In Proceedings of the 12th NASA formal methods symposium (NFM’20)
In the context of parallel SATisfiability solving, this paper presents an implementation and evaluation of a clause strengthening algorithm. The developed component can be easily combined with (virtually) any CDCL-like SAT solver. Our implementation is integrated as a part of Painless, a generic and modular framework for building parallel SAT solvers.
In Proceedings of the 23rd international conference on theory and applications of satisfiability testing (SAT’20)
Modern parallel SAT solvers rely heavily on effective clause sharing policies for their performance. The core problem being addressed by these policies can be succinctly stated as “the problem of identifying high-quality learnt clauses” that when shared between the worker nodes of parallel solvers results in improved performance than otherwise. The term “high-quality clauses” is often defined in terms of metrics that solver designers have identified over years of empirical study. Some of the more well-known metrics to identify high-quality clauses for sharing include clause length, literal block distance (LBD), and clause usage in propagation. In this paper, we propose a new metric aimed at identifying high-quality learnt clauses and a concomitant clause-sharing policy based on a combination of LBD and community structure of Boolean formulas. The concept of community structure has been proposed as a possible explanation for the extraordinary performance of SAT solvers in industrial instances. Hence, it is a natural candidate as a basis for a metric to identify high-quality clauses. To be more precise, our metric identifies clauses that have low LBD and low community number as ones that are high-quality for applications such as verification and testing. The community number of a clause C measures the number of different communities of a formula that the variables in C span. We perform extensive empirical analysis of our metric and clause-sharing policy, and show that our method significantly outperforms state-of-the-art techniques on the benchmark from the parallel track of the last four SAT competitions.
In Proceedings of the 25th international conference on tools and algorithms for the construction and analysis of systems (TACAS’19)
Over the last decade, parallel SATisfiability solving has been widely studied from both theoretical and practical aspects. There are two main approaches. First, divide-and-conquer (D&C) splits the search space, each solver being in charge of a particular subspace. The second one, portfolio launches multiple solvers in parallel, and the first to find a solution ends the computation. However although D&C based approaches seem to be the natural way to work in parallel, portfolio ones experimentally provide better performances. An explanation resides on the difficulties to use the native formulation of the SAT problem (i.e., the CNF form) to compute an a priori good search space partitioning (i.e., all parallel solvers process their subspaces in comparable computational time). To avoid this, dynamic load balancing of the search subspaces is implemented. Unfortunately, this is difficult to compare load balancing strategies since state-of-the-art SAT solvers appropriately dealing with these aspects are hardly adaptable to various strategies than the ones they have been designed for. This paper aims at providing a way to overcome this problem by proposing an implementation and evaluation of different types of divide-and- conquer inspired from the literature. These are relying on the Painless framework, which provides concurrent facilities to elaborate such parallel SAT solvers. Comparison of the various strategies are then discussed.
In Proceedings of the 20th international conference on theory and applications of satisfiability testing (SAT’17)
Over the last decade, parallel SAT solving has been widely studied from both theoretical and practical aspects. There are now numerous solvers that dier by parallelization strategies, programming languages, concurrent programming, involved libraries, etc. Hence, comparing the eciency of the theoretical approaches is a challenging task. Moreover, the introduction of a new approach needs either a deep understanding of the existing solvers, or to start from scratch the implementation of a new tool. We present PaInleSS: a framework to build parallel SAT solvers for many-core environments. Thanks to its genericity and modularity, it provides the implementation of basics for parallel SAT solving like clause exchanges, Portfolio and Divide-and-Conquer strategies. It also enables users to easily create their own parallel solvers based on new strategies. Our experiments show that our framework compares well with some of the best state-of-the-art solvers.
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