Restivo Salemi property for $α$-power free languages with $α\geq 5$ and $k\geq 3$ letters

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: Rukavicka, Josef
Format: Preprint
Published: 2023
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866908338481004544
author Rukavicka, Josef
author_facet Rukavicka, Josef
contents In 2009, Shur published the following conjecture: Let $L$ be a power-free language and let $e(L)\subseteq L$ be the set of words of $L$ that can be extended to a bi-infinite word respecting the given power-freeness. If $u, v \in e(L)$ then $uwv \in e(L)$ for some word $w$. Let $L_{k,α}$ denote an $α$-power free language over an alphabet with $k$ letters, where $α$ is a positive rational number and $k$ is positive integer. We prove the conjecture for the languages $L_{k,α}$, where $α\geq 5$ and $k\geq 3$.
format Preprint
id arxiv_https___arxiv_org_abs_2312_10061
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Restivo Salemi property for $α$-power free languages with $α\geq 5$ and $k\geq 3$ letters
Rukavicka, Josef
Formal Languages and Automata Theory
Discrete Mathematics
68R15
In 2009, Shur published the following conjecture: Let $L$ be a power-free language and let $e(L)\subseteq L$ be the set of words of $L$ that can be extended to a bi-infinite word respecting the given power-freeness. If $u, v \in e(L)$ then $uwv \in e(L)$ for some word $w$. Let $L_{k,α}$ denote an $α$-power free language over an alphabet with $k$ letters, where $α$ is a positive rational number and $k$ is positive integer. We prove the conjecture for the languages $L_{k,α}$, where $α\geq 5$ and $k\geq 3$.
title Restivo Salemi property for $α$-power free languages with $α\geq 5$ and $k\geq 3$ letters
topic Formal Languages and Automata Theory
Discrete Mathematics
68R15
url https://arxiv.org/abs/2312.10061