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    Achlioptas, Dimitris and Moore, Cristopher 2006. Randomk‐SAT: Two Moments Suffice to Cross a Sharp Threshold. SIAM Journal on Computing, Vol. 36, Issue. 3, p. 740.

    Plagne, Alain 2006. On threshold properties of <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="" xmlns:xs="" xmlns:xsi="" xmlns="" xmlns:ja="" xmlns:mml="" xmlns:tb="" xmlns:sb="" xmlns:ce="" xmlns:xlink="" xmlns:cals=""><mml:mi>k</mml:mi></mml:math>-SAT: An additive viewpoint. European Journal of Combinatorics, Vol. 27, Issue. 7, p. 1186.

    Franco, John 2005. Typical case complexity of Satisfiability Algorithms and the threshold phenomenon. Discrete Applied Mathematics, Vol. 153, Issue. 1-3, p. 89.

    Franco, John and Swaminathan, Ram 2003. On good algorithms for determining unsatisfiability of propositional formulas. Discrete Applied Mathematics, Vol. 130, Issue. 2, p. 129.

    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.

    Bollobás, Béla Borgs, Christian Chayes, Jennifer T. Kim, Jeong Han and Wilson, David B. 2001. The scaling window of the 2-SAT transition. Random Structures & Algorithms, Vol. 18, Issue. 3, p. 201.

    Dubois, Olivier 2001. Upper bounds on the satisfiability threshold. Theoretical Computer Science, Vol. 265, Issue. 1-2, p. 187.

  • 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:
  • Published online: 01 September 2008

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
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