A note on cellular automata
In this note, we give a new totally topological definition of cellular automata over groups. We show that every continuous self-map of the shift space A^G can be represented as a G-sequence of cellular automata. In the case of a finitely generated group G and a finite alphabet A, we prove that the...
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| Format: | Article |
| Language: | English |
| Published: |
Aracne
2021-12-01
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| Series: | Advances in Group Theory and Applications |
| Subjects: | |
| Online Access: | http://www.advgrouptheory.com/journal/Files/click_url.php?id=Volumes/12/Shahryari.pdf |
| Summary: | In this note, we give a new totally topological definition of cellular automata over groups. We show that every continuous self-map of the shift space A^G can be
represented as a G-sequence of cellular automata. In the case of a finitely generated group G and a finite alphabet A, we prove that the set of all cellular automata is discrete in the uniform metric space of continuous self-maps of A^G. |
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| ISSN: | 2499-1287 |