Complexity of Linear Equations and Infinite Gadgets

Fuente: arXiv
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Main Authors: Grebík, Jan, Vidnyánszky, Zoltán
Format: Preprint
Published: 2025
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author Grebík, Jan
Vidnyánszky, Zoltán
author_facet Grebík, Jan
Vidnyánszky, Zoltán
contents 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 $Σ^1_2$-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.
format Preprint
id arxiv_https___arxiv_org_abs_2501_06114
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Complexity of Linear Equations and Infinite Gadgets
Grebík, Jan
Vidnyánszky, Zoltán
Logic
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 $Σ^1_2$-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.
title Complexity of Linear Equations and Infinite Gadgets
topic Logic
url https://arxiv.org/abs/2501.06114