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On synchronized sequences and their separators

Arturo CarpiCristiano 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 CarpiCristiano 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...

On the distribution of characteristic parameters of words II

Arturo CarpiAldo de Luca — 2002

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The characteristic parameters K w and R w of a word w over a finite alphabet are defined as follows: K w is the minimal natural number such that w has no repeated suffix of length K w and R w is the minimal natural number such that w has no right special factor of length R w . In a previous paper, published on this journal, we have studied the distributions of these parameters, as well as the distribution of the maximal length of a repetition, among the words of each length on a given alphabet. In this paper...

On the distribution of characteristic parameters of words

Arturo CarpiAldo de Luca — 2002

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

For any finite word w on a finite alphabet, we consider the basic parameters R w and K w of w defined as follows: R w is the minimal natural number for which w has no right special factor of length R w and K w is the minimal natural number for which w has no repeated suffix of length K w . In this paper we study the distributions of these parameters, here called characteristic parameters, among the words of each length on a fixed alphabet.

On the distribution of characteristic parameters of words

Arturo CarpiAldo de Luca — 2010

RAIRO - Theoretical Informatics and Applications

For any finite word on a finite alphabet, we consider the basic parameters and of defined as follows: is the minimal natural number for which has no right special factor of length and is the minimal natural number for which has no repeated suffix of length . In this paper we study the distributions of these parameters, here called characteristic parameters, among the words of each length...

On the distribution of characteristic parameters of words II

Arturo CarpiAldo de Luca — 2010

RAIRO - Theoretical Informatics and Applications

The characteristic parameters and of a word over a finite alphabet are defined as follows: is the minimal natural number such that has no repeated suffix of length and is the minimal natural number such that has no right special factor of length . In a previous paper, published on this journal, we have studied the distributions of these parameters, as well as the distribution of the maximal...

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