On the K‐sat model with large number of clauses

We show that in the K‐sat model with N variables and αN clauses, the expected ratio of the smallest number of unsatisfied clauses to the number of variables is α/2K−αc∗(N)/2K up to smaller order terms o(α) as α→∞ uniformly in N, where c∗(N) is the expected normalized maximum energy of some specific...

Full description

Saved in:
Bibliographic Details
Published inRandom structures & algorithms Vol. 52; no. 3; pp. 536 - 542
Main Author Panchenko, Dmitry
Format Journal Article
LanguageEnglish
Published Hoboken Wiley Subscription Services, Inc 01.05.2018
Subjects
K‐sat model
Mathematical models
p‐spin models
Spin glasses
Online AccessGet full text

Cover

More Information
Summary:We show that in the K‐sat model with N variables and αN clauses, the expected ratio of the smallest number of unsatisfied clauses to the number of variables is α/2K−αc∗(N)/2K up to smaller order terms o(α) as α→∞ uniformly in N, where c∗(N) is the expected normalized maximum energy of some specific mixed p‐spin spin glass model. The formula for the limit of c∗(N) is well known in the theory of spin glasses.
Bibliography:Funding information
NSERC (to D.P)
ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.20748