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The asymptotic order of the random k-SAT threshold

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2 Author(s)
Achlioptas, D. ; Microsoft Corp., Redmond, WA, USA ; Moore, C.

Form a random k-SAT formula on n variables by selecting uniformly and independently m=rn clauses out of all 2k (kn) possible k-clauses. The satisfiability threshold conjecture asserts that for each k there exists a constant rk such that, as n tends to infinity, the probability that the formula is satisfiable tends to 1 if rk and to 0 if r>rk. It has long been known that 2k/kk<2k. We prove that rk>2k-1 ln 2-dk, where dk→(1+ln2)/2. Our proof also allows a blurry glimpse of the "geometry" of the set of satisfying truth assignments.

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Foundations of Computer Science, 2002. Proceedings. The 43rd Annual IEEE Symposium on

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