The overlap gap between left-infinite and right-infinite words

In this talk I will present ultimate periodicity properties related to overlaps between the suffixes of a left-infinite word $\lambda$ and the prefixes of a right-infinite word $\rho$. I will talk about a result that states that the set of minimum lengths of words $x$ and $x'$ such that $x\lambda_n = \rho_nx'$ or $\lambda_nx = x'\rho_n$ is finite, where n runs over positive integers and $\lambda_n$ and $\rho_n$ are respectively the suffix of $\lambda$ and the prefix of $\rho$ of length $n$, if and only if $\lambda$ and $\rho$ are ultimately periodic words of the form $\lambda = u^{-\infty}v$ and $\rho = wu^{\infty}$ for some finite words $u$, $v$ and $w$. This is a joint work with José Carlos Costa (Universidade do Minho) and M. Lurdes Teixeira (Universidade do Minho).

Date and Venue

Start Date
Online Zoom meeting
End Date


Conceição Nogueira

Speaker's Institution

Polytechnic Institute of Leiria/CMAT (University of Minho)



Semigroups, Automata and Languages