A spectral technique for random satisfiable 3CNF formulas

Let I be a random 3CNF formula generated by choosing a truth assignment for variables x1, . . . , xn uniformly at random and including every clause with i literals set true by with probability pi, independently. We show that for any constants 0 2, 3 1 there is a constant dmin so that for all d dmin a spectral algorithm similar to the graph coloring algorithm of [3] will find a satisfying assignment with high probability for p1 = d/n2 , p2 = 2d/n2 , and p3 = 3d/n2 . Appropriately setting the i's yields natural distributions on satisfiable 3CNFs, not-all-equal-sat 3CNFs, and exactly-one-sat 3CNFs.

• Type: Journal
• Year: 2008
• Where: RSA
• Authors: Abraham Flaxman
• Keywords: Probability Pi, Random 3CNF Formula, RSA 2008, Truth Assignment