金句记录

 

	假定大家熟悉命题逻辑以及DP算法。 In the following discussions, we assume that the reader is familiar with propositional logic and the Davis-Putnam method [3]. 文献： 3. Davis, M., G. Logemann, and D. Loveland. A machine program for theorem- proving. Communications of the Association for Computing Machinery 5, 7 (July 1962), 394-397.
	Our new trail saving technique offers different tradeoffs in comparison with chronological backtracking and often yields superior performance. 与按时间顺序回溯相比，我们新的跟踪保存技术提供了不同的权衡，并且通常会产生卓越的性能。
	Using C-bt is not a panacea however. Its application must be limited for peak effectiveness. 然而，使用C-bt并不是万能的。必须限制其应用以达到最佳效果。
	许多成功的SAT求解器都基于DPLL过程，其现代化身由图1的伪代码描述。 Many successful SAT solvers are based on the DPLL procedure, whose modern incarnations are described by the pseudocode of Fig. 1.
	Despite remarkable advancesin both algorithms and computing power, significant yetgeneric improvements have remained elusive, generatingan increased interest in new optimization approachesthat are broadly applicable and radically different fromtraditional operations research tools. 尽管在算法和计算能力方面都取得了显着进步，但重大的通用改进仍然难以捉摸，这引起了人们对新优化方法的兴趣，这些方法具有广泛的适用性，与传统的运筹学工具截然不同。
	We have performed many experiments on decision and deletion heuristics in solvers of the MapleSAT family [16,19,15,14,17,22] , which have performed very well in recent SAT solver competitions.   14. Stepan Kochemazov, Oleg Zaikin, Victor Kondratiev, and Alexander Semenov. Maplelcmdistchronobt-dl, duplicate learnts heuristic-aided solvers at the sat race 2019. Proceedings of SAT Race, pages 24–24, 2019. 15. Jia Hui Liang, Vijay Ganesh, Pascal Poupart, and Krzysztof Czarnecki. Learning rate based branching heuristic for sat solvers. In International Conference on Theory and Applications of Satisfiability Testing, pages 123–140. Springer, 2016. 16. Jia Hui Liang, Chanseok Oh, Vijay Ganesh, Krzysztof Czarnecki, and Pascal Poupart. Maple-comsps, maplecomsps lrb, maplecomsps chb. SAT Competition, page 52, 2016.  17. Alexander Nadel and Vadim Ryvchin. Chronological backtracking. In International Conference on Theory and Applications of Satisfiability Testing, pages 111–121. Springer, 2018. 19. Chanseok Oh. Improving SAT solvers by exploiting empirical characteristics of CDCL. PhD thesis, New York University, 2016. 22. Xindi Zhang and Shaowei Cai. Relaxed backtracking with rephasing. SAT COMPETITION 2020, page 15.
	‘’‘’Even if the theoretical reasons behind the practical success of SAT solvers are largely unclear, we know in practice what ingredients are needed, and how they must be incorporated in any SAT solver targeting application instances.‘’‘’ 即使SAT求解器实际成功背后的理论原因很大程度上还不清楚，但我们在实践中知道需要什么成分，以及它们必须如何整合到任何针对应用实例的SAT求解器中。
	子句生成程序 Gilles Audemard，Laurent Simon: On the Glucose SAT Solver A CDCL-based SAT solver can be formulated as a resolution proof system.[48,11]. Consequently, the practical incarnation of modern SAT solvers can be seen as a clauses producer procedure with a deletion strategy. 译文：一个基于cdcl的SAT求解器可以被表述为一个解决证明系统。48,11.因此，现代SAT求解器的实际体现可以被视为具有删除策略的子句生成程序。
	We address this particular problem in this paper and provide two contribu tions. First, an analytic and empirical analysis that substantiates the observations about work repetition in modern SAT solvers that use non–chronological backtracking. Second, a low–overhead technique that helps reduce work repetition in such solvers.  我们在本文中解决了这个特殊的问题，并提供了两个贡献。首先，分析和实证分析证实了使用非时间回溯的现代SAT解算器中关于工作重复的观察。其次，低开销技术有助于减少此类求解器的重复工作。
	We briefly review the CDCL algorithm [3, 6].  We assume that the reader is familiar with notions of propositional satisfiability (propositional variable, literal, clause, unit clause, unit propagation, and so on).  我们假设读者熟悉命题可满足性的概念(命题变量、文字、子句、单位子句、单位传播等等)。CDCL算法重复以下两个操作，直到发生冲突。   We assume that the reader is familiar with notions of propositional satisfiability (propositional variable, literal, clause, unit clause, unit propagation, and so on). The CDCL algorithm repeats the following two operations until a conflict occurs. 1. Unit propagation: the unassigned literal in each unit clause is assigned as true to satisfy the clause. This operation repeats until there is no unit clause. 2. Decision: when no unit clauses exist, an unassigned literal is selected and a truth value (true or false) is assigned to it. 参考文献：命题逻辑及CDCL求解器基本概念最早引用文献 3. Bayardo Jr., R.J., Schrag, R.: Using CSP look-back techniques to solve real-world SAT instances. In: Proceedings of the 14th National Conference on Artificial Intelligence (AAAI 1997), pp. 203–208 (1997)   6. Marques-Silva, J.P., Sakallah, K.A.: GRASP: a search algorithm for propositional satisfiability. IEEE Trans. Comput. 48(5), 506–521 (1999)
	文献： Making Deduction More Effective in SAT Solvers Satisfiability (SAT) solvers often benefit from trans formations of the formula to be decided that allow them to do more through deduction and decrease their reliance on enumeration. 满足性 （SAT） 求解器通常受益于待决定公式的转换形式，这使他们能够通过演绎做更多的事情，并减少对 enu meration 的依赖。
	结果表明，除了一个大规模的测试问题实例之外，GridSAT为所有测试问题实例提供了加速。 We present GridSAT, a parallel and complete satisfiability solver designed to solve non-trivial SAT problem instances using a large number of widely distributed and heterogeneous resources. The GridSAT parallel algorithm uses intelligent backtracking, distributed and carefully scheduled sharing of learned clauses, and clause reduction. Our implementation focuses on dynamic resource acquisition and release to optimize application execution. We show how the large number of computational resources that are available from a Grid can be managed effectively for the application by an automatic scheduler and effective implementation. GridSAT execution speed is compared against the best sequential solver as rated by the SAT2002 competition using a wide variety of problem instances. The results show that GridSAT delivers speed-up for all but one of the test problem instances that are of significant size. In addition, we describe how GridSAT has solved previously unsolved satisfiability problems and the domain science contribution these results make. 我们提出了GridSAT，一个并行的完全可满足性求解器，旨在使用大量广泛分布的异构资源来解决非平凡SAT问题实例。GridSAT并行算法使用智能回溯、分布式和精心安排的学习子句共享以及子句缩减。我们的实现侧重于动态资源获取和释放，以优化应用程序的执行。我们展示了如何通过自动调度器和有效的实现来有效地管理网格中的大量计算资源。GridSAT的执行速度与SAT2002竞赛评定的最佳顺序求解器进行了比较，使用了各种各样的问题实例。结果表明，除了一个大规模的测试问题实例之外，GridSAT为所有测试问题实例提供了加速。此外，我们描述了GridSAT如何解决以前未解决的可满足性问题，以及这些结果对领域科学的贡献。   文献：GridSAT: A Chaff-based Distributed SAT Solver for the Grid