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Growth properties of power-free languages
The aim of this paper is to survey the area formed by the intersection of two popular lines of
research in formal language theory. The first line, originated by Thue in 1906, concerns …
research in formal language theory. The first line, originated by Thue in 1906, concerns …
On Abelian repetition threshold
We study the avoidance of Abelian powers of words and consider three reasonable
generalizations of the notion of Abelian power to fractional powers. Our main goal is to find …
generalizations of the notion of Abelian power to fractional powers. Our main goal is to find …
[HTML][HTML] Subword complexity and power avoidance
We begin a systematic study of the relations between subword complexity of infinite words
and their power avoidance. Among other things, we show that–the Thue–Morse word has …
and their power avoidance. Among other things, we show that–the Thue–Morse word has …
Growth rates of complexity of power-free languages
We present a new fast algorithm for calculating the growth rate of complexity for regular
languages. Using this algorithm we develop a space and time efficient method to …
languages. Using this algorithm we develop a space and time efficient method to …
Two-sided bounds for the growth rates of power-free languages
The growth properties of power-free languages over finite alphabets are studied. A method
to obtain sharp two-sided bounds of the growth rate of β-power-free languages for arbitrary …
to obtain sharp two-sided bounds of the growth rate of β-power-free languages for arbitrary …
Finding lower bounds on the growth and entropy of subshifts over countable groups
We provide a lower bound on the growth of a subshift based on a simple condition on the set
of forbidden patterns defining that subshift. Aubrun, Barbieri, and Thomassé showed a …
of forbidden patterns defining that subshift. Aubrun, Barbieri, and Thomassé showed a …
On the growth rates of complexity of threshold languages
Threshold languages, which are the (k/(k–1))+-free languages over k-letter alphabets with
k≥ 5, are the minimal infinite power-free languages according to Dejean's conjecture, which …
k≥ 5, are the minimal infinite power-free languages according to Dejean's conjecture, which …
A new hierarchy for automaton semigroups
We define a new strict and computable hierarchy for the family of automaton semigroups,
which reflects the various asymptotic behaviors of the state-activity growth. This hierarchy …
which reflects the various asymptotic behaviors of the state-activity growth. This hierarchy …
Growth of power-free languages over large alphabets
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 …
function α (k, β) whose values are the exponential growth rates of β-power-free languages …
Avoiding square-free words on free groups
We consider sets of factors that can be avoided in square-free words on two-generator free
groups. The elements of the group are presented in terms of {0, 1, 2, 3} such that 0 and 2 …
groups. The elements of the group are presented in terms of {0, 1, 2, 3} such that 0 and 2 …