Eulerian entropy and non-repetitive subword complexity
نویسندگان
چکیده
منابع مشابه
Estimation of Entropy from Subword Complexity
Subword complexity is a function that describes how many different substrings of a given length are contained in a given string. In this paper, two estimators of block entropy are proposed, based on the profile of subword complexity. The first estimator works well only for IID processes with uniform probabilities. The second estimator provides a lower bound of block entropy for any strictly sta...
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Sequences of characters called words or strings are widely studied in combinatorics, and used in various fields of sciences (e.g. chemistry, physics, social sciences, biology [2, 3, 4, 11] etc.). The elements of a word are called letters. A contiguous part of a word (obtained by erasing a prefix or/and a suffix) is a subword or factor. If we erase arbitrary letters from a word, what is obtained...
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We begin a systematic study of the relations between subword complexity of infinite words and their power avoidance. Among other things, we show that – the Thue-Morse word has the minimum possible subword complexity over all overlapfree binary words and all (73)-power-free binary words, but not over all ( 7 3) +-power-free binary words; – the twisted Thue-Morse word has the maximum possible sub...
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We show that the subword complexity function ρx(n), which counts the number of distinct factors of length n of a sequence x, is k-synchronized in the sense of Carpi if x is k-automatic. As an application, we generalize recent results of Goldstein. We give analogous results for the number of distinct factors of length n that are primitive words or powers. In contrast, we show that the function t...
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The subword complexity of an infinite word ξ is a function f (ξ, n) returning the number of finite subwords (factors, infixes) of length n of ξ. In the present paper we investigate infinite words for which the set of subwords occurring infinitely often is a regular language. Among these infinite words we characterise those which are eventually recurrent. Furthermore, we derive some results comp...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2012
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2011.11.013