Entropy 2015, 17(8), 5903-5919; https://doi.org/10.3390/e17085903
Maximal Repetitions in Written Texts: Finite Energy Hypothesis vs. Strong Hilberg Conjecture
Institute of Computer Science, Polish Academy of Sciences, ul. Jana Kazimierza 5, 01-248 Warszawa, Poland
Academic Editor: J. A. Tenreiro Machado
Received: 22 May 2015 / Revised: 17 August 2015 / Accepted: 19 August 2015 / Published: 21 August 2015
(This article belongs to the Section Complexity)
Abstract
The article discusses two mutually-incompatible hypotheses about the stochastic mechanism of the generation of texts in natural language, which could be related to entropy. The first hypothesis, the finite energy hypothesis, assumes that texts are generated by a process with exponentially-decaying probabilities. This hypothesis implies a logarithmic upper bound for maximal repetition, as a function of the text length. The second hypothesis, the strong Hilberg conjecture, assumes that the topological entropy grows as a power law. This hypothesis leads to a hyperlogarithmic lower bound for maximal repetition. By a study of 35 written texts in German, English and French, it is found that the hyperlogarithmic growth of maximal repetition holds for natural language. In this way, the finite energy hypothesis is rejected, and the strong Hilberg conjecture is partly corroborated. View Full-TextKeywords:
finite energy processes; Hilberg’s conjecture; entropy rate; maximal repetition; natural language
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Dębowski, Ł. Maximal Repetitions in Written Texts: Finite Energy Hypothesis vs. Strong Hilberg Conjecture. Entropy 2015, 17, 5903-5919.