Maximal Repetitions in Written Texts: Finite Energy Hypothesis vs. Strong Hilberg Conjecture

Entropy

Łukasz Dᆛowski¹ 

[1] Institute of Computer Science, Polish Academy of Sciences, ul. Jana Kazimierza 5, 01-248 Warszawa, Poland; E-Mail

关键词: finite energy processes;    Hilberg’s conjecture;    entropy rate;    maximal repetition;    natural language;   

DOI  :  10.3390/e17085903

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the author; licensee MDPI, Basel, Switzerland.