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Analytic and Algorithmic Solution of Random Satisfiability Problems

M. Mézard, G. Parisi and R. Zecchina
Science
New Series, Vol. 297, No. 5582 (Aug. 2, 2002), pp. 812-815
Stable URL: http://www.jstor.org/stable/3831989
Page Count: 4
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Analytic and Algorithmic Solution of Random Satisfiability Problems
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Abstract

We study the satisfiability of random Boolean expressions built from many clauses with K variables per clause (K-satisfiability). Expressions with a ratio α of clauses to variables less than a threshold αc 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 αc, where the proliferation of metastable states is responsible for the onset of complexity in search algorithms. We introduce a class of optimization algorithms that can deal with these metastable states; one such algorithm has been tested successfully on the largest existing benchmark of K-satisfiability.

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