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Spin Glass Cavity Method in Random K-Satisfiability Problem

Study on structure changes in solution space with constraint density increase. Investigates communities of solutions in single solution clusters of a Random K-Satisfiability problem using the Spin Glass Cavity Method. Analyzes Replica Symmetry Equations for stability and explores Threshold Temperature in the 1RSB scenario.

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Spin Glass Cavity Method in Random K-Satisfiability Problem

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

  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

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