Growth Properties of Power-Free Languages
- Cite this paper as:
- Shur A.M. (2011) Growth Properties of Power-Free Languages. In: Mauri G., Leporati A. (eds) Developments in Language Theory. DLT 2011. Lecture Notes in Computer Science, vol 6795. Springer, Berlin, Heidelberg
The aim of this paper is to give a short survey of the area formed by the intersection of two popular lines of investigation in formal language theory. The first line, originated by Thue in 1906, concerns about repetition-free words and languages. The second line is the study of growth functions for words and languages; it can be traced back to the classical papers by Morse and Hedlund on symbolic dynamics (1938, 1940). Growth functions of repetition-free languages are investigated since 1980’s. Most of the results were obtained for power-free languages, but some ideas can be applied for languages avoiding patterns and Abelian-power-free languages as well.
In this paper, we present key contributions to the area, its state-of-the-art, and conjectures that suggest answers to some natural unsolved problems. Also, we pay attention to the tools and techniques that made possible the progress in the area and suggest some technical results that would be useful to solve open problems.
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