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Abstract

A simple first moment argument shows that in a randomly chosen k-SAT formula with m clauses over n boolean variables, the fraction of satisfiable clauses is at most 1–2 − − k+o(1) as m/n→∞ almost surely. In this paper, we deal with the corresponding algorithmic strong refutation problem: given a random k-SAT formula, can we find a certificate that the fraction of satisfiable clauses is at most 1–2 − −  k+o(1) in polynomial time? We present heuristics based on spectral techniques that in the case k=3, m≥ln (n)6 n 3/2 and in the case k=4, mCn 2 find such certificates almost surely, where C denotes a constant. Our methods also apply to some hypergraph problems.

Keywords

Polynomial Time Algorithm Chromatic Number Triple System Satisfying Assignment Spectral Technique 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Amin Coja-Oghlan
    • 1
  • Andreas Goerdt
    • 2
  • André Lanka
    • 2
  1. 1.Institut für InformatikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Fakultät für InformatikTechnische Universität ChemnitzChemnitzGermany

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