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randomboolean linear systems.

RAIRO - Theoretical Informatics and Applications (1)

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Smooth and sharp thresholds for random {k}-XOR-CNF satisfiability
Nadia Creignou, Hervé Daudé
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 37 / Issue 2 / April 2003

Published online by Cambridge University Press:

15 November 2003, pp. 127-147

Print publication:

April 2003
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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.