Descriptive Complexity of Sensitivity of Cellular Automata
Dynamical Systems
2025-05-06 v2 Computational Complexity
Logic
Abstract
We study the computational complexity of determining whether a cellular automaton is sensitive to initial conditions. We show that this problem is -complete in dimension 1 and -complete in dimension 2 and higher. This solves a question posed by Sablik and Theyssier.
Keywords
Cite
@article{arxiv.2504.05012,
title = {Descriptive Complexity of Sensitivity of Cellular Automata},
author = {Tom Favereau and Ville Salo},
journal= {arXiv preprint arXiv:2504.05012},
year = {2025}
}
Comments
16 pages, 4 figures, accepted to AUTOMATA 2025. Addressed referee comments