In this article we describe and evaluate optimized compact data structures for watching literals. Experiments with our SAT solver PicoSAT show that this low-level optimization not only saves memory, but also turns out to speed up the SAT solver considerably. We also discuss how to store proof traces compactly in memory and further unique features of PicoSAT including an aggressive restart schedule. Keywords: SAT solver, watched literals, occurrence lists, proof traces, restarts

In order to facilitate automated reasoning about large Boolean combinations of nonlinear arithmetic constraints involving transcendental functions, we provide a tight integration of recent SAT solving techniques with interval-based arithmetic constraint solving. Our approach deviates substantially from lazy theorem proving approaches in that it directly controls arithmetic constraint propagation from the SAT solver rather than delegating arithmetic decisions to a subordinate solver. Through this tight integration, all the algorithmic enhancements that were instrumental to the enormous performance gains recently achieved in propositional SAT solving carry over smoothly to the rich domain of non-linear arithmetic constraints. As a consequence, our approach is able to handle large constraint systems with extremely complex Boolean structure, involving Boolean combinations of multiple thousand arithmetic constraints over some thousands of variables.

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

Conflict driven clause learning, one of the most important component of modern SAT solvers, is also recognized as very important in parallel SAT solving. Indeed, it allows clause sharing between multiple processing units working on related (sub-)problems. However, without limitation, sharing clauses might lead to an exponential blow up in communication or to the sharing of irrelevant clauses. This paper, proposes two innovative policies to dynamically adjust the size of shared clauses between any pair of processing units. The first approach controls the overall number of exchanged clauses whereas the second additionally exploits the relevance quality of shared clauses. Experimental results show important improvements of the state-of the-art parallel SAT solver.

This article describes PaMiraXT, a powerful parallel SAT algorithm. PaMiraXT follows a master/client model based on message passing, making it suitable for any kind of workstation cluster. For the clients, MiraXT is used, which itself is thread-based parallel solver designed to take advantage of current and future shared memory multiprocessor systems. We highlight design and implementation details that allow the threads/clients to run and cooperate efficiently. Experimental results show that MiraXT compares well to other state-of-the-art SAT algorithms. In single-threaded mode, it outperforms MiniSat2, PicoSAT 535, and RSat 2.01, while in multi-threaded mode, MiraXT provides cutting edge performance, as it solves significantly more instances within the given time limit. A case study, using three copies of MiraXT with a total of 8 threads as clients, underlines the potential of PaMiraXT, resulting in a speedup of 5.62 on the industrial benchmarks of the 2007 SAT competition. Keywords:

Abstract. This paper presents the concept of parallelisation of a solver for Answer Set Programming (ASP). While there already exist some approaches to parallel ASP solving, there was a lack of a parallel version of the powerful clasp solver. We implemented a parallel version of clasp based on message-passing. Experimental results on Blue Gene P/L indicate the potential of such an approach.

Abstract. In this paper, we explore the two well-known principles of diversification and intensification in portfolio-based parallel SAT solving. These dual concepts play an important role in several search algorithms including local search, and appear to be a key point in modern parallel SAT solvers. To study their tradeoff, we define two roles for the computational units. Some of them classified as Masters perform an original search strategy, ensuring diversification. The remaining units, classified as Slaves are there to intensify their master’s strategy. Several important questions have to be answered. The first one is what information should be given to a slave in order to intensify a given search effort? The second one is, how often, a subordinated unit has to receive such information? Finally, the question of finding the number of subordinated units and their connections with the search efforts has to be answered. Our results lead to an original intensification strategy which outperforms the best parallel SAT solver ManySAT, and solves some open SAT instances.

Intractability of the problem no longer daunting � Can regularly handle practical instances with millions of variables and constraints SAT has matured from theoretical interest to practical impact

Current SAT solvers are well engineered and highly efficient, and significant research effort has been put into creating data structures that can produce maximal efficiency for the core propagation engine within SAT solvers. However, there is still substantial room for improvement. As the disparity between CPU speeds and cache sizes have increased, cache conscious data structures and algorithms have become very important. They are even more important in the context of parallel SAT solving, as issues like cache contention and main memory contention can dramatically slow down a parallel SAT solver. We present a series of data structure and algorithmic modifications that are able to increase the core propagation speed of MiniSat 2.0 by an average of 80 % on a set of medium sized industrial instances, and increase the speed of a parallelized version of MiniSat running with 8 threads by 140 % on those same instances. Keywords: Boolean satisfiability, cache-aware data structures