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Biased random satisfiability problems: From easy to hard instances

Ramezanpour, A ; Sharif University of Technology | 2005

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  1. Type of Document: Article
  2. DOI: 10.1103/PhysRevE.71.066101
  3. Publisher: 2005
  4. Abstract:
  5. In this paper we study biased random K-satisfiability (K-SAT) problems in which each logical variable is negated with probability p. This generalization provides us a crossover from easy to hard problems and would help us in a better understanding of the typical complexity of random K-SAT problems. The exact solution of 1-SAT case is given. The critical point of K-SAT problems and results of replica method are derived in the replica symmetry framework. It is found that in this approximation αcp-(K-1) for p→0. Solving numerically the survey propagation equations for K=3 we find that for p
  6. Keywords:
  7. K-satisfiability (K-SAT) ; Replica symmetry ; Approximation theory ; Numerical analysis ; Probability ; Problem solving
  8. Source: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics ; Volume 71, Issue 6 , 2005 ; 15393755 (ISSN)
  9. URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.71.066101