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 k3 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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