Growth properties of power-free languages

AM Shur - Computer Science Review, 2012‏ - Elsevier
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 …

On Abelian repetition threshold

AV Samsonov, AM Shur - RAIRO-Theoretical Informatics and …, 2012‏ - cambridge.org
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 …

[HTML][HTML] Subword complexity and power avoidance

J Shallit, A Shur - Theoretical Computer Science, 2019‏ - Elsevier
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 …

Growth rates of complexity of power-free languages

AM Shur - Theoretical Computer Science, 2010‏ - Elsevier
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 …

Two-sided bounds for the growth rates of power-free languages

AM Shur - Developments in Language Theory: 13th International …, 2009‏ - Springer
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 …

Finding lower bounds on the growth and entropy of subshifts over countable groups

M Rosenfeld - Groups, Geometry, and Dynamics, 2025‏ - ems.press
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 …

On the growth rates of complexity of threshold languages

AM Shur, IA Gorbunova - RAIRO-Theoretical Informatics and …, 2010‏ - cambridge.org
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 …

A new hierarchy for automaton semigroups

L Bartholdi, T Godin, I Klimann, C Noûs… - International Journal of …, 2020‏ - World Scientific
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 …

Growth of power-free languages over large alphabets

AM Shur - Theory of Computing Systems, 2014‏ - Springer
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 …

Avoiding square-free words on free groups

G Badkobeh, T Harju, P Ochem, M Rosenfeld - Theoretical Computer …, 2022‏ - Elsevier
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 …