Skip to main content
Log in

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

  • Original Paper
  • Published:
Combinatorica Aims and scope Submit manuscript

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

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

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alan Frieze*.

Additional information

* 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.

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00493-005-0017-3

Mathematics Subject Classification (2000):

Navigation