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

Nadia CreignouHervé Daudé — 2003

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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 .

Smooth and sharp thresholds for random -XOR-CNF satisfiability

Nadia CreignouHervé Daudé — 2010

RAIRO - Theoretical Informatics and Applications

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

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