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.

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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

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Computer Science
  • Electronic Mail
  • Hypotheses
  • Mathematics
  • Permutations
  • Power Series
  • Probability
  • Sequences
  • Transitions
  • Universities

Fields of Study

  • Computer science
  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Systems Analysis and Design