The satisfiability threshold and solution geometry of random linear - - PowerPoint PPT Presentation

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Mar 30, 2023 20 likes •135 views

The satisfiability threshold and solution geometry of random linear equations over finite fields Jane Gao (jane.gao@monash.edu) School of Mathematical Sciences Examples k-SAT k-NAESAT k-XORSAT k-colouring of graphs

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The satisfiability threshold and solution geometry of random linear equations over finite fields

Jane Gao

(jane.gao@monash.edu)

School of Mathematical Sciences

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Examples

k-SAT
k-NAESAT
k-XORSAT
k-colouring of graphs
2-colouring of k-uniform hyper graphs
Potts model
Ising model (ferromagnetic, antiferromagnetic)
graph matching (monomer-dimer model)
independent set (hard core model)
SK model
mixed p-spin model

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‹#› K-SAT threshold

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Main challenge: large deviation

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[Krzakala, Montanari, Ricci-Tersenghi, Semerjian, Zdeborova 2007]

Phase transitions of the solution geometry

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Lottery effect kills the second moment method

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Replica symmetry (correlation decay)

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Solution clusters

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