Title

Probability of pure literals

Document Type

Article

Publication Date

1-1-1999

Abstract

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-clauses (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 ∞ 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≥λ>1. But if n/m≤λ<1 and ε<1/4, with probability approaching 1 if the pure literal rule is applied as often as possible, then at least m clauses will remain. ε

Publication Name

Journal of Logic and Computation

Volume Number

9

First Page

501

Last Page

513

Issue Number

4

DOI

10.1093/logcom/9.4.501

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