Analytic and algorithmic solution of random satisfiability problems.

  title={Analytic and algorithmic solution of random satisfiability problems.},
  author={Marc M{\'e}zard and Giorgio Parisi and Riccardo Zecchina},
  volume={297 5582},
We study the satisfiability of random Boolean expressions built from many clauses with K variables per clause (K-satisfiability). Expressions with a ratio alpha of clauses to variables less than a threshold alphac are almost always satisfiable, whereas those with a ratio above this threshold are almost always unsatisfiable. We show the existence of an intermediate phase below alphac, where the proliferation of metastable states is responsible for the onset of complexity in search algorithms. We… CONTINUE READING
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