Decidability and Characterization of Expansivity for Group Cellular Automata
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914096380641280 |
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| author | Castronuovo, Niccolo' Dennunzio, Alberto Margara, Luciano |
| author_facet | Castronuovo, Niccolo' Dennunzio, Alberto Margara, Luciano |
| contents | Group cellular automata are continuous, shift-commuting endomorphisms of $G^\mathbb{Z}$, where $G$ is a finite group. We provide an easy-to-check characterization of expansivity for group cellular automata on abelian groups and we prove that expansivity is a decidable property for general (non-abelian) groups. Moreover, we show that the class of expansive group cellular automata is strictly contained in that of topologically transitive injective group cellular automata. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14568 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decidability and Characterization of Expansivity for Group Cellular Automata Castronuovo, Niccolo' Dennunzio, Alberto Margara, Luciano Formal Languages and Automata Theory Discrete Mathematics Group cellular automata are continuous, shift-commuting endomorphisms of $G^\mathbb{Z}$, where $G$ is a finite group. We provide an easy-to-check characterization of expansivity for group cellular automata on abelian groups and we prove that expansivity is a decidable property for general (non-abelian) groups. Moreover, we show that the class of expansive group cellular automata is strictly contained in that of topologically transitive injective group cellular automata. |
| title | Decidability and Characterization of Expansivity for Group Cellular Automata |
| topic | Formal Languages and Automata Theory Discrete Mathematics |
| url | https://arxiv.org/abs/2510.14568 |