Smooth and sharp thresholds for random $k$-XOR-CNF satisfiability
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 37 (2003) no. 2, pp. 127-147.

The aim of this paper is to study the threshold behavior for the satisfiability property of a random $k$-XOR-CNF formula or equivalently for the consistency of a random Boolean linear system with $k$ variables per equation. For $k\ge 3$ we show the existence of a sharp threshold for the satisfiability of a random $k$-XOR-CNF formula, whereas there are smooth thresholds for $k=1$ and $k=2$.

DOI : https://doi.org/10.1051/ita:2003014
Classification : 05C80,  68R05,  60C05
Mots clés : threshold phenomenon, satisfiability, phase transition, random boolean linear systems
@article{ITA_2003__37_2_127_0,
author = {Creignou, Nadia and Daud\'e, Herv\'e},
title = {Smooth and sharp thresholds for random ${k}$-XOR-CNF satisfiability},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {127--147},
publisher = {EDP-Sciences},
volume = {37},
number = {2},
year = {2003},
doi = {10.1051/ita:2003014},
zbl = {1112.68390},
mrnumber = {2015688},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ita:2003014/}
}
Creignou, Nadia; Daudé, Hervé. Smooth and sharp thresholds for random ${k}$-XOR-CNF satisfiability. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 37 (2003) no. 2, pp. 127-147. doi : 10.1051/ita:2003014. http://www.numdam.org/articles/10.1051/ita:2003014/

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