Papers by Sorin Constantinescu
Theoretical Computer Science, 2005
The well known Fine and Wilf's theorem for words states that if a word has two periods and its le... more The well known Fine and Wilf's theorem for words states that if a word has two periods and its length is at least as long as the sum of the two periods minus their greatest common divisor, then the word also has as period the greatest common divisor. We generalise this result for an arbitrary number of periods. Our bound is strictly better in some cases than previous generalisations. Moreover, we prove it optimal. We show also that any extremal word is unique up to letter renaming and give an algorithm to compute both the bound and a corresponding extremal word.
The Lempel-Ziv complexity is a fundamental measure of complexity for words, closely connected wit... more The Lempel-Ziv complexity is a fundamental measure of complexity for words, closely connected with the famous LZ77 compression algorithm. We investigate this complexity measure for one of the most important families of infinite words in combinatorics, namely the fixed points of morphisms. We give a complete characterization of the complexity classes which are Θ(1), Θ(log n), and Θ(n 1/k ), k ∈ N, k ≥ 2, depending on the periodicity of the word and the growth function of the morphism. The relation with the well-known classification of Ehrenfeucht, Lee, Rozenberg, and Pansiot for factor complexity classes is also investigated. The two measures complete each other, giving an improved picture for the complexity of these infinite words.
Fineand Wilf'stheoremforabelianperiods
Siam Journal on Discrete Mathematics, 2007
The Lempel-Ziv complexity is a fundamental measure of complexity for words, closely connected wit... more The Lempel-Ziv complexity is a fundamental measure of complexity for words, closely connected with the famous LZ77 compression algorithm. We investigate this complexity measure for one of the most important families of infinite words in combinatorics, namely the fixed points of morphisms. We give a complete characterization of the complexity classes which are Θ(1), Θ(log n), and Θ(n 1/k ), k ∈ N, k ≥ 2, depending on the periodicity of the word and the growth function of the morphism. The relation with the well-known classification of Ehrenfeucht, Lee, Rozenberg, and Pansiot for factor complexity classes is also investigated. The two measures complete each other, giving an improved picture for the complexity of these infinite words.
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Papers by Sorin Constantinescu