SAT及其能解决的问题及其文献

 1. 早期文献提到的SAT应用及编码

文献title：Adding a New Conflict Based Branching Heuristic in two Evolved DPLL SAT Solvers。   前沿部分提到了一些应用及其文献引用： Given a propositional formula, determining whether there exists a truth assignment for its propo- sitional variables such that the formula evaluates to true is called the propositional Satisfiability problem, commonly abbreviated as SAT. Extensive references can be found in [4, 12, 20]. Many problems arising from different fields, such as artificial intelligence, logic circuit design and test- ing, cryptography, database systems, software verification, are usually encoded as SAT. Moreover, SAT carries considerable theoretical interest as the original NP-complete problem [5, 8]. From the practical point of view, this implies that investing on the cleverness of the solution algorithm can result in very large savings in computational times. The above has motivated a wide stream of research in practically efficient SAT solvers. As a consequence, many algorithms for solving the SAT problem have been proposed, based on different techniques (see for instance [6, 7, 9, 12, 15]). Computational improvements in this field are impressive, see e.g. [15].

文献title：Conflict Analysis in Search Algorithms for Satisfiability 第二段开头： Most of the recently proposed improvements to the basic Davis-Putnam procedure [2, 5, 8, 111 can be distinguished based on their decision making heuristics or their use of preprocessing or relaxation techniques. Common to all these approaches, however, is the chronological nature of backtracking. Nevertheless, non-chronological backtracking techniques have been extensively studied and applied to different areas of Artificial Intelligence, particularly Truth Maintenance Systems (TMS), Constraint Satisfaction Problems (CSP) and Automated Reasoning, in some cases with very promising experimental results. (Bibliographic references to work in these areas can be found in [10].)   @inproceedings{DBLP:conf/ictai/SilvaS96, author = {Jo{\~{a}}o P. Marques Silva and Karem A. Sakallah}, title = {Conflict Analysis in Search Algorithms for Satisfiability}, booktitle = {Eigth International Conference on Tools with Artificial Intelligence, {ICTAI} '96, Toulouse, France, November 16-19, 1996}, pages = {467--469}, publisher = {{IEEE} Computer Society}, year = {1996}, url = {https://doi.org/10.1109/TAI.1996.560789}, doi = {10.1109/TAI.1996.560789}, timestamp = {Fri, 24 Mar 2023 00:04:31 +0100}, biburl = {https://dblp.org/rec/conf/ictai/SilvaS96.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }

 

 

