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

Author

Listed:
  • Guangyan Zhou

    (Beijing Technology and Business University)

  • Zongsheng Gao

    (Beihang University)

Abstract

A k-CNF formula is said to be p-satisfiable if there exists a truth assignment satisfying a fraction of $$1-2^{-k}+p2^{-k}$$ 1 - 2 - k + p 2 - 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.

Suggested Citation

  • Guangyan Zhou & Zongsheng Gao, 2018. "On the lower bounds of random Max 3 and 4-SAT," Journal of Combinatorial Optimization, Springer, vol. 35(4), pages 1286-1299, May.
    • Handle: RePEc:spr:jcomop:v:35:y:2018:i:4:d:10.1007_s10878-018-0267-9
    DOI: 10.1007/s10878-018-0267-9
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    References listed on IDEAS

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    1. Brian Borchers & Judith Furman, 1998. "A Two-Phase Exact Algorithm for MAX-SAT and Weighted MAX-SAT Problems," Journal of Combinatorial Optimization, Springer, vol. 2(4), pages 299-306, December.
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