Abstract
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.
Index
Terms
Available to subscribers and IEEE members.
References
Available to subscribers and IEEE members.
Citing Documents
Available to subscribers and IEEE members.
Cart