2. 近期文献提到的SAT应用

	%SAT及其能解决的问题 The CDCL SAT solver is an important tool for solving large real-world problems, and has been widely used in software debugging, design verification, cryptography, artificial intelligence and other fields. The powerful capabilities of modern CDCL solver comes from the fact that the framework contains many key components that work together under the guidance of various heuristic strategies. %CDCL求解框架各种策略的组合产生强大的求解问题能力 Despite the hardness, modern CDCL SAT solvers can solve large real-world problems from important domains, such as hardware design verification [8], software debugging [4], planning [21], and encryption [18, 23], sometimes with surprising efficiency. This is the result of a careful combination of its key components, such as preprocessing [6, 10] and inprocessing [11, 17], robust branching heuristics [13, 14, 19], efficient restart policies [2, 20], intelligent conflict analysis [22], and effective clause learning [19]. Min Li, Zhengyuan Shi, Qiuxia Lai, Sadaf Khan, Shaowei Cai, Qiang Xu: On EDA-Driven Learning for SAT Solving. DAC 2023: 1-6
	The Boolean satisfiability (SAT) problem, which determines whether a combination of binary input variables exists to satisfy a given Boolean formula, has a broad range of applications, such as planning [1], scheduling [2], and verification [3].   electronic design automation (EDA)  @inproceedings{DBLP:conf/dac/LiSLKCX23, author = {Min Li and Zhengyuan Shi and Qiuxia Lai and Sadaf Khan and Shaowei Cai and Qiang Xu}, title = {On EDA-Driven Learning for {SAT} Solving}, booktitle = {60th {ACM/IEEE} Design Automation Conference, {DAC} 2023, San Francisco, CA, USA, July 9-13, 2023}, pages = {1--6}, publisher = {{IEEE}}, year = {2023}, url = {https://doi.org/10.1109/DAC56929.2023.10248001}, doi = {10.1109/DAC56929.2023.10248001}, timestamp = {Mon, 05 Feb 2024 20:28:08 +0100}, biburl = {https://dblp.org/rec/conf/dac/LiSLKCX23.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }   planning  dblp中搜索Planning as satisfiability可得较多的文献，其中最早及近期的文献如下： @inproceedings{DBLP:conf/ecai/KautzS92, author = {Henry A. Kautz and Bart Selman}, editor = {Bernd Neumann}, title = {Planning as Satisfiability}, booktitle = {10th European Conference on Artificial Intelligence, {ECAI} 92, Vienna, Austria, August 3-7, 1992. Proceedings}, pages = {359--363}, publisher = {John Wiley and Sons}, year = {1992}, timestamp = {Wed, 31 Jul 2019 08:45:08 +0200}, biburl = {https://dblp.org/rec/conf/ecai/KautzS92.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} } @inproceedings{DBLP:conf/aips/ButtnerR05, author = {Markus B{\"{u}}ttner and Jussi Rintanen}, editor = {Susanne Biundo and Karen L. Myers and Kanna Rajan}, title = {Satisfiability Planning with Constraints on the Number of Actions}, booktitle = {Proceedings of the Fifteenth International Conference on Automated Planning and Scheduling {(ICAPS} 2005), June 5-10 2005, Monterey, California, {USA}}, pages = {292--299}, publisher = {{AAAI}}, year = {2005}, url = {http://www.aaai.org/Library/ICAPS/2005/icaps05-030.php}, timestamp = {Fri, 05 Feb 2021 17:14:47 +0100}, biburl = {https://dblp.org/rec/conf/aips/ButtnerR05.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} } @inproceedings{DBLP:conf/etfa/ErosDFB21, author = {Endre Er{\'{o}}s and Martin Dahl and Petter Falkman and Kristofer Bengtsson}, title = {Evaluation of high level methods for efficient planning as satisfiability}, booktitle = {26th {IEEE} International Conference on Emerging Technologies and Factory Automation, {ETFA} 2021, Vasteras, Sweden, September 7-10, 2021}, pages = {1--8}, publisher = {{IEEE}}, year = {2021}, url = {https://doi.org/10.1109/ETFA45728.2021.9613254}, doi = {10.1109/ETFA45728.2021.9613254}, timestamp = {Thu, 05 Oct 2023 17:14:10 +0200}, biburl = {https://dblp.org/rec/conf/etfa/ErosDFB21.