Look-ahead versus look-back for satisfiability problems

Abstract

CNF propositional satisfiability (SAT) is a special kind of the more general Constraint Satisfaction Problem (CSP). While lookback techniques appear to be of little use to solve hard random SAT problems, it is supposed that they are necessary to solve hard structured SAT problems. In this paper, we propose a very simple DPL procedure called Satz which only employs some look-ahead techniques: a variable ordering heuristic, a forward consistency checking (Unit Propagation) and a limited resolution before the search, where the heuristic is itself based on unit propagation. Satz is favorably compared on random 3-SAT problems with three DPL procedures among the best in the literature for these problems. Furthermore on a great number of problems in 4 well known SAT benchmarks Satz reaches or outspeeds the performance of three other DPL procedures among the best in the literature for structured SAT problems. The comparative results suggest that a suitable exploitation of look-ahead techniques, while very simple and efficient for random SAT problems, may allow to do without sophisticated look-back techniques in a DPL procedure.