English

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 Σ21\Sigma^1_2-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.

Keywords

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}
}
R2 v1 2026-06-28T21:02:50.908Z