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On synchronized sequences and their separators

Arturo Carpi; Cristiano Maggi — 2001

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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

On synchronized sequences and their separators

Arturo Carpi; Cristiano Maggi — 2010

RAIRO - Theoretical Informatics and Applications

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 is strictly...

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