no. 2
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≥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 : 10.1051/ita:2003014
Classification : 05C80, 68R05, 60C05
Mots clés : threshold phenomenon, satisfiability, phase transition, random boolean linear systems 
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     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},
     mrnumber = {2015688},
     zbl = {1112.68390},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita:2003014/}
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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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