Growth of power-free languages over large alphabets

Authors:
Arseny M. Shur
Affiliations:
Ural State University
Venue:
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Year:
2010

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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.