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.

Much research in the area of constraint processing has recently been focused on extracting small unsatisfiable "cores" from unsatisfiable constraint systems with the goal of finding minimal unsatisfiable subsets (MUSes). While most techniques have provided ways to find an approximation of an MUS (not necessarily minimal), we have developed a sound and complete algorithm for producing all MUSes of an unsatisfiable constraint system. In this paper, we describe a relationship between satisfiable and unsatisfiable subsets of constraints that we subsequently use as the foundation for MUS extraction algorithms, implemented for Boolean satisfiability constraints. The algorithms provide a framework with which many related subproblems can be solved, including relaxations of completeness to handle intractable instances, and we develop several variations of the basic algorithms to illustrate this. Experimental results demonstrate the performance of our algorithms, showing how the base algorithms run quickly on many instances, while the variations are valuable for producing results on instances whose complete results are intractably large. Furthermore, our algorithms are shown to perform better than the existing algorithms for solving either of the two distinct phases of our approach.

This paper introduces GRASP (Generic seaRch

Instances of the Boolean satisfiability problem (SAT) arise in many areas of circuit design and verification. These instances are typically constructed from some human-designed artifact, and thus are likely to possess much inherent symmetry and sparsity. Previous work [4] has shown that exploiting symmetries results in vastly reduced SAT solver run times, often with the search for the symmetries themselves dominating the total SAT solving time. Our contribution is twofold. First, we dissect the algorithms behind the venerable nauty [9] package, particularly the partition refinement procedure responsible for the majority of search space pruning as well as the majority of run time overhead. Second, we present a new symmetry-detection tool, saucy, which outperforms nauty by several orders of magnitude on the large, structured CNF formulas generated from typical EDA problems.

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