Descriptive Complexity of Sensitivity of Cellular Automata
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909600622575616 |
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| author | Favereau, Tom Salo, Ville |
| author_facet | Favereau, Tom Salo, Ville |
| contents | We study the computational complexity of determining whether a cellular automaton is sensitive to initial conditions. We show that this problem is $Π^0_2$-complete in dimension 1 and $Σ^0_3$-complete in dimension 2 and higher. This solves a question posed by Sablik and Theyssier. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05012 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Descriptive Complexity of Sensitivity of Cellular Automata Favereau, Tom Salo, Ville Dynamical Systems Computational Complexity Logic 37B15 (Primary), 68Q80 (Secondary) We study the computational complexity of determining whether a cellular automaton is sensitive to initial conditions. We show that this problem is $Π^0_2$-complete in dimension 1 and $Σ^0_3$-complete in dimension 2 and higher. This solves a question posed by Sablik and Theyssier. |
| title | Descriptive Complexity of Sensitivity of Cellular Automata |
| topic | Dynamical Systems Computational Complexity Logic 37B15 (Primary), 68Q80 (Secondary) |
| url | https://arxiv.org/abs/2504.05012 |