... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400-variable 3-SAT problems in about 2 hours on the average. In general, it can solve hard n-variable random 3-SAT problems with search trees of size O(2 n=18:7 ). In addition to justifying these claims, this dissertation describes the most significant achievements of other researchers in this area, and discusses all of the widely known general techniques for speeding up SAT search algorithms. It should be useful to anyone interested in NP-complete problems or combinatorial optimization in general, and it should be particularly useful to researchers in either Artificial Intelligence or Operations Research.

. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computer-aided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...

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In this paper, we present PQSOLVE, a distributed theorem-prover for Quantified Boolean Formulae. First, we introduce our sequential algorithm QSOLVE, which uses new heuristics and improves the use of known heuristics to prune the search tree. As a result, QSOLVE is more efficient than the QSAT-solvers previously known. We have parallelized QSOLVE. The resulting distributed QSAT-solver PQSOLVE uses parallel search techniques, which we have developed for distributed game tree search. PQSOLVE runs efficiently on distributed systems, i. e. parallel systems without any shared memory. We briefly present experiments that show a speedup of about 114 on 128 processors. To the best of our knowledge we are the first to introduce an efficient parallel QSAT-solver.

We address the parallelization and distributed execution of an algorithm from the area of symbolic computation: propositional satisfiability (SAT) checking with dynamic learning. Our parallel programming models are strict multithreading for the core SAT checking procedure, complemented by mobile agents realizing a distributed dynamic learning process. Individual threads treat dynamically created subproblems, while mobile agents collect and distribute pertinent knowledge obtained during the learning process. The parallel algorithm runs on top of our parallel system platform DOTS (Distributed Object-Oriented Threads System), which provides support for our parallel programming models in highly heterogeneous distributed systems. We present performance measurements evaluating the performance gains by our approach in different application domains with practical significance. Key words: parallel symbolic computation, parallel propositional satisfiability checking, distributed multithreading 1

This thesis describes the design and implementation of a highly optimized, multithreaded algorithm for the propositional satisfiability problem. The algorithm is based on the Davis-Logemann-Loveland sequential algorithm, but includes many of the optimization techniques introduced in recent years. The document provides experimental results for the execution of the parallel algorithm on a variety of multiprocessor machines with shared memory architecture. In particular, the overwhelming e#ect of parallel execution on the performance of processor cache is studied.

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The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worst-case exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and hardware verification [29–31, 228], automatic test pattern generation [138, 221], planning [129, 197], scheduling [103], and even challenging problems from algebra [238]. Annual SAT competitions have led to the development of dozens of clever implementations of such solvers [e.g. 13,

It is shown how a large class of applications can be parallelized by modeling them as tree shaped computations. In particular this class contains many highly irregular and completely unpredictable computations as they occur in heuristic search.

In this paper, ManySAT a new portfolio-based parallel SAT solver is thoroughly described. The design of ManySAT benefits from the main weaknesses of modern SAT solvers: their sensitivity to parameter tuning and their lack of robustness. ManySAT uses a portfolio of complementary sequential algorithms obtained through careful variations of the standard DPLL algorithm. Additionally, each sequential algorithm shares clauses to improve the overall performance of the whole system. This contrasts with most of the parallel SAT solvers generally designed using the divide-and-conquer paradigm. Experiments on many industrial SAT instances, and the first rank obtained by ManySAT in the parallel track of the 2008 SAT-Race clearly show the potential of our design philosophy. Keywords: parallel search, dynamic restarts, extended clause learning