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }   scheduling @article{DBLP:journals/anor/Horbach10, author = {Andrei Horbach}, title = {A Boolean satisfiability approach to the resource-constrained project scheduling problem}, journal = {Ann. Oper. Res.}, volume = {181}, number = {1}, pages = {89--107}, year = {2010}, url = {https://doi.org/10.1007/s10479-010-0693-2}, doi = {10.1007/S10479-010-0693-2}, timestamp = {Thu, 13 Aug 2020 12:40:20 +0200}, biburl = {https://dblp.org/rec/journals/anor/Horbach10.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }     verification @article{DBLP:journals/pieee/VizelWM15, author = {Yakir Vizel and Georg Weissenbacher and Sharad Malik}, title = {Boolean Satisfiability Solvers and Their Applications in Model Checking}, journal = {Proc. {IEEE}}, volume = {103}, number = {11}, pages = {2021--2035}, year = {2015}, url = {https://doi.org/10.1109/JPROC.2015.2455034}, doi = {10.1109/JPROC.2015.2455034}, timestamp = {Sat, 30 Sep 2023 10:23:39 +0200}, biburl = {https://dblp.org/rec/journals/pieee/VizelWM15.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} } hardware and software verification  @inproceedings{DBLP:conf/date/Velev02, author = {Miroslav N. Velev}, title = {Using Rewriting Rules and Positive Equality to Formally Verify Wide-Issue Out-of-Order Microprocessors with a Reorder Buffer}, booktitle = {2002 Design, Automation and Test in Europe Conference and Exposition {(DATE} 2002), 4-8 March 2002, Paris, France}, pages = {28--35}, publisher = {{IEEE} Computer Society}, year = {2002}, url = {https://doi.org/10.1109/DATE.2002.998246}, doi = {10.1109/DATE.2002.998246}, timestamp = {Fri, 24 Mar 2023 00:02:46 +0100}, biburl = {https://dblp.org/rec/conf/date/Velev02.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
	Satisfiability checking (SAT) is one of the well known NP-hard problems [15] in both theoretical and practical computer science. There are several real-world applications that are actually tackled by modelling parts of these problems as SAT instances like hardware and software verification [34], planning [23], and bioinformatics [28].   hardware and software verification   @inproceedings{DBLP:conf/date/Velev02, author = {Miroslav N. Velev}, title = {Using Rewriting Rules and Positive Equality to Formally Verify Wide-Issue Out-of-Order Microprocessors with a Reorder Buffer}, booktitle = {2002 Design, Automation and Test in Europe Conference and Exposition {(DATE} 2002), 4-8 March 2002, Paris, France}, pages = {28--35}, publisher = {{IEEE} Computer Society}, year = {2002}, url = {https://doi.org/10.1109/DATE.2002.998246}, doi = {10.1109/DATE.2002.998246}, timestamp = {Fri, 24 Mar 2023 00:02:46 +0100}, biburl = {https://dblp.org/rec/conf/date/Velev02.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }   bioinformatics  生物信息学  在dblp中搜索作者João P. Marques Silva  –  João Paulo Marques Silva得到很多模型检验、sat形式化及应用方面的文献 @inproceedings{DBLP:conf/sat/LynceM06, author = {In{\^{e}}s Lynce and Jo{\~{a}}o Marques{-}Silva}, editor = {Armin Biere and Carla P. Gomes}, title = {{SAT} in Bioinformatics: Making the Case with Haplotype Inference}, booktitle = {Theory and Applications of Satisfiability Testing - {SAT} 2006, 9th International Conference, Seattle, WA, USA, August 12-15, 2006, Proceedings}, series = {Lecture Notes in Computer Science}, volume = {4121}, pages = {136--141}, publisher = {Springer}, year = {2006}, url = {https://doi.org/10.1007/11814948\_16}, doi = {10.1007/11814948\_16}, timestamp = {Mon, 24 Feb 2020 19:23:28 +0100}, biburl = {https://dblp.org/rec/conf/sat/LynceM06.