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Sponsored Artificial Intelligence: A Modern Approach, Global Edition Artificial Intelligence: A Modern Approach, Global Edition

Author

Jeff Xu

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Preprint Sep 2026

Certifiable Near-Optimality: A Simple Framework for Unifying Search and Refutation for (Semi)random CSPs

A classical problem in average-case complexity is the study of random constraint satisfaction problems (CSPs). Random CSPs are traditionally studied in two different settings: refutation, where the instances are uniformly random and thus unsatisfiable with high probability, and search, where the instances are drawn fro...

Prashanti Anderson, Peter Manohar, Jeff Xu · 0 citations
Preprint Sep 2026

Sharp Lovasz-Theta Bounds on Random Graphs

It is well known that the \Lovasz-Theta function of a random graph $G(n,\tfrac{1}{2})$ is $\Theta(\sqrt{n})$. More precisely, it is tightly concentrated in the interval \( [\sqrt{n},\, 2\sqrt{n}], \) where the upper bound follows from an explicit dual witness for the associated semidefinite program. Numerical evidence...

Aaron Potechin, Jeff Xu · 0 citations

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