Accession Number : ADA325939

Title :   The Probability of Pure Literals,

Corporate Author : MICHIGAN STATE UNIV EAST LANSING DEPT OF MATHEMATICS

Personal Author(s) : Rosenthal, John W. ; Plotkin, J. M. ; Franco, John

PDF Url : ADA325939

Report Date : 1993

Pagination or Media Count : 22

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.

Descriptors :   *MATHEMATICAL MODELS, *PROBABILITY, *HEURISTIC METHODS, ALGORITHMS, RANDOM VARIABLES, ERROR ANALYSIS, ASYMPTOTIC NORMALITY.

Subject Categories : Operations Research
      Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE