This paper introduces GRASP (Generic seaRch Algorithm for the Satisjiability Problem), an integrated algorithmic framework for SAT that un.$es several previously proposed searchpruning techniques and facilitates ident$cation of additional ones. GRASP is premised on the inevitability of confzicts during search and its most distinguishing feature is the augmentation of basic backtracking search with a powerfil confzict analysis procedure. Analyzing confzicts to determine their cawes enables GRASP to backtrack non-chronologically 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 andpreempt the occurrence of similar conficts later on in the search. Finally, straightjwward bookkeeping of the causality chains leading up to conflicts allows GRASP to identifi assignments that are necessary for a solution to be found. fiperimental results obtained from a large number of benchmarks, including many from the $eld of test pattern generation, indicate that application of the proposed confzict analysis techniques to SATalgorithm can be extremely effectivefor a large number of representative classes of SAT instances. 1

This paper introduces GRASP (Generic seaRch Algorithm for the Sati$ability Problem), a new search algorithm for Propositional Satisjability (SAT). GRASP incorporates several search-pruning techniques, some of which are spec$c to SAT whereas others find equivalent in other fieh ofArt$cial Intelligence. GRASP is premised on the inevitability of conflicts during search and its most distinguishing feature is the augmentation of basic backtracking search with a

This paper presents the multi-valued SAT solver CAMA. CAMA generalizes the recently developed speed-up techniques used in state-of-the-art binary SAT solvers, such as the two-literalwatching scheme for Boolean constraint propagation (BCP), conflict-based learning with identifying the first unique implication point (UIP), and non-chronological back-tracking. In addition, a novel minimum value set (MVS) technique is introduced for improving the efficiency of conflict-based learning. By analyzing the conflict clauses, MVS can potentially prune conflicting space that has not been searched before. Two different decision heuristics are discussed and evaluated. Finally the performance of CAMA is compared with Chaff using on a one-hot-encoding scheme. The experimental results show that, for MV-SAT problems with large variable domains, CAMA outperforms Chaff. 1

Recursive Learning (RL) is a circuit-structure-based method for computing all necessary assignments. Recursive learning technique can be combined with different CAD algorithms and techniques in testing, verification and optimization. In particular, it is used for Automatic test pattern generation(ATPG) which has been applied to many areas of logic synthesis and formal verification including combinational verification and logic minimization. Satisfiability (SAT)-based-ATPG is one of the most efficient algorithms in testing. In this project, we investigate applying recursive learning to the SAT-based-ATPG. We then use the revised the SAT-based-ATPG for combinational logic verification. The SAT-based-ATPG with global implication heuristics (iterated global implications) is very efficient and it does not seem to leave much room for improvement. However, our preliminary results show that adding recursive learning information does speed up the SAT-base-ATPG for combinational logic verification. 1

An algorithmic procedure for computing the minimum number of test patterns in automatic test pattern generation can have important theoretical and practical consequences. Existing solutions for solving this problem require the simultaneous consideration of all test patterns for all faults in a circuit. In this paper we describe integer linear program (ILP) formulations for computing the minimum number of tests, with the objective of providing new insights on potential approaches for solving this problem. The proposed ILP formulations can be represented in polynomial space, in contrast with existing solutions which have worst-case exponential-size representations. Furthermore, we describe several techniques for reducing the size of the proposed ILP formulations. These techniques include, for example, identification of fault independence relations and removal of redundant faults by preprocessing.