nite alphabet A is said to be overlap free if it contains no factor of the form xuxux where x is a letter and u a possibly empty word In this paper we study the number un of overlap free binary words of length n which is known to be bounded by a polynomial in n First we describe a bijection between the set of overlap free words and a rational language This yields recurrence relation...
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ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2011
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196711006558