Complexity of Linear Equations and Infinite Gadgets
Logic
2025-01-13 v1
Abstract
We investigate the descriptive set-theoretic complexity of the solvability of a Borel family of linear equations over a finite field. Answering a question of Thornton, we show that this problem is already hard, namely -complete. This implies that the split between easy and hard problems is at a different place in the Borel setting than in the case of the CSP Dichotomy.
Cite
@article{arxiv.2501.06114,
title = {Complexity of Linear Equations and Infinite Gadgets},
author = {Jan Grebík and Zoltán Vidnyánszky},
journal= {arXiv preprint arXiv:2501.06114},
year = {2025}
}