On the possibility of faster SAT algorithms [chapter]

Mihai Pătraşcu, Ryan Williams
2010 Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms  
We describe reductions from the problem of determining the satisfiability of Boolean CNF formulas (CNF-SAT) to several natural algorithmic problems. We show that attaining any of the following bounds would improve the state of the art in algorithms for SAT: • an O(n k−ε ) algorithm for k-Dominating Set, for any k ≥ 3, • a (computationally efficient) protocol for 3-party set disjointness with o(m) bits of communication, • an n o(d) algorithm for d-SUM, • an O(n 2−ε ) algorithm for 2-SAT with m =
more » ... n 1+o(1) clauses, where two clauses may have unrestricted length, and • an O((n + m) k−ε ) algorithm for HornSat with k unrestricted length clauses. One may interpret our reductions as new attacks on the complexity of SAT, or sharp lower bounds conditional on exponential hardness of SAT.
doi:10.1137/1.9781611973075.86 dblp:conf/soda/PatrascuW10 fatcat:lomltgvirfahxo34h25wbqatkq