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }    circuit design @article{DBLP:journals/tcad/StephanBS96, author = {Paul R. Stephan and Robert K. Brayton and Alberto L. Sangiovanni{-}Vincentelli}, title = {Combinational test generation using satisfiability}, journal = {{IEEE} Trans. Comput. Aided Des. Integr. Circuits Syst.}, volume = {15}, number = {9}, pages = {1167--1176}, year = {1996}, url = {https://doi.org/10.1109/43.536723}, doi = {10.1109/43.536723}, timestamp = {Thu, 24 Sep 2020 11:26:56 +0200}, biburl = {https://dblp.org/rec/journals/tcad/StephanBS96.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }   neural network verification @inproceedings{DBLP:conf/aaai/NarodytskaKRSW18, author = {Nina Narodytska and Shiva Prasad Kasiviswanathan and Leonid Ryzhyk and Mooly Sagiv and Toby Walsh}, editor = {Sheila A. McIlraith and Kilian Q. Weinberger}, title = {Verifying Properties of Binarized Deep Neural Networks}, booktitle = {Proceedings of the Thirty-Second {AAAI} Conference on Artificial Intelligence, (AAAI-18), the 30th innovative Applications of Artificial Intelligence (IAAI-18), and the 8th {AAAI} Symposium on Educational Advances in Artificial Intelligence (EAAI-18), New Orleans, Louisiana, USA, February 2-7, 2018}, pages = {6615--6624}, publisher = {{AAAI} Press}, year = {2018}, url = {https://doi.org/10.1609/aaai.v32i1.12206}, doi = {10.1609/AAAI.V32I1.12206}, timestamp = {Mon, 04 Sep 2023 16:50:26 +0200}, biburl = {https://dblp.org/rec/conf/aaai/NarodytskaKRSW18.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
	MaxSAT 在学术研究领域和工业应用领域 基于搜索信息反馈策略的MaxSAT非完备 求解算法 徐振兴 何 琨 李初民   刘燕丽   郑迥之 . MaxSAT 在学术研究领域和工业应用领域都 展现出了重要的价值. MaxSAT问题的定义特别基 础而且抽象，因此有极其强大的表达能力，很多学术 界及工业界的问题都能转化为MaxSAT问题求解. 在学术研究领域，许多其它组合优化问题，如最大团 问题［2］ 、相关聚类问题［3］ 、最小顶点覆盖问题［4］ 等，都 能经过编码转化为MaxSAT问题，而且MaxSAT求 解技术也能直接或者间接应用［5-7］ 在这些问题的求 解上，促进了这些组合优化问题求解技术的发展与 进步. 在工业应用领域，随着求解技术的不断进步， MaxSAT能高效地解决更多的工业问题 . MaxSAT 求解技术广泛应用在各行各业，应用领域包括电路 设计自动化［8-9］ 、优化癌症治疗设计［10］ 、最小校正集 计数问题［11］ 、企业对企业会议安排［12-13］ 、高校课表排 班问题［14］ 、组缺陷测试［15］ 、检测硬件木马［16］ 、线性时 序逻辑［17］ 等. 参 考 文 献 ［1］ Cook S A. The complexity of theorem-proving procedures// Proceedings of the Third Annual ACM Symposium on Theory of Computing. Shaker Heights， USA，1971：151-158 ［2］ Zuckerman D. Linear degree extractors and the inapproximability of max clique and chromatic number//Proceedings of the Thirty-Eighth Annual ACM Symposium on Theory of Computing. Seattle， USA，2006：681-690 ［3］ Bansal N， Blum A， Chawla S. Correlation clustering. Machine Learning，2004，56（1-3）：89-113 ［4］ Dinur I， Safra S. On the hardness of approximating minimum vertex cover. Annals of Mathematics，2005，162（1）：439-485 ［5］ Li C， Quan Z. An efficient branch-and-bound algorithm based on maxsat for the maximum clique problem//Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence. Atlanta， USA，2010：128-133 ［6］ Fang Z， Li C， Xu K. An exact algorithm based on maxsat reasoning for the maximum weight clique problem. Journal of Artificial Intelligence Research，2016，55：799-833 ［7］ Berg J， Järvisalo M. Cost-optimal constrained correlation clustering via weighted partial maximum satisfiability. Artificial Intelligence，2017，244 ：110-142 ［8］ Chen Y， Safarpour S， Veneris A G， et al. Spatial and temporal design debug using partial maxsat//Proceedings of the Nineteenth ACM Great Lakes Symposium on VLSI. Boston Area， USA，2009：345-350 ［9］ Chen Y， Safarpour S， Marques-Silva J， et al. Automated design debugging with maximum satisfiability. