Random k-Sat: A Tight Threshold For Moderately Growing k

We consider a random instance I of k-SAT with n variables and m clauses, where k=k(n) satisfies k—log2 n→∞. Let m 0=2k nln2 and let ∈=∈(n)>0 be such that ∈n→∞. We prove that

$$ {}^{{\lim }}_{{n \to \infty }} \Pr {\left( {I\;{\text{is}}\;{\text{satisfiable}}} \right)} = \left\{ {^{{1\;m \leqslant {\left( {1 - \in } \right)}m_{0} }}_{{0\;m \geqslant {\left( {1 + \in } \right)}m_{0} }} .} \right. $$

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Correspondence to Alan Frieze*.

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* Supported in part by NSF grant CCR-9818411.

† Research supported in part by the Australian Research Council and in part by Carneegie Mellon University Funds.

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Frieze*, A., Wormald†, N.C. Random k-Sat: A Tight Threshold For Moderately Growing k . Combinatorica 25, 297–305 (2005). https://doi.org/10.1007/s00493-005-0017-3

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Mathematics Subject Classification (2000):

  • 05D40
  • 68Q25