English

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 Π20\Pi^0_2-complete in dimension 1 and Σ30\Sigma^0_3-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