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

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2 Author(s)
Chvatal, V. ; Dept. of Comput. Sci., Rutgers Univ., New Brunswick, NJ, USA ; Reed, B.

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)2k; the authors complement this observation by proving that F is satisfiable with probability 1-o(1) whenever c<(0.25)2k/k; in fact, they present a linear-time algorithm that satisfies F with probability 1-o(1). In addition, they establish a threshold for 2-SAT: if k = 2 then F is satisfiable with probability 1-o(1) whenever c<1 and unsatisfiable with probability 1-o(1) whenever c>1

Published in:

Foundations of Computer Science, 1992. Proceedings., 33rd Annual Symposium on

Date of Conference:

24-27 Oct 1992