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

Guangyan Zhou () and Zongsheng Gao
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Guangyan Zhou: Beijing Technology and Business University
Zongsheng Gao: Beihang University

Journal of Combinatorial Optimization, 2018, vol. 35, issue 4, No 15, 1286-1299

Abstract: 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.

Keywords: Maximum satisfiability; The second moment method; Weighting scheme (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-018-0267-9

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