@MISC{Rosenthal_theprobability, author = {John W. Rosenthal and J. M. Plotkin}, title = {The Probability of Pure Literals}, year = {} }

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Abstract

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. Specifically, 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. Keywords: 2-SAT , constant degree model, Davis-Putnam Procedure, pure literal (heuristic), probability of a pure literal 1 1