Setting 2 variables at a time yields a new lower bound for random 3 - SAT
نویسنده
چکیده
Let X be a set of n Boolean variables and denote by C(X) the set of all 3lauses overX, i.e. the set of all 8 n3 possible disjun tions of three distin t, nonomplementary literals from variables in X. Let F (n;m) be a random 3-SAT formula formed by sele ting, with repla ement, m lauses uniformly at random from C(X) and taking their onjun tion. The satis ability threshold onje ture asserts that there exists a onstant r3 su h that as n!1, F (n; rn) is satis able with probability that tends to 1 if r < r3, but unsatis able with probability that tends to 1 if r > r3. Experimental eviden e suggests r3 4:2. We prove r3 > 3:145 improving over the previous best lower bound r3 > 3:003 due to Frieze and Suen. For this, we introdu e a satis ability heuristi that works iteratively, permanently setting the value of a pair of variables in ea h round. The framework we develop for the analysis of our heuristi allows us to also derive most previous lower bounds for random 3-SAT in a uniform manner and with little e ort.
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