Subshifts, MSO Logic, and Collapsing Hierarchies
Dynamical Systems
2014-06-30 v1 Formal Languages and Automata Theory
Logic in Computer Science
Logic
Abstract
We use monadic second-order logic to define two-dimensional subshifts, or sets of colorings of the infinite plane. We present a natural family of quantifier alternation hierarchies, and show that they all collapse to the third level. In particular, this solves an open problem of [Jeandel & Theyssier 2013]. The results are in stark contrast with picture languages, where such hierarchies are usually infinite.
Cite
@article{arxiv.1406.7155,
title = {Subshifts, MSO Logic, and Collapsing Hierarchies},
author = {Ilkka Törmä},
journal= {arXiv preprint arXiv:1406.7155},
year = {2014}
}
Comments
12 pages, 5 figures. To appear in conference proceedings of TCS 2014, published by Springer