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On the Lower Bounds of Random Max 3 and 4-SAT

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Frontiers in Algorithmics (FAW 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9711))

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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.

Partially supported by NSFC 11301091.

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Authors and Affiliations

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

    Guangyan Zhou

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  1. Guangyan Zhou
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Correspondence to Guangyan Zhou .

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Editors and Affiliations

  1. Shandong University, Jinan, China

    Daming Zhu

  2. MS EC-31, University of Texas at Dallas, Richardson, Texas, USA

    Sergey Bereg

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© 2016 Springer International Publishing Switzerland

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Zhou, G. (2016). On the Lower Bounds of Random Max 3 and 4-SAT. In: Zhu, D., Bereg, S. (eds) Frontiers in Algorithmics. FAW 2016. Lecture Notes in Computer Science(), vol 9711. Springer, Cham. https://doi.org/10.1007/978-3-319-39817-4_26

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  • DOI: https://doi.org/10.1007/978-3-319-39817-4_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-39816-7

  • Online ISBN: 978-3-319-39817-4

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