The number of solutions for random regular NAE-SAT
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440_2021_1029_ReferencePDF.pdf
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1.28 MB
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a32445975f442baca8ffccf06666d78e
Author(s)
Sly, Allan
Sun, Nike
Zhang, Yumeng
Date Issued
November 20, 2021
Publisher
Springer Berlin Heidelberg
Citation
Sly, Allan, Sun, Nike and Zhang, Yumeng. 2021. "The number of solutions for random regular NAE-SAT."
Version
Author's final manuscript
Abstract
Abstract
Recent work has made substantial progress in understanding the transitions of random constraint satisfaction problems. In particular, for several of these models, the exact satisfiability threshold has been rigorously determined, confirming predictions of statistical physics. Here we revisit one of these models, random regular k-nae-sat: knowing the satisfiability threshold, it is natural to study, in the satisfiable regime, the number of solutions in a typical instance. We prove here that these solutions have a well-defined free energy (limiting exponential growth rate), with explicit value matching the one-step replica symmetry breaking prediction. The proof develops new techniques for analyzing a certain “survey propagation model” associated to this problem. We believe that these methods may be applicable in a wide class of related problems.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00440-021-01029-5
