Biased random satisfiability problems: From easy to hard instances

Details Biased random satisfiability problems: From easy to hard instances Biased random satisfiability problems: From easy to hard instances

2004-11-17

arxiv.org/abs/cond-mat/0411433v2

Phys. Rev. E 71, 066101 (2005)

Physics

Condensed Matter

Disordered Systems and Neural Networks

17 pages, 8 figures

Scientific paper

10.1103/PhysRevE.71.066101

In this paper we study biased random 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 $\alpha_c \propto p^{-(K-1)}$ for $p\to 0$. Solving numerically the survey propagation equations for K=3 we find that for $p

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