- Published 2006 in Random Struct. Algorithms

Using the cavity equations of Mézard, Parisi, and Zecchina [Science 297 (2002), 812; Mézard and Zecchina, Phys Rev E 66 (2002), 056126] we derive the various threshold values for the number of clauses per variable of the random K-satisfiability problem, generalizing the previous results to K ≥ 4. We also give an analytic solution of the equations, and some closed expressions for these thresholds, in an expansion around large K . The stability of the solution is also computed. For anyK , the satisfiability threshold is found to be in the stable region of the solution, which adds further credit to the conjecture that this computation gives the exact satisfiability threshold. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 28, 000–000, 2006

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@article{Mertens2006ThresholdVO,
title={Threshold values of Random K-SAT from the cavity method},
author={Stephan Mertens and Marc M{\'e}zard and Riccardo Zecchina},
journal={Random Struct. Algorithms},
year={2006},
volume={28},
pages={340-373}
}