The Probability of Pure Literals

We describe an error in earlier probabilistic analyses of the pure literal heuristic as a procedure for solving k-SAT. All probabilistic analyses are in the constant degree model in which a random instance C of k-SAT consists of m clauses selected independently and uniformly (with replacement) from the set of all k-clauses over n variables. We provide a new analysis for k = 2. Speciically, we show with probability approaching 1 as m goes to 1 one can apply the pure literal rule repeatedly to a random instance of 2-SAT until the number of clauses is \small" provided n=m > 1. But if n=m < 1, with probability approaching 1 if the pure literal rule is applied as much as possible, then at least m 1=5 clauses will remain. (heuristic), probability of a pure literal