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On possible growths of arithmetical complexity

Anna E. Frid — 2006

RAIRO - Theoretical Informatics and Applications

The arithmetical complexity of infinite words, defined by Avgustinovich, Fon-Der-Flaass and the author in 2000, is the number of words of length which occur in the arithmetical subsequences of the infinite word. This is one of the modifications of the classical function of subword complexity, which is equal to the number of factors of the infinite word of length . In this paper, we show that the orders of growth of the arithmetical complexity can behave as many sub-polynomial functions. More precisely,...

On automatic infinite permutations

Anna FridLuca Zamboni — 2012

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

An infinite permutation is a linear ordering of N. We study properties of infinite permutations analogous to those of infinite words, and show some resemblances and some differences between permutations and words. In this paper, we try to extend to permutations the notion of automaticity. As we shall show, the standard definitions which are equivalent in the case of words are not equivalent in the context of permutations. We investigate the relationships between these definitions and prove that...

On automatic infinite permutations

Anna FridLuca Zamboni — 2012

RAIRO - Theoretical Informatics and Applications

An infinite permutation is a linear ordering of N. We study properties of infinite permutations analogous to those of infinite words, and show some resemblances and some differences between permutations and words. In this paper, we try to extend to permutations the notion of automaticity. As we shall show, the standard definitions which are equivalent in the case of words are not equivalent in the context of permutations. We investigate the relationships...

On automatic infinite permutations

Anna FridLuca Zamboni — 2012

RAIRO - Theoretical Informatics and Applications

An infinite permutation is a linear ordering of N. We study properties of infinite permutations analogous to those of infinite words, and show some resemblances and some differences between permutations and words. In this paper, we try to extend to permutations the notion of automaticity. As we shall show, the standard definitions which are equivalent in the case of words are not equivalent in the context of permutations. We investigate the relationships...

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