Exhaustive enumeration unveils clustering and freezing in random 3-SAT

John Ardelius, Lenka Zdeborová

Published 2008-04-02, updated 2008-04-14Version 2

We study geometrical properties of the complete set of solutions of the random 3-satisfiability problem. We show that even for moderate system sizes the number of clusters corresponds surprisingly well with the theoretic asymptotic prediction. We locate the freezing transition in the space of solutions which has been conjectured to be relevant in explaining the onset of computational hardness in random constraint satisfaction problems.