Threshold values of Random K-SAT from the cavity method

Stephan Mertens; Marc Mezard; Riccardo Zecchina

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Threshold values of Random K-SAT from the cavity method

Stephan Mertens·Marc Mezard·Riccardo Zecchina

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Abstract

Using the cavity equations of \cite{mezard:parisi:zecchina:02,mezard:zecchina:02}, we derive the various threshold values for the number of clauses per variable of the random $K$-satisfiability problem, generalizing the previous results to $K \ge 4$. 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 any $K$, 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.

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cs.CC cond-mat.dis-nn cs.DM

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BibTeX RIS

Stephan Mertens, Marc Mezard, Riccardo Zecchina. 2005-02-24. Threshold values of Random K-SAT from the cavity method. https://arxiv.org/abs/cs/0309020

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