Don's conjecture for binary completely reachable automata: an approach and its limitations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866917617760993280 |
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| author | Casas, David Volkov, Mikhail V. |
| author_facet | Casas, David Volkov, Mikhail V. |
| contents | A deterministic finite automaton in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. It was conjectured that in each completely reachable automaton with $n$ states, every set of $k>0$ states is the image of a word of length at most $n(n-k)$. We confirm the conjecture for completely reachable automata with two input letters satisfying certain restrictions on the action of the letters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00077 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Don's conjecture for binary completely reachable automata: an approach and its limitations Casas, David Volkov, Mikhail V. Formal Languages and Automata Theory 68Q45 A deterministic finite automaton in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. It was conjectured that in each completely reachable automaton with $n$ states, every set of $k>0$ states is the image of a word of length at most $n(n-k)$. We confirm the conjecture for completely reachable automata with two input letters satisfying certain restrictions on the action of the letters. |
| title | Don's conjecture for binary completely reachable automata: an approach and its limitations |
| topic | Formal Languages and Automata Theory 68Q45 |
| url | https://arxiv.org/abs/2311.00077 |