Length-k-overlap-free Binary Infinite Words
نویسندگان
چکیده
منابع مشابه
Length-k-overlap-free Binary Infinite Words
We study length-k-overlap-free binary infinite words, i.e., binary infinite words which can contain only overlaps xyxyx with |x| ≤ k− 1. We prove that no such word can be generated by a morphism, except if k = 1. On the other hand, for every k ≥ 2, there exist length-k-overlap-free binary infinite words which are not length-(k−1)-overlap-free. As an application, we prove that, for every non-neg...
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Let t be the infinite fixed point, starting with 1, of the morphism μ : 0 → 01, 1→ 10. An infinite word over {0, 1} is said to be overlap-free if it contains no factor of the form axaxa, where a ∈ {0, 1} and x ∈ {0, 1}∗. We prove that the lexicographically least infinite overlap-free binary word beginning with any specified prefix, if it exists, has a suffix which is a suffix of t. In particula...
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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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Let t be the innnite xed point, starting with 1, of the morphism : 0 ! 01, 1 ! 10. An innnite word over f0;1g is said to be overlap-free if it contains no factor of the form axaxa, where a 2 f0;1g and x 2 f0;1g. We prove that the lexicographically least innnite overlap-free binary word beginning with any speciied preex, if it exists, has a suux which is a suux of t. In particular, the lexicogra...
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We consider a measure of similarity for infinite words that generalizes the notion of asymptotic or natural density of subsets of natural numbers from number theory. We show that every overlap-free infinite binary word, other than the Thue-Morse word t and its complement t, has this measure of similarity with t between 1 4 and 3 4 . This is a partial generalization of a classical 1927 result of...
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ژورنال
عنوان ژورنال: Fundamenta Informaticae
سال: 2012
ISSN: 0169-2968
DOI: 10.3233/fi-2012-682