A NN Algorithm for Hard Satisfiability Problems†

Satisfiability (SAT) refers to the task of finding a truth assignment that makes an arbitrary boolean expression true. For example, the boolean expression a & b is true iff the boolean variables a and b are true. Satisfiability is of interest to the logic, operations research, and computational complexity communities. Due to the emphasis of the logic community, traditional satisfiability algorithms tend to be sound and complete. However, Selman et al. (1992) point out that there exists a class of satisfiability problems that are extremely hard for these algorithms. Their response has been to create a greedy algorithm (GSAT) that is sound, yet incomplete (i.e., there is no guarantee that GSAT will find a satisfying assignment if one exists). The advantage of GSAT is that it can often solve problems that are extremely difficult for the traditional algorithms.