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arXiv · 2504.05012

Descriptive Complexity of Sensitivity of Cellular Automata

Tom Favereau·Ville Salo
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Abstract

We study the computational complexity of determining whether a cellular automaton is sensitive to initial conditions. We show that this problem is $\Pi^0_2$-complete in dimension 1 and $\Sigma^0_3$-complete in dimension 2 and higher. This solves a question posed by Sablik and Theyssier.

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Tom Favereau, Ville Salo. 2025-04-07. Descriptive Complexity of Sensitivity of Cellular Automata. https://arxiv.org/abs/2504.05012

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