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Journal of Logic and Computation 1999 9(4):501-513; doi:10.1093/logcom/9.4.501
© 1999 by Oxford University Press
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The probability of pure literals

JW RosenthalA1, JM PlotkinA2 and J FrancoA

A1 Department of Mathematics and Computer Science, Ithaca College, Ithaca, NY 14850, USA E-mail: rosentha@ithaca.edu A2 Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA E-mail: plotkin@math.msu.edu A Department of Computer Science, University of Cincinnati, Cincinnati, OH 45221, USA E-mail: franco@gauss.ececs.uc.edu

We describe an error in earlier probabilistic analyses of the pure literal heuristic as a procedure for solving the satisfiability problem for sets of 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 {infty} 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 ≥ {lambda} > 1. But if n/m ≤ {lambda} < 1 and {epsilon} < 1/4, with probability approaching 1 if the pure literal rule is applied as often as possible, then at least m{epsilon} clauses will remain.

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


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