GRASP: a search algorithm for propositional satisfiability

TLDR

GRASP incorporates several powerful search‑pruning techniques, some specific to SAT and others similar to approaches in other AI fields, that have proven effective across a wide variety of SAT problems. This paper introduces GRASP, a new search algorithm for propositional satisfiability. GRASP augments basic backtracking with a conflict‑analysis procedure that enables nonchronological backtracking, preempts similar conflicts by recording causes, and identifies necessary assignments through bookkeeping of causality chains. Experimental results from many benchmarks indicate that applying the proposed conflict‑analysis techniques to SAT algorithms can be extremely effective for a large number of representative classes of SAT instances.

Abstract

This paper introduces GRASP (Generic seaRch Algorithm for the Satisfiability Problem), a new search algorithm for Propositional Satisfiability (SAT). GRASP incorporates several search-pruning techniques that proved to be quite powerful on a wide variety of SAT problems. Some of these techniques are specific to SAT, whereas others are similar in spirit to approaches in other fields of Artificial Intelligence. GRASP is premised on the inevitability of conflicts during the search and its most distinguishing feature is the augmentation of basic backtracking search with a powerful conflict analysis procedure. Analyzing conflicts to determine their causes enables GRASP to backtrack nonchronologically to earlier levels in the search tree, potentially pruning large portions of the search space. In addition, by "recording" the causes of conflicts, GRASP can recognize and preempt the occurrence of similar conflicts later on in the search. Finally, straightforward bookkeeping of the causality chains leading up to conflicts allows GRASP to identify assignments that are necessary for a solution to be found. Experimental results obtained from a large number of benchmarks indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely effective for a large number of representative classes of SAT instances.