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

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Abstract

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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Beijing Technology and Business University, Beijing, 100048, China

    Guangyan Zhou

  2. School of Mathematics and Systems Science, Beihang University, Beijing, 100191, China

    Zongsheng Gao

Authors
  1. Guangyan Zhou
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  2. Zongsheng Gao
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Corresponding author

Correspondence to Guangyan Zhou.

Additional information

Research supported by National Natural Science Fund of China (Grant Nos. 11626039, 61702019), Beijing committee project of talented youth (2016000020124G028).

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Zhou, G., Gao, Z. On the lower bounds of random Max 3 and 4-SAT. J Comb Optim 35, 1286–1299 (2018). https://doi.org/10.1007/s10878-018-0267-9

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  • DOI: https://doi.org/10.1007/s10878-018-0267-9

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