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Let $\varPhi$ be a uniformly distributed random $k$-SAT formula with $n$variables and $m$ clauses. For clauses/variables ratio $m/n \leqr_{k\text{-SAT}} \sim 2^k\ln2$ the formula $\varPhi$ is satisfiable with highprobability. However, no efficient algorithm is known to provably find asatisfying assignment beyond $m/n \sim 2k \ln(k)/k$ with a non-vanishingprobability. Non-rigorous statistical mechanics work on $k$-CNF led to thedevelopment of a new efficient "message passing algorithm" called \emph{SurveyPropagation Guided Decimation} [M\'ezard et al., Science 2002]. Experimentsconducted for $k=3,4,5$ suggest that the algorithm finds satisfying assignmentsclose to $r_{k\text{-SAT}}$. However, in the present paper we prove that thebasic version of Survey Propagation Guided Decimation fails to solve random$k$-SAT formulas efficiently already for $m/n=2^k(1+\varepsilon_k)\ln(k)/k$with $\lim_{k\to\infty}\varepsilon_k= 0$ almost a factor $k$ below$r_{k\text{-SAT}}$.

Analysing Survey Propagation Guided Decimation on Random Formulas