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

Published online by Cambridge University Press:  15 November 2003

Nadia Creignou  and
Hervé Daudé
Nadia Creignou
Affiliation:
LIF, UMR 6166 du CNRS, Université de la Méditerranée, 163, avenue de Luminy, 13288 Marseille, France; creignou@lif.univ-mrs.fr.
Hervé Daudé
Affiliation:
LATP, UMR 6632 du CNRS, Université de Provence, 39 rue Joliot-Curie, 13453 Marseille, France; daude@gyptis.univ-mrs.fr.
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Abstract

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.

Keywords

Threshold phenomenonsatisfiabilityphase transitionrandom Boolean linear systems.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 37 , Issue 2 , April 2003 , pp. 127 - 147
Copyright
© EDP Sciences, 2003

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