Growth of Power-Free Languages over Large Alphabets

Authors:
Arseny M. Shur
Affiliations:
Ural Federal University, Ekaterinburg, Russia
Venue:
Theory of Computing Systems
Year:
2014

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Abstract

We study growth properties of power-free languages over finite alphabets. We consider the function 驴(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 prove asymptotic formulas for this function for the case β驴2 and suggest such formulas for the case β驴(k,β).