Geodesic
Growth rates of power-free languages
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2009), pp. 82-88

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We propose a new fast algorithm for calculating the growth rate of complexity for regular languages. Based on this algorithm, we develop an efficient universal method of estimating the upper bound of the growth rates for power-free languages. Through extensive computer-assisted studies we sufficiently improve all known upper bounds for growth rates of such languages, obtain a lot of new bounds, and discover some general regularities.
Keywords: power-free languages, regular languages, combinatorial complexity, growth rate. 
@article{IVM_2009_9_a8,
     author = {A. M. Shur},
     title = {Growth rates of power-free languages},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {82--88},
     publisher = {mathdoc},
     number = {9},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_9_a8/}
}
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A. M. Shur. Growth rates of power-free languages. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2009), pp. 82-88. http://geodesic.mathdoc.fr/item/IVM_2009_9_a8/