Multidimensional tilings and MSO logic
Formal Languages and Automata Theory
2025-05-26 v1 Dynamical Systems
Logic
Abstract
We define sets of coulourings of the infinite discrete plane using monadic second order (MSO) formulas. We determine the complexity of deciding whether such a formula defines a subshift, parametrized on the quantifier alternation complexity of the formula. We also study the complexities of languages of MSO-definable sets, giving either an exact classification or upper and lower bounds for each quantifier alternation class.
Cite
@article{arxiv.2505.17699,
title = {Multidimensional tilings and MSO logic},
author = {Rémi Pallen and Ilkka Törmä},
journal= {arXiv preprint arXiv:2505.17699},
year = {2025}
}
Comments
15+11 pages, 4+2 figures. To be presented at Computability in Europe 2025