Spin Glass Cavity Method in Random K-Satisfiability Problem

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Presentation transcript:

Spin Glass Cavity Method in Random K-Satisfiability Problem Ma Hui 2009-12-22

Random K-Satisfiability Problem

Structure of Solution Space changes as the constraint density increases

The Communities in a Single Solution Cluster Haijun Zhou, Hui Ma, Communities of solutions in Single Solution Clusters of a Random K-Satisfiability Formula, Phys. Rev. E Accepted 12Nov,2009

From SAT to Max-SAT

Replica Symmetry Equations and Its Stability Analysis Method for Replica Symmetry method: 1.Deviation of two replicas 2.Convergence of the belief propagation 3.Numerical instability towards 1RSB(m=1) solutions

The Threshold Temperature: Td &Trs

1RSB scenario

1RSB Stability Analysis Two kinds of Stability 1. Iteration Stability 2.Stability to Bug proliferation

The Sample figure for Bug Proliferation

Thanks