Finding almost-satisfying assignments

Abstract

There are only three non-trivial classes of conjunctive Boolean formula or constraint satisfaction problems for which satisfiability can be decided in polynomial time. These three classes are LIN, 2-SAT and HORN-SAT. The 2-SAT and HORN-SAT are essentially, the non-trivial classes of formula for which almost-satisfying assignments can be found in polynomial time (assuming P≠NP).