Restivo Salemi property for $α$-power free languages with $α\geq 5$ and $k\geq 3$ letters
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866908338481004544 |
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| 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 |
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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 |