Satisfiability Threshold for Random Regular nae-sat
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220_2015_2492_ReferencePDF.pdf
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8.64 MB
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Author(s)
Ding, Jian
Sly, Allan
Sun, Nike
Date Issued
November 2015
Journal
Communications in Mathematical Physics
Publisher
Springer-Verlag
Citation
Ding, Jian, Allan Sly, and Nike Sun. “Satisfiability Threshold for Random Regular Nae-Sat.” Communications in Mathematical Physics 341, no. 2 (November 26, 2015): 435–489. © 2015 Springer-Verlag
Version
Author's final manuscript
Abstract
We consider the random regular k-nae- sat problem with n variables, each appearing in exactly d clauses. For all k exceeding an absolute constant k[subscript 0] , we establish explicitly the satisfiability threshold d⋆≡d⋆(k). We prove that for dd⋆ the problem is unsatisfiable with high probability. If the threshold d⋆ lands exactly on an integer, we show that the problem is satisfiable with probability bounded away from both zero and one. This is the first result to locate the exact satisfiability threshold in a random constraint satisfaction problem exhibiting the condensation phenomenon identified by Krz̧akała et al. [Proc Natl Acad Sci 104(25):10318–10323, 2007]. Our proof verifies the one-step replica symmetry breaking formalism for this model. We expect our methods to be applicable to a broad range of random constraint satisfaction problems and combinatorial problems on random graphs.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00220-015-2492-8
