Smooth and sharp thresholds for random $k$-XOR-CNF satisfiability

Creignou, Nadia; Daudé, Hervé

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 $k=2$.

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