DOI: 10.1088/1742-5468/2008/04/p04004. Clusters of solutions and replica symmetry breaking in random k-satisfiability

Clusters of solutions and replica symmetry breaking in random k-satisfiability

10.1088/1742-5468/2008/04/p04004

Crossref journal-article

IOP Publishing

Journal of Statistical Mechanics: Theory and Experiment (266)

Abstract

We study the set of solutions of random k-satisfiability formulas through the cavity method. It is known that, for an interval of the clause-to-variables ratio, this decomposes into an exponential number of pure states (clusters). We refine substantially this picture by: (i) determining the precise location of the clustering transition; (ii) uncovering a second ‘condensation’ phase transition in the structure of the solution set for k≥4. These results both follow from computing the large deviation rate of the internal entropy of pure states. From a technical point of view our main contributions are a simplified version of the cavity formalism for special values of the Parisi replica symmetry breaking parameter m (in particular for m = 1 via a correspondence with the tree reconstruction problem) and new large-k expansions.

Bibliography

Montanari, A., Ricci-Tersenghi, F., & Semerjian, G. (2008). Clusters of solutions and replica symmetry breaking in random k-satisfiability. Journal of Statistical Mechanics: Theory and Experiment, 2008(04), P04004.

Authors 3

Andrea Montanari (first)
Federico Ricci-Tersenghi (additional)
Guilhem Semerjian (additional)

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Dates

Type	When
Created	17 years, 4 months ago (April 8, 2008, 11:17 p.m.)
Deposited	8 months, 2 weeks ago (Dec. 12, 2024, 6:14 a.m.)
Indexed	2 months, 4 weeks ago (May 30, 2025, 10:06 a.m.)
Issued	17 years, 4 months ago (April 1, 2008)
Published	17 years, 4 months ago (April 1, 2008)
Published Online	17 years, 4 months ago (April 8, 2008)
Published Print	17 years, 4 months ago (April 1, 2008)

Funders 0

None

BibTeX

@article{Montanari_2008, title={Clusters of solutions and replica symmetry breaking in random k-satisfiability}, volume={2008}, ISSN={1742-5468}, url={http://dx.doi.org/10.1088/1742-5468/2008/04/p04004}, DOI={10.1088/1742-5468/2008/04/p04004}, number={04}, journal={Journal of Statistical Mechanics: Theory and Experiment}, publisher={IOP Publishing}, author={Montanari, Andrea and Ricci-Tersenghi, Federico and Semerjian, Guilhem}, year={2008}, month=apr, pages={P04004} }

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