Marion Le Gonidec (2008)
RAIRO - Theoretical Informatics and Applications
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In this article, we study the complexity of drunken man infinite words. We show that these infinite words, generated by a deterministic and complete countable automaton, or equivalently generated by a substitution over a countable alphabet of constant length, have complexity functions equivalent to (log ) when goes to infinity.
L'ubomíra Balková, Edita Pelantová, Štěpán Starosta (2010)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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The properties characterizing sturmian words are considered for words on multiliteral alphabets. We summarize various generalizations of sturmian words to multiliteral alphabets and enlarge the list of known relationships among these generalizations. We provide a new equivalent definition of rich words and make use of it in the study of generalizations of sturmian words based on palindromes. We also collect many examples of infinite words to illustrate differences in the generalized...
Sergey V. Avgustinovich, Julien Cassaigne, Anna E. Frid (2006)
RAIRO - Theoretical Informatics and Applications
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Arithmetical complexity of a sequence is the number of words of length that can be extracted from it according to arithmetic progressions. We study uniformly recurrent words of low arithmetical complexity and describe the family of such words having lowest complexity.
Michelangelo Bucci, Aldo de Luca, Alessandro De Luca, Luca Q. Zamboni (2008)
RAIRO - Theoretical Informatics and Applications
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In this paper, we solve some open problems related to (pseudo)palindrome closure operators and to the infinite words generated by their iteration, that is, standard episturmian and pseudostandard words. We show that if is an involutory antimorphism of , then the right and left -palindromic closures of any factor of a -standard word are also factors of some -standard word. We also introduce the class of pseudostandard words with “seed”, obtained by iterated pseudopalindrome closure...
Gwénaël Richomme, Kalle Saari, Luca Q. Zamboni (2010)
RAIRO - Theoretical Informatics and Applications
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Among the various ways to construct a characteristic Sturmian word, one of the most used consists in defining an infinite sequence of prefixes that are standard. Nevertheless in any characteristic word , some standard words occur that are not prefixes of . We characterize all standard words occurring in any characteristic word (and so in any Sturmian word) using firstly morphisms, then standard prefixes and finally palindromes.