Publicação
The overlap gap between left-infinite and right-infinite words
| Resumo: | We study ultimate periodicity properties related to overlaps between the suffixes of a left-infinite word λ and the prefixes of a right-infinite word ρ. The main theorem states that the set of minimum lengths of words x and x' such that xλ_n =ρ_n x' or λ_n x=x'ρ_n is finite, where n runs over positive integers and λ_n and ρ_n are respectively the suffix of λ and the prefix of ρ of length n, if and only if λ and ρ are ultimately periodic words of the form λ=...uuv and ρ=wuu... for some finite words u, v and w. |
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| Autores principais: | Costa, José Carlos |
| Outros Autores: | Nogueira, Conceição; Teixeira, Maria Lurdes |
| Assunto: | Infinite word Overlap Ultimately periodic Ciências Naturais::Ciências da Computação e da Informação |
| Ano: | 2022 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| Resumo: | We study ultimate periodicity properties related to overlaps between the suffixes of a left-infinite word λ and the prefixes of a right-infinite word ρ. The main theorem states that the set of minimum lengths of words x and x' such that xλ_n =ρ_n x' or λ_n x=x'ρ_n is finite, where n runs over positive integers and λ_n and ρ_n are respectively the suffix of λ and the prefix of ρ of length n, if and only if λ and ρ are ultimately periodic words of the form λ=...uuv and ρ=wuu... for some finite words u, v and w. |
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