On Countable SFT Covers of Sparse Multidimensional Shift Spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918162071552000 |
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| author | Törmä, Ilkka |
| author_facet | Törmä, Ilkka |
| contents | A multidimensional sofic shift is called countably covered if it has an SFT cover containing only countably many configurations. In contrast to the one-dimensional setting, not all countable sofic shifts are countably covered. We investigate the existence of countable covers for gap width shifts, where the number of nonzero symbols in a configuration is bounded by a function of the minimum distance between two such symbols. As our main results, we characterize those one-dimensional gap width shifts whose two-dimensional lift is a countably covered sofic shift, and show that a large class of two-dimensional gap width shifts are countably covered. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_14967 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Countable SFT Covers of Sparse Multidimensional Shift Spaces Törmä, Ilkka Dynamical Systems Formal Languages and Automata Theory 37B51 A multidimensional sofic shift is called countably covered if it has an SFT cover containing only countably many configurations. In contrast to the one-dimensional setting, not all countable sofic shifts are countably covered. We investigate the existence of countable covers for gap width shifts, where the number of nonzero symbols in a configuration is bounded by a function of the minimum distance between two such symbols. As our main results, we characterize those one-dimensional gap width shifts whose two-dimensional lift is a countably covered sofic shift, and show that a large class of two-dimensional gap width shifts are countably covered. |
| title | On Countable SFT Covers of Sparse Multidimensional Shift Spaces |
| topic | Dynamical Systems Formal Languages and Automata Theory 37B51 |
| url | https://arxiv.org/abs/2409.14967 |