1.学习子句生成器
Gilles Audemard proposed to renew the vision of CDCL solvers,instead of seeing them as an improvement of a DPLL search, seeing them as clauses producers. Gilles Audemard 提议更新 CDCL 求解器的愿景,不是将它们视为 DPLL 搜索的改进,而是将它们视为子句生产者。 Gilles Audemard, Laurent Simon:
@article{DBLP:journals/ijait/AudemardS18, author = {Gilles Audemard and Laurent Simon}, title = {On the Glucose {SAT} Solver}, journal = {Int. J. Artif. Intell. Tools}, volume = {27}, number = {1}, pages = {1840001:1--1840001:25}, year = {2018}, url = {https://doi.org/10.1142/S0218213018400018}, doi = {10.1142/S0218213018400018}, timestamp = {Tue, 12 May 2020 16:53:25 +0200}, biburl = {https://dblp.org/rec/journals/ijait/AudemardS18.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} } |
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2.强化学习
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Exponential Recency Weighted Average Branching Heuristic for SAT SolversInspired by the bandit framework and reinforcement learning, we learn to choose good variables to branch based on past experience. Our goal is to leverage the theory and practice of a rich sub-field of reinforcement learning to plain and design an effective branching heuristic for solving real-world problems. 译文:受到bandit框架和强化学习的启发,我们学会根据过去的经验选择好的变量进行分支。我们的目标是利用理论和实践的丰富子领域的强化学习,以平原和设计一个有效的分支启发式解决实际问题。 分支决策变元的选择包含强化学习的思想 |
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Improving SAT Solver Heuristics with Graph Networks and Reinforcement Learning
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Adaptive Restart and CEGAR-Based Solver for Inverting Cryptographic Hash FunctionsMapleCrypt has two key features, namely, a multi-armed bandit based adaptive restart (MABR) policy and a counterexample-guided abstraction refinement (CEGAR) technique.译文:将固定目标的哈希函数反演问题简化为布尔逻辑的可满足性问题,并使用MapleCrypt构造这些目标的前像。MapleCrypt有两个关键特性,即基于多武装强盗的自适应重启(MABR)策略和反例引导的抽象细化(CEGAR)技术 The MABR technique uses reinforcement learning to adaptively choose between different restart policies during the run of the solver.译文:MABR技术使用强化学习来在求解器运行过程中自适应地选择不同的重启策略。 |
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3.结构探测的视角
4. 特殊子句有限传播——体现了什么原理?强化学习?桥接变元?简化?
Specific clauses (and their variants) that are known to be studied include \textit{Glue clauses} and \textit{Core clauses}, as well as \textit{Duplicate Learnt Clauses}. They are either judged to be of high quality, or they are speculated to carry important information. All of them have been experimentally proven to play an important role in improving the ability to solve. %子句尺寸最小的glue子句在早期文献加强的重视成为研究的热点。
%core first %这是与保留高质量的子句长久保留不被删除的策略的技术路线是一脉相承。在文献中,学习子句被按照质量高低分配到Core、Iter2、Local中,不同的集合元素的生存期(保留期限)被区别对待。这里的质量标准通常是LBD或子句中文字数量。Core集合中的子句被永久保留;Iter2中的子句被继续评价考察决定是否流动到其它两个集合;Local中的子句被定期删除至少一半数量。 %复制子句
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5. 引擎
文献名:On the Glucose SAT Solver
When they were introduced fifteen years ago, CDCL SAT solvers (Conflict Driven Clause Learning) were presented as an extension of the DPLL algorithm with additional features such as clause learning, based on top of an efficient data structure (2 Watched Literals) for Unit Propagation detections, giving an efficient Boolean Constraint Propagation engine (BCP). Now, it is well admitted that they have to be seen as a mix of backtrack algorithms and resolution engines. Furthermore, is has been proved that CDCL SAT solvers are more powerful than DPLL ones, i.e., there exist formulas on which the proof (the proof can be seen as a special trace of solver’s run) can be polynomial (w.r.t. to the number of variables) for CDCL solvers whereas, it is necessary exponential for DPLL ones. The opposite is not true.
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我整理写在文档中:Structure Time Scale of the CDCL SAT Solver
正式的文章标题为:Instance Assignment Coverage Feature for Operation Control of SAT Solve
\subsection{Cognitive diversity of CDCL} In the research to improve the performance of the solver, new and innovative ideas and methods are constantly emerging based on the different perspectives of understanding CDCL.
Dynamic adaptive disposition has been widely used in CDCL solvers. In the process of solving, the learning clause generation \cite{Gelder11a,0001LM21}, intelligent backtrace \cite{SilvaS96,AudemardBHJS08,NadelR18}, and adaptive restart \cite{AudemardS12,Biere08,ZulkoskiMWRLCG18} are all direct manifestations of this technical idea. Block of Text Distance (LBD) is a criterion for evaluating the quality of sentences learnedcite{AudemardS09}. The LBD value of the learning clause involved in Boolean constraint propagation is constantly re-evaluated to keep the minimum value for the entire search period. According to the dynamic change of the LBD value of the existing learning clause, it can be moved in different clause sets \cite{abs-2110-14187}. A. Goultiaeva demonstrated that CDCL can be reformulated as a local search algorithm that through clause learning is able to prove UNSAT \cite{GoultiaevaB12}. This novel cognitive perspective was considered to open up avenues for further research and algorithm design at that time. By the bandit framework and the view of reinforcement learning, Liang et al. propose LRB and CHB branching heuristic successively to choose some variables involved in recent conflicts to branch\cite{LiangGZZC15,LiangGPC16CHB,LiangGPC16}. The intuition is that assignments of these variables are likely to generate further conflicts, leading to useful learned clauses and thus pruning the search space. The idea of hybrid dominance was adopted very early. Shallow composition involves concatenating different branching decision heuristics to take advantage of different strategies\cite{AudemardS18,XiaoLLMLL19}. The latest innovation of deep collaboration is the relaxation of the CDCL framework to take advantage of the conflict frequency of variables in local search are exploited in the phase selection and branching heuristics of CDCL, while invoking the local search solver in the promising branch to search for nearby models\cite{CaiZ22}.
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