| Issue |
RAIRO-Theor. Inf. Appl.
Volume 37, Number 2, April/June 2003
|
|
|---|---|---|
| Page(s) | 127 - 147 | |
| DOI | https://doi.org/10.1051/ita:2003014 | |
| Published online | 15 November 2003 | |
Smooth and sharp thresholds for random {k}-XOR-CNF satisfiability
1
LIF, UMR 6166 du CNRS,
Université de la Méditerranée,
163, avenue de Luminy,
13288 Marseille, France; creignou@lif.univ-mrs.fr.
2
LATP, UMR 6632 du CNRS, Université de Provence, 39 rue Joliot-Curie, 13453 Marseille, France; daude@gyptis.univ-mrs.fr.
Received:
September
2001
Accepted:
March
2003
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.
Mathematics Subject Classification: 05C80 / 68R05 / 60C05
Key words: Threshold phenomenon / satisfiability / phase transition / random Boolean linear systems.
© EDP Sciences, 2003
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