The Tribonacci constant and finite automata
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911219369115648 |
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| author | Shallit, Jeffrey |
| author_facet | Shallit, Jeffrey |
| contents | We show that there is no automaton accepting the Tribonacci representations of $n$ and $x$ in parallel, where $ψ= 1.839\cdots$ is the Tribonacci constant, and $x= \lfloor n ψ\rfloor$. Similarly, there is no Tribonacci automaton generating the Sturmian characteristic word with slope $ψ-1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10834 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Tribonacci constant and finite automata Shallit, Jeffrey Formal Languages and Automata Theory Discrete Mathematics Number Theory We show that there is no automaton accepting the Tribonacci representations of $n$ and $x$ in parallel, where $ψ= 1.839\cdots$ is the Tribonacci constant, and $x= \lfloor n ψ\rfloor$. Similarly, there is no Tribonacci automaton generating the Sturmian characteristic word with slope $ψ-1$. |
| title | The Tribonacci constant and finite automata |
| topic | Formal Languages and Automata Theory Discrete Mathematics Number Theory |
| url | https://arxiv.org/abs/2510.10834 |