The $k$-XORSAT threshold revisited
Combinatorics
2023-01-24 v1 Discrete Mathematics
Abstract
We provide a simplified proof of the random -XORSAT satisfiability threshold theorem. As an extension we also determine the full rank threshold for sparse random matrices over finite fields with precisely non-zero entries per row. This complements a result from [Ayre, Coja-Oghlan, Gao, M\"uller: Combinatorica 2020]. The proof combines physics-inspired message passing arguments with a surgical moment computation.
Cite
@article{arxiv.2301.09287,
title = {The $k$-XORSAT threshold revisited},
author = {Amin Coja-Oghlan and Mihyun Kang and Lena Krieg and Maurice Rolvien},
journal= {arXiv preprint arXiv:2301.09287},
year = {2023}
}