GRASP: a search algorithm for propositional satisfiability

Abstract

AbstractÐThis 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 ªrecordingº 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.

QBF Reasoning on Real-World Instances

“…With learning as introduced for QBFs by [10], the reasons computed may be stored as constraints to avoid repeating the same search. In particular, although learning did not emerge from the QBF evaluation as an all-time winner [8], its effectiveness on real-world test cases is a consolidated result in the SAT literature (see, e.g., [11,14,12]), and positive results have been reported also for QBF reasoning (see, e.g., [10,15]). …”

“…Once QUBE++ has learned the constraint, it backjumps to the node at the maximum decision level among the literals in the reason, excluding l. We say that l is a Unique Implication Point (UIP) and therefore the lookback in QUBE++ is UIP-based. Notice that our definition of UIP generalizes to QBF the concepts first described by [11] and used in the SAT solver GRASP. On a SAT instance, QUBE++ lookback scheme behaves similarly to the "1-UIP-learning" scheme used in ZCHAFF and described in [16].…”

“…The techniques are: (i) efficient detection of unit and monotone literals using lazy data structures as in [9]; (ii) learning, as introduced in [10], with improvements that generalize the techniques first used in SAT by GRASP [11]; (iii) a branching strategy that exploits information gleaned from the input formula initially, and leverages the information extracted in the learning phase. Using formal verification and planning benchmarks from the QBF evaluation [8], we conducted an experimental campaign to highlight the relative efficiency of the above techniques, and of their combination: the results show that each single technique contributes to the effectiveness of QUBE++ and that the resulting system is a clear improvement over current state-of-the-art QBF solvers.…”

Zchaff2004: An Efficient SAT Solver

“…1 The solver decision level is updated appropriately after the backtrack. The reader is referred to [27,28] for details of conflict analysis. The solver enters decision level 0 only when making an assignment that is implied by the CNF formula and a backtrack to level 0 indicates that some variable is implied by the CNF formula to be both true and false i.e.…”

“…Conflict driven clause learning along with non-chronological backtracking were first incorporated into a SAT solver in GRASP [27] and relsat [15]. These techniques are essential for efficient solving of structured problems.…”