The Probability of Pure Literals,
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 infinity 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, with probability approaching 1 if the pure literal rule is applied as much as possible, then at least m(1/5) clauses will remain.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1993
- Accession Number
- ADA325939
Entities
People
- J. M. Plotkin
- John Franco
- John W. Rosenthal
Organizations
- Michigan State University