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    Fernandez de la Vega, Wenceslas and Karpinski, Marek 2007. 1.0957-Approximation Algorithm for Random MAX-3SAT. RAIRO - Operations Research, Vol. 41, Issue. 1, p. 95.


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    Kaporis, Alexis C. Kirousis, Lefteris M. and Lalas, Efthimios 2003. Selecting Complementary Pairs of Literals. Electronic Notes in Discrete Mathematics, Vol. 16, p. 47.


    Achlioptas, D. and Moore, C. 2002. The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.. p. 779.

    Achlioptas, Dimitris Kirousis, Lefteris M. Kranakis, Evangelos and Krizanc, Danny 2001. Rigorous results for random (2+p)-SAT. Theoretical Computer Science, Vol. 265, Issue. 1-2, p. 109.


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  • Combinatorics, Probability and Computing, Volume 4, Issue 3
  • September 1995, pp. 189-195

On Random 3-sat

  • A. El Maftouhi (a1) and W. Fernandez De La Vega (a1)
  • DOI: http://dx.doi.org/10.1017/S0963548300001590
  • Published online: 01 September 2008
Abstract

Let S be a set of m clauses each containing three literals chosen at random in a set {p1, ¬p1,…,pn, ¬pn} of n propositional variables and their negations. Let be the set of all such S with m = cn for a fixed c > 0. We show, improving significantly over the first moment upper bound , that if m and n tend to infinity with , then almost all are unsatisfiable.

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[1]A. Bender (1975) Central and Local Limit Theorems Applied to Asymptotic Enumeration. J. Comb. Theory (A) 15 91111.

[2]B. Bollobás (1985) Random Graphs. Academic Press.

[3]M. T. Chao and J. Franco (1986) Probabilistic Analysis of Two Heuristics For the 3-Satisfiability Problem. Siam J. Comput. 15(4).

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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
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