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems，2010，29（11）：1804-1817 ［10］ Lin P C K， Khatri S P. Application of Max-SAT-based ATPG to optimal cancer therapy design. BMC genomics，2012，13（6）：1-10 ［11］ Morgado A， Liffiton M H， Marques-Silva J. MaxSAT-based MCS enumeration//Proceedings of the Eighth International Haifa Verification Conference. Haifa， Israel，2012：86-101 ［12］ Bofill M， Garcia M， Suy J， et al. MaxSAT-based scheduling of B2B meetings//Proceedings of the International Conference on Integration of Constraint Programming， Artificial Intelligence， and Operations Research. Barcelona， Spain，2015：65-73 ［13］ Bofill M， Giráldez-Cru J， Suy J， et al. A study on implied constraints in a MaxSAT approach to B2B problems// Proceedings of the Twenty-Second International Conference of the Catalan Association for Artificial Intelligence. Mallorca， Spain，2019：183-192 ［14］ Demirovic E， Musliu N. MaxSAT-based large neighborhood search for high school timetabling. Computers & Operations Research，2017，78：172-180 ［15］ Ciampiconi L， Ghosh B， Scarlett J， et al. A MaxSAT-based framework for group testing//Proceedings of the AAAI Conference on Artificial Intelligence. New York， USA， 2020， 34（06）：10144-10152 ［16］ Saikko P， Malone B M， Järvisalo M. MaxSAT-based cutting planes for learning graphical models//Proceedings of the International Conference on Integration of Constraint Programming， Artificial Intelligence， and Operations Research. Barcelona， Spain，2015：347-356 ［17］ Gaglione J R， Neider D， Roy R， et al. Learning linear temporal properties from noisy data： a MaxSAT-based approach// Proceedings of the International Symposium on Automated Technology for Verification and Analysis. Gold Coast， Australia，2021：74-90 ［18］ Liu Y， Li C， He K. Improving lower bounds in MAXSAT complete algorithm based optimizing inconsistent set. Chinese Journal of Computers，2013，36（10）：2087-2095. （刘燕丽，李初民，何琨 . 基于优化冲突集提高下界的 MAXSAT 完备算法. 计算机学报，2013，36（10）：2087-2095） ［ 19］ Zheng Y， Xue J， Ling H. Combinatorial optimization problem reduction and algorithm derivation. Journal of Software， 2011， 22（9）：1985-1993 （郑宇军，薛锦云，凌海风.组合优化问题简约与算法推演.软件学 报，2011，22（9）：1985-1993） ［20］ Zhang X， Li Z. Research on feature selection algorithms based on natural evolution strategy. Journal of Software， 2020， 31 （12）：3733-3752 （张鑫，李占山 . 自然进化策略的特征选择算法研究 . 软件学报， 2020，31（12）：3733-3752） ［21］ Yin M， Zhou J， Sun J， et al. Heuristic survey propagation algorithm for solving QBF problem. Journal of Software，2011， 22（7）：1538-155 （殷明浩，周俊萍，孙吉贵等.求解QBF问题的启发式调查传播算 法.软件学报，2011，22（7）：1538-155） ［22］ He K， Zheng J. Survey on algorithms for the maximum satisfiability problem. Journal of Huazhong University of Science and Technology （Natural Science Edition）， 2022， 50 （2）：82-95 （何琨，郑迥之.最大可满足性问题的算法研究综述.华中科技大 学学报（自然科学版），2022，50（2）：82-95） ［23］ Festa P， Pardalos P M， Pitsoulis L S， et al. GRASP with path relinking for the weighted MAXSAT problem. ACM Journal of Experimental Algorithmics，2007，11：2-4 ［24］ Luo C， Cai S， Wu W， et al. CCLS： an efficient local search algorithm for weighted maximum satisfiability. IEEE Transactions on Computers，2014，64（7）：1830-1843 ［25］ Xu Z， He K， Li C. An iterative Path-Breaking approach with mutation and restart strategies for the MAX-SAT problem. Computers & Operations Research，2019，104：49-58 ［26］ Cai S， Luo C， Thornton J， et al. Tailoring local search for partial MaxSAT//Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence. Quebec City， Canada， 2014：2623-2629 ［27］ Luo C， Cai S， Su K， et al. CCEHC： an efficient local search algorithm for weighted partial maximum satisfiability. Artificial Intelligence，2017，243：26-44 ［28］ Cai S， Su K. Configuration checking with aspiration in local search for SAT//Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence and the Twenty-Fourth Innovative Applications of Artificial Intelligence Conference. Toronto， Canada，2012：434-440 ［29］ Lei Z， Cai S. Solving （weighted） partial MaxSAT by dynamic local search for SAT//Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence. Stockholm， Sweden，2018：1346-1352 ［30］ Lei Z. Novel algorithms of maximum satisfiability and its extensions. Beijing： University of Chinese Academy of Sciences，2021 （雷震东.最大可满足性及其拓展问题的求解.北京：中国科学院 大学，2021）

