1. Spin Glass Cavity Method in Random K-Satisfiability Problem
Ma Hui

2. Random K-Satisfiability Problem

3. Structure of Solution Space changes as the constraint density increases

4. 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

5. From SAT to Max-SAT

6. 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

7. The Threshold Temperature: Td &Trs

8. 1RSB scenario

9. 1RSB Stability Analysis
Two kinds of Stability
1. Iteration Stability
2.Stability to Bug proliferation

10. The Sample figure for Bug Proliferation

11. Thanks