# One-step replica symmetry breaking of random regular NAE-SAT

@article{Nam2022OnestepRS, title={One-step replica symmetry breaking of random regular NAE-SAT}, author={Danny Nam and Allan Sly and Youngtak Sohn}, journal={2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)}, year={2022}, pages={310-318} }

In a broad class of sparse random constraint satisfaction problems (CSP), deep heuristics from statistical physics predict that there is a condensation phase transition before the satisfiability threshold, governed by one-step replica symmetry breaking (1RSB). In fact, in random regular k-NAE-SAT, which is one of such random CSPS, it was verified [1] that its free energy is well-defined and the explicit value follows the 1RSB prediction. However, for any model of sparse random CSP, it has been…

## 3 Citations

### Fast sampling of satisfying assignments from random k-SAT

- Mathematics, Computer ScienceArXiv
- 2022

A novel approach to bound the sum of inﬂuences in the k -SAT model which turns out to be robust against the presence of high-degree variables and allows for fast mixing results of a uniform-block Glauber dynamics on a carefully selected subset of the variables.

### The Algorithmic Phase Transition of Random k-SAT for Low Degree Polynomials

- Computer Science2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)
- 2022

It is proved that the class of low degree polynomial algorithms cannot find a satisfying assignment at clause density within a constant factor of that achieved by Fix, the first hardness result for any class of algorithms at clause densities within a constants factor.

### Free Energy Subadditivity for Symmetric Random Hamiltonians

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We consider a random Hamiltonian H : Σ → R deﬁned on a compact space Σ that admits a transitive action by a compact group G . When the law of H is G -invariant, we show its expected free energy…

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