Combinatorial sharpness criterion and phase transition classification for random CSPs

Authors:
Nadia Creignou;Hervé Daudé
Affiliations:
LIF, UMR CNRS 6166, Université de la Méditerranée, 163, avenue de Luminy, 13 288 Marseille, France;LIF, UMR CNRS 6166, Université de la Méditerranée, 163, avenue de Luminy, 13 288 Marseille, France and LATP, UMR CNRS 6632, Université de Provence, 39, rue Joliot-Curie, 13 453 ...
Venue:
Information and Computation
Year:
2004

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Abstract

We investigate the nature of the phase transition (sharp or coarse) for random constraint satisfaction problems. We first give a sharp threshold criterion specified for CSPs, which is derived from Friedgut-Bourgain's one. Thus, we get a complete and precise classification of the nature of the threshold for symmetric Boolean CSPs. In particular we show that it is governed by two local properties strongly related to the problems 1-SAT and 2-XOR-SAT.