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

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 37, Issue: 2, page 127-147
- ISSN: 0988-3754

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topCreignou, Nadia, and Daudé, Hervé. "Smooth and sharp thresholds for random {k}-XOR-CNF satisfiability." RAIRO - Theoretical Informatics and Applications 37.2 (2010): 127-147. <http://eudml.org/doc/92718>.

@article{Creignou2010,

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.
},

author = {Creignou, Nadia, Daudé, Hervé},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Threshold phenomenon; satisfiability; phase transition; random
Boolean linear systems.; threshold phenomenon},

language = {eng},

month = {3},

number = {2},

pages = {127-147},

publisher = {EDP Sciences},

title = {Smooth and sharp thresholds for random \{k\}-XOR-CNF satisfiability},

url = {http://eudml.org/doc/92718},

volume = {37},

year = {2010},

}

TY - JOUR

AU - Creignou, Nadia

AU - Daudé, Hervé

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

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

PB - EDP Sciences

VL - 37

IS - 2

SP - 127

EP - 147

AB -
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.

LA - eng

KW - Threshold phenomenon; satisfiability; phase transition; random
Boolean linear systems.; threshold phenomenon

UR - http://eudml.org/doc/92718

ER -

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