Journal of Combinatorial Optimization

, Volume 35, Issue 4, pp 1286–1299 | Cite as

On the lower bounds of random Max 3 and 4-SAT



A k-CNF formula is said to be p-satisfiable if there exists a truth assignment satisfying a fraction of \(1-2^{-k}+p2^{-k}\) of its clauses. We obtain better lower bounds for random 3 and 4-SAT to be p-satisfiable. The technique we use is a delicate weighting scheme of the second moment method, where for every clause we give appropriate weight to truth assignments according to their number of satisfied literal occurrences.


Maximum satisfiability The second moment method Weighting scheme 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsBeijing Technology and Business UniversityBeijingChina
  2. 2.School of Mathematics and Systems ScienceBeihang UniversityBeijingChina

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