Year: 2026
Type: preprint
Abstract: We prove that for any cocompact Fuchsian group the class of Medvedev degrees attained by subshifts of finite type is the class of $Π_1^0$ degrees. This result relies on the construction of a rigid hierarchical structure in a graph model of the hyperbolic plane, and on the fact that every such group admits a representation in $\operatorname{PSL}_2(\mathbb{R})$ such that the matrices in the image have coefficients that are computable real numbers.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7211900604