Abstract
We study growth properties of power-free languages over finite alphabets. We consider the function α(k,β) whose values are the exponential growth rates of β-power-free languages over k-letter alphabets and clarify its asymptotic behaviour. Namely, we suggest the laws of the asymptotic behaviour of this function when k tends to infinity and prove some of them as theorems. In particular, we obtain asymptotic formulas for α(k,β) for the case β ≥ 2.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Berstel, J.: Growth of repetition-free words – a review. Theor. Comput. Sci. 340, 280–290 (2005)
Berstel, J., Karhumäki, J.: Combinatorics on words: A tutorial. Bull. Eur. Assoc. Theor. Comput. Sci. 79, 178–228 (2003)
Brandenburg, F.-J.: Uniformly growing k-th power free homomorphisms. Theor. Comput. Sci. 23, 69–82 (1983)
Carpi, A.: On Dejean’s conjecture over large alphabets. Theor. Comp. Sci. 385, 137–151 (2007)
Crochemore, M., Mignosi, F., Restivo, A.: Automata and forbidden words. Inform. Processing Letters 67(3), 111–117 (1998)
Currie, J.D., Rampersad, N.: A proof of Dejean’s conjecture, http://arxiv.org/PScache/arxiv/pdf/0905/0905.1129v3.pdf
Cvetković, D.M., Doob, M., Sachs, H.: Spectra of graphs. Theory and applications, 3rd edn. Johann Ambrosius Barth, Heidelberg (1995)
Dejean, F.: Sur un Theoreme de Thue. J. Comb. Theory, Ser. A 13(1), 90–99 (1972)
Gantmacher, F.R.: Application of the theory of matrices. Interscience, New York (1959)
Lothaire, M.: Combinatorics on words. Addison-Wesley, Reading (1983)
Morse, M., Hedlund, G.A.: Symbolic dynamics. Amer. J. Math. 60, 815–866 (1938)
Rao, M.: Last Cases of Dejean’s Conjecture. In: Proceedings of the 7th International Conference on Words, Salerno, Italy, paper no. 115 (2009)
Shur, A.M.: Comparing complexity functions of a language and its extendable part. RAIRO Theor. Inf. Appl. 42, 647–655 (2008)
Shur, A.M.: Combinatorial complexity of regular languages. In: Hirsch, E.A., Razborov, A.A., Semenov, A., Slissenko, A. (eds.) Computer Science – Theory and Applications. LNCS, vol. 5010, pp. 289–301. Springer, Heidelberg (2008)
Shur, A.M.: Growth rates of complexity of power-free languages. Submitted to Theor. Comp. Sci. (2008)
Shur, A.M.: Two-sided bounds for the growth rates of power-free languages. In: Diekert, V., Nowotka, D. (eds.) DLT 2009. LNCS, vol. 5583, pp. 466–477. Springer, Heidelberg (2009)
Shur, A.M.: Growth rates of power-free languages. Russian Math. (Iz VUZ) 53(9), 73–78 (2009)
Shur, A.M., Gorbunova, I.A.: On the growth rates of complexity of threshold languages. RAIRO Theor. Inf. Appl. 44, 175–192 (2010)
Thue, A.: Über unendliche Zeichenreihen, Kra. Vidensk. Selsk. Skrifter. I. Mat.-Nat. Kl., Christiana 7, 1–22 (1906)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Shur, A.M. (2010). Growth of Power-Free Languages over Large Alphabets. In: Ablayev, F., Mayr, E.W. (eds) Computer Science – Theory and Applications. CSR 2010. Lecture Notes in Computer Science, vol 6072. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13182-0_35
Download citation
DOI: https://doi.org/10.1007/978-3-642-13182-0_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13181-3
Online ISBN: 978-3-642-13182-0
eBook Packages: Computer ScienceComputer Science (R0)