an:07048093
Zbl 07048093
Zhou, Guangyan
On the lower bounds of random MAX 3 and 4-SAT
EN
Zhu, Daming (ed.) et al., Frontiers in algorithmics. 10th international workshop, FAW 2016, Qingdao, China, June 30 -- July 2, 2016. Proceedings. Cham: Springer (ISBN 978-3-319-39816-7/pbk; 978-3-319-39817-4/ebook). Lecture Notes in Computer Science 9711, 269-278 (2016).
2016
a
68Wxx
maximum satisfiability; the second moment method; weighting scheme
Summary: 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.
For the entire collection see [Zbl 1407.68047].