3.

A New Solver for the Minimum Weighted Vertex Cover Problem Given a vertex-weighted graph <span class="MathJax_Preview"><span id="MathJax-Element-1-Frame" class="MathJax_SVG" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mo fence="false" stretchy="false">⟨</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo fence="false" stretchy="false">⟩</mo></math>"><span class="MJX_Assistive_MathML">G=⟨V,E⟩, the minimum weighted vertex cover (MWVC) problem is to choose a subset of vertices with minimum total weight such that every edge in the graph has at least one of its endpoints chosen. While there are good solvers for the unweighted version of this NP-hard problem, the weighted version—i.e., the MWVC problem—remains understudied despite its common occurrence in many areas of AI—like combinatorial auctions, weighted constraint satisfaction, and probabilistic reasoning. In this paper, we present a new solver for the MWVC problem based on a novel reformulation to a series of SAT instances using a primal-dual approximation algorithm as a starting point. We show that our SAT-based MWVC solver (SBMS) significantly outperforms other methods.

 

 

4. SAT扩展问题-1 最小不可满足集问题——元器件故障诊断

极小不可满足集(minimal unsatisfiable subset, MUS)是 SAT 问题的扩展问题。在现实中许多重要问题可以编码为 MUS 问题进行求解，MUS 的主要应用包括本体中不一致性检测问题[6-7]、关系规范调试问题[8-9]、过度约束的时序分析问题[10]、描述逻辑中的公理精确定位问题[11]、硬件模型验证问题[12]等问题。如何高效求解MUS 问题对人工智能的很多领域都有深远意义。 基于模型诊断[13]是人工智能领域中针对问题进行故障检测及定位的关键方法。基于模型诊断中求解诊断解的一个关键思想是根据系统观测以及系统描述先求得极小冲突集，之后对所有极小冲突集求解极小碰集，即得到诊断结果。极小冲突集问题是基于模型诊断中的重要组成部分，而如何高效的求解出极小冲突集成为研究难点。 Minimal unsatisfiable subset (MUS) 在基于图结构求解方法中，MARCO 方法是目前采用极大化模型求解 MUS 效率最高的方法，但此方法未对求解空间进行进一步有效剪枝。针对 MARCO 方法的不足，结合可满足问题求解复杂度低于不可满足问题的特征，提出基于双模型即极大-中间化模型的 MARCO-MAM 方法求解 MUS。此方法对中间模型求解若得到极大可满足子集，则缩减 MUS 的无解空间，进而缩减未探索空间来提高 MUS求解效率；如果中间模型求解得到不可满足集合，则减少了单一 MUS 的不可满足迭代求解次数。此方法避免了 MARCO 方法单一极大化模型求解 MUS 时未有效利用其他优化技术对求解空间进行剪枝的问题。实验结果表明，与 MARCO 方法相比 MARCO-MAM 方法效率较高，尤其在大规模问题或较大搜索空间时效率提高更为明显。 在基于树结构求解极小冲突集问题中，MCS-SFFO 方法以反向深度的方式遍历集合枚举树(Set Enumeration Tree, SE-Tree)，然后针对故障输出无关元件的组合进行剪枝。本文在 MCS-SFFO 方法的基础上，结合电路的故障逻辑关系提出求解极小冲突集的进一步剪枝方法 MCS-FLR，首先提出单元件非冲突集定理，对单元件集合进行剪枝，避免了对无解空间中单元件节点的访问；其次，提出非极小冲突集定理，推证得出故障输出相关元件集的超集都是冲突集，故对有解空间中的非极小解进行剪枝。MCS-FLR 方法在 MCS-SFFO 方法基础上减少了大量有解空间和部分无解空间调用 SAT 求解器的次数，节省了求解时间。实验结果表明，相比于 MCS-SFFO 方法，MCS-FLR 方法求解效率有显著提高。