HypBinRes, a particular form of hyper-resolution, was first employed in the SAT solver 2CLS+EQ. In 2CLS+EQ, HypBinRes and equality reduction are used at every node of a DPLL search tree, pruning much of the search tree.

Boolean satisfiability (SAT) is NP-complete. No known algorithm for SAT is of polynomial time complexity. Yet, many of the SAT instances generated as a means of solving real-world electronic design automation problems are simple enough, structurally, that modern solvers can decide them efficiently. Consequently, SAT solvers are widely used in industry for logic verification. The most robust solver algorithms are poorly understood and only vaguely described in the literature of the field. We refine these algorithms, and present them clearly. We introduce several new techniques for Boolean constraint propagation that substantially improve solver efficiency. We explain why literal count decision strategies succeed, and on that basis, we introduce a new decision strategy that outperforms the state of the art. The culmination of this work is the most powerful SAT solver publically available.

Abstract. In 1997 we presented ten challenges for research on satisfiability testing [1]. In this paper we review recent progress towards each of these challenges, including our own work on the power of clause learning and randomized restart policies. 1

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Abstract—By adapting to computations that are not so well-supported by general-purpose processors, reconfigurable systems achieve significant increases in performance. Such computational systems use high-capacity programmable logic devices and are based on processing units customized to the requirements of a particular application. A great deal of the research effort in this area is aimed at accelerating the solution of combinatorial optimization problems. Special attention in this context was given to the Boolean satisfiability (SAT) problem resulting in a considerable number of different architectures being proposed. This paper presents the stateof-the-art in reconfigurable hardware SAT satisfiers. The analysis and classification of existing systems has been performed according to such criteria as algorithmic issues, reconfiguration modes, the execution model, the programming model, logic capacity, and performance. Index Terms—Boolean satisfiability, reconfigurable computing, FPGA, hardware acceleration. 1

Abstract. Structural logical formulas sometimes yield a substantial fraction of so called equivalence clauses after translation to CNF. Probably the best known example of this is the parity-family. Large instances of such CNF formulas cannot be solved in reasonable time if no detection of, and extra reasoning with, these clauses is incorporated. That is, in solving these formulas, there is a more or less separate algorithmic device dealing with the equivalence clauses, called equivalence reasoning, and another dealing with the remaining clauses. In this paper we propose a way to align these two reasoning devices by introducing parameters for which we establish optimal values over a variety of existing benchmarks. We obtain a truly convincing speed-up in solving such formulas with respect to the best solving methods existing so far. 1

competitions In 2005 there were numerous “competitive events ” in the area of automated reasoning (in the broad sense): The Tenth CASC competition[23], the First Satisfiability Modulo Theory Competition[3], the First CSP competition, the Fourth SAT competition, the Third QBF evaluation and the First Pseudo Boolean evaluation, etc. Starting such an event is suitable for promoting a common input format and to build a repository of benchmarks in that format: this was the motivation behind the SMT and CSP competitions and the PB evaluation. The First QBF evaluation was also organized two years ago in that spirit and the renewal since then allowed to impose the QDimacs input format and to increase both the number of solvers and benchmarks available each year. More mature events, such as the CASC competitions, are a bit different: both the pool of benchmarks (TPTP) and the pool of solvers are quite stable and the competitions allow to track the progress of new versions of those solvers on a well studied set of benchmarks. The SAT competitions are again different: the first SAT competition is older than

Abstract An encoding for bounded model checking!-regular properties ispresented. It uses weak alternating parity automata as the specification model for such properties. 1 Introduction Bounded model checking [1] is an automatic verification technique for linear time properties that is successfully employed in industrial settings [2]. Since only paths of a given length through a transition system are considered, it is not complete but an approximation method, relying on the fact that unsatisfied formulas often have short counterexamples. It is known from BDD-based symbolic model checking [3] that transition systems can be encoded as boolean functions, and that these encodings can be significantly smaller than explicit representations. This, together with the boundedness and the fact that models are linear structures make the problem suitable for a reduction to SAT-- the satisfiability problem for propositional logic. This way, advantage is taken of the immense progress made in the area of satisfiability solving in recent years [9].

We introduce the march dl satisfiability (SAT) solver, a successor of march eq. The latter was awarded state-of-the-art in two categories during the Sat 2004 competition. The focus lies on presenting those features that are new in march dl. Besides a description, each of these features is illustrated with some experimental results. By extending the preprocessor, using adaptive heuristics, and by using a new branching strategy, march dl is able to solve nearly all benchmarks faster than its predecessor. Moreover, various instances which were beyond the reach of march eq, can now be solved- relatively easily- due to these new features.

This paper presents GASAT, a hybrid algorithm for the satisfiability problem (SAT). The main feature of GASAT is that it includes a recombination stage based on a specific crossover and a tabu search stage. We have conducted experiments to evaluate the different components of GASAT and to compare its overall performance with state-ofthe-art SAT algorithms. These experiments show that GASAT provides very competitive results.