Displaying similar documents to “On the product of balanced sequences”

On the product of balanced sequences

Antonio Restivo, Giovanna Rosone (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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The product  =  ⊗  of two sequences and is a naturally defined sequence on the alphabet of pairs of symbols. Here, we study when the product of two balanced sequences is balanced too. In the case and are binary sequences, we prove, as a main result, that, if such a product is balanced and () = 4, then is an ultimately periodic sequence of a very special form. The case of arbitrary alphabets is approached in the last section. The partial results obtained and the problems proposed...

On synchronized sequences and their separators

Arturo Carpi, Cristiano Maggi (2010)

RAIRO - Theoretical Informatics and Applications

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We introduce the notion of a -synchronized sequence, where is an integer larger than 1. Roughly speaking, a sequence of natural numbers is said to be -synchronized if its graph is represented, in base , by a right synchronized rational relation. This is an intermediate notion between -automatic and -regular sequences. Indeed, we show that the class of -automatic sequences is equal to the class of bounded -synchronized sequences and that the class of -synchronized sequences...

Complexity of infinite words associated with beta-expansions

Christiane Frougny, Zuzana Masáková, Edita Pelantová (2010)

RAIRO - Theoretical Informatics and Applications

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We study the complexity of the infinite word associated with the Rényi expansion of in an irrational base . When is the golden ratio, this is the well known Fibonacci word, which is Sturmian, and of complexity . For such that is finite we provide a simple description of the structure of special factors of the word . When =1 we show that . In the cases when or max} we show that the first difference of the complexity function takes value in for every , and consequently we determine...

Hereditary properties of words

József Balogh, Béla Bollobás (2010)

RAIRO - Theoretical Informatics and Applications

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Let be a hereditary property of words, , an infinite class of finite words such that every subword (block) of a word belonging to is also in . Extending the classical Morse-Hedlund theorem, we show that either contains at least words of length for every  or, for some , it contains at most words of length for every . More importantly, we prove the following quantitative extension of this result: if has words of length then, for every , it contains at most ⌈( + 1)/2⌉⌈( + 1)/2⌈...