Proving Properties of $φ$-Representations with the Walnut Theorem-Prover
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910258811633664 |
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| author | Shallit, Jeffrey |
| author_facet | Shallit, Jeffrey |
| contents | We revisit a classic theorem of Frougny and Sakarovitch concerning automata for $φ$-representations, and show how to obtain it in a different and more computationally direct way. Using it, we can find simple, induction-free proofs of existing results in the literature about these representations, in a uniform and straightforward manner. In particular, we can easily and "automatically'' recover many of the results of recent papers of Dekking and Van Loon. We also obtain a number of new results on $φ$-representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_02672 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Proving Properties of $φ$-Representations with the Walnut Theorem-Prover Shallit, Jeffrey Number Theory Discrete Mathematics Formal Languages and Automata Theory We revisit a classic theorem of Frougny and Sakarovitch concerning automata for $φ$-representations, and show how to obtain it in a different and more computationally direct way. Using it, we can find simple, induction-free proofs of existing results in the literature about these representations, in a uniform and straightforward manner. In particular, we can easily and "automatically'' recover many of the results of recent papers of Dekking and Van Loon. We also obtain a number of new results on $φ$-representations. |
| title | Proving Properties of $φ$-Representations with the Walnut Theorem-Prover |
| topic | Number Theory Discrete Mathematics Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2305.02672 |