On the satisfiability and maximum satisfiability of random 3-CNF formulas

We analyze the pure literal rule heuristic for computing a satisfying assignment to a random 3-CNF formula with n variables. We show that the pure literal rule by itself finds satisfying assignments for almost all 3-CNF formulas with up to 1.63n clauses, but it fails for more than 1.7n clauses. As an aside we show that the value of maximum satisfiability for random 3-CNF formulas is tightly concentrated around its mean.

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