Mick gets some (the odds are on his side) (satisfiability)

  • Authors:
  • V. Chvatal;B. Reed

  • Affiliations:
  • Dept. of Comput. Sci., Rutgers Univ., New Brunswick, NJ, USA;-

  • Venue:
  • SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
  • Year:
  • 1992

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Abstract

Consider a randomly generated boolean formula F (in the conjunctive normal form) with m clauses of size k over n variables; k is fixed at any value greater than 1, but n tends to infinity and m = (1 + o(1))cn for some c depending only on k. It is easy to see that F is unsatisfiable with probability 1-o(1) whenever c(ln 2)2/sup k/; the authors complement this observation by proving that F is satisfiable with probability 1-o(1) whenever c1.