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On Random 3-sat

  • A. El Maftouhi (a1) and W. Fernandez De La Vega (a1)

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
  • URL: /core/journals/combinatorics-probability-and-computing
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