Probability of pure literals
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
Journal of Logic and Computation
Rosenthal, John W.; Plotkin, J. M.; and Franco, John, "Probability of pure literals" (1999). Faculty Articles Indexed in Scopus. 2374.