Balanced K-SAT and Biased random K-SAT on trees
Statistical Mechanics
2013-05-01 v1 Artificial Intelligence
Computational Complexity
Abstract
We study and solve some variations of the random K-satisfiability problem - balanced K-SAT and biased random K-SAT - on a regular tree, using techniques we have developed earlier(arXiv:1110.2065). In both these problems, as well as variations of these that we have looked at, we find that the SAT-UNSAT transition obtained on the Bethe lattice matches the exact threshold for the same model on a random graph for K=2 and is very close to the numerical value obtained for K=3. For higher K it deviates from the numerical estimates of the solvability threshold on random graphs, but is very close to the dynamical 1-RSB threshold as obtained from the first non-trivial fixed point of the survey propagation algorithm.
Keywords
Cite
@article{arxiv.1212.1942,
title = {Balanced K-SAT and Biased random K-SAT on trees},
author = {Sumedha and Supriya Krishnamurthy and Sharmistha Sahoo},
journal= {arXiv preprint arXiv:1212.1942},
year = {2013}
}
Comments
22 pages, 7 figures