Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2005-06-02
Theoretical Computer Science 393 (2008) 260-279
Physics
Condensed Matter
Disordered Systems and Neural Networks
Scientific paper
10.1016/j.tcs.2008.01.005
We investigate geometrical properties of the random K-satisfiability problem using the notion of x-satisfiability: a formula is x-satisfiable if there exist two SAT assignments differing in Nx variables. We show the existence of a sharp threshold for this property as a function of the clause density. For large enough K, we prove that there exists a region of clause density, below the satisfiability threshold, where the landscape of Hamming distances between SAT assignments experiences a gap: pairs of SAT-assignments exist at small x, and around x=1/2, but they donot exist at intermediate values of x. This result is consistent with the clustering scenario which is at the heart of the recent heuristic analysis of satisfiability using statistical physics analysis (the cavity method), and its algorithmic counterpart (the survey propagation algorithm). The method uses elementary probabilistic arguments (first and second moment methods), and might be useful in other problems of computational and physical interest where similar phenomena appear.
Daude Herve
Mezard Marc
Mora Thierry
Zecchina Riccardo
No associations
LandOfFree
Pairs of SAT Assignment in Random Boolean Formulae does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Pairs of SAT Assignment in Random Boolean Formulae, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Pairs of SAT Assignment in Random Boolean Formulae will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-434533