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Decidability for Sturmian words [PDF]
Logical Methods in Computer Science, 2022 We show that the first-order theory of Sturmian words over Presburger arithmetic is decidable. Using a general adder recognizing addition in Ostrowski numeration systems by Baranwal, Schaeffer and Shallit, we prove that the first-order expansions of ...
Shallit, Jeffrey +5 more
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Abelian returns in Sturmian words [PDF]
Journal of Combinatorial Theory, Series A, 2011 In this paper we study an abelian version of the notion of return word. Our main result is a new characterization of Sturmian words via abelian returns. Namely, we prove that a word is Sturmian if and only if each of its factors has two or three abelian ...
Luca Q. Zamboni +3 more
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Various Properties of Sturmian Words
Acta Polytechnica, 2005 This overview paper is devoted to Sturmian words. The first part summarizes different characterizations of Sturmian words. Besides the well known theorem of Hedlund and Morse it also includes recent results on the characterization of Sturmian words using
P. Baláži, Baláži, P.
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Lyndon factorization of sturmian words
Discrete Mathematics, 2000 We express any general characteristic sturmian word as a unique infinite non-increasing product of Lyndon words. Using this identity, we give a new ω-division for characteristic sturmian words.
Melançon, Guy, Guy Melançon
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Harmonic and gold Sturmian words
European Journal of Combinatorics, 2004 In the combinatorics of Sturmian words an essential role is played by the set PER of all finite words w on the alphabet A = {a, b} having two periods p and q which are coprime and such that the length of w is p + q - 2.
CARPI, Arturo, de Luca A.
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Quasiperiodic Sturmian words and morphisms
Theoretical Computer Science, 2006 We characterize all quasiperiodic Sturmian words: A Sturmian word is not quasiperiodic if and only if it is a Lyndon word.
Gwénaël Richomme +5 more
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Return words in Sturmian and episturmian words [PDF]
RAIRO - Theoretical Informatics and Applications, 2002 Considering each occurrence of a word w in a recurrent infinite word, we define the set of return words of w to be the set of all distinct words beginning with an occurrence of w and ending exactly just before the next occurrence of w in the infinite ...
Laurent Vuillon, Jacques Justin
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On the arithmetical complexity of Sturmian words
Theoretical Computer Science, 2007 Using the geometric dual technique by Berstel and Pocchiola, we give a uniform O(n3) upper bound for the arithmetical complexity of a Sturmian word. We also give explicit expressions for the arithmetical complexity of Sturmian words of slope between 1/3 ...
Cassaigne, J., Frid, A.E.
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Privileged Words and Sturmian Words [PDF]
, 2016 This dissertation has two almost unrelated themes: privileged words and Sturmian words. Privileged words are a new class of words introduced recently.
Peltomäki, Jarkko
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Sturmian words: dynamical systems and derivated words
, 2005 peer reviewedIn a preceding article, we have studied the family of words derivated from characteristic Sturmian words. This study has lead to a new proof of the characterization of characteristic Sturmian words which are fixed points of morphisms.
Bruyère, Véronique, Araújo, Isabel M.
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