早期文献给出的SAT术语

 

 

	SAT问题的通俗表述 Given a propositional formula, determining whether there exists a truth assignment for its propositional variables such that the formula evaluates to true is called the propositional Satisfiability problem, commonly abbreviated as SAT.
	完备算法与不完备算法的表述 A solution method is said to be complete if it guarantees (given enough time) to find a solution if it exists, or prove lack of solution otherwise. Incomplete, or stochastic, methods, on the contrary, cannot guarantee finding the solution, although they may scale better than complete methods on some large satisfiable problems.
	sat已被证明是NP完全问题 Moreover, SAT carries considerable theoretical interest as the original NP-complete problem [A5, A8]. A5.  S.A. Cook. The Complexity of Theorem-Proving Procedures. In Proceedings of Third Annual ACM Symposium on Theory of Computing, 1971. A8. M.R. Garey and D.S. Johnson. Computers and Intractability: A Guide to the Theory of NPCompleteness. W.H. Freeman and co., San Francisco, 1979.
	主要组件及其对应来源文献  Modern implementations of CDCL SAT solvers employ a lot of heuristics. Some of them can be considered baseline, such as： the Variable State Independent Decaying Sum (VSIDS) [B6], restarts [B7], Literal Block Distance (LBD) [B8]. Learnt Clause Minimization (LCM) [B9], Distance (Dist) heuristic [B10], Chronological Backtracking (ChronoBT) [B11], duplicate learnts heuristic [B12], Conflict History-Based (CHB) heuristic [B13], Learning Rate-based Branching (LRB) heuristic [B14], and the SLS component [B15].   [B6] Moskewicz, M.W.; Madigan, C.F.; Zhao, Y.; Zhang, L.; Malik, S. Chaff: Engineering an efficient SAT solver. In Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232), Las Vegas, NV, USA, 22 June 2001; pp. 530–535. [B7] Luby, M.; Sinclair, A.; Zuckerman, D. Optimal speedup of Las Vegas algorithms. Inf. Process. Lett. 1993, 47, 173–180. [B8] Audemard, G.; Simon, L. Predicting Learnt Clauses Quality in Modern SAT Solvers. In Proceedings of the 21st International Jont Conference on Artifical Intelligence, Pasadena, CA, USA, 11–17 July 2009; IJCAI’09. pp. 399–404. [B9] Luo, M.; Li, C.M.; Xiao, F.; Manyà, F.; Lü, Z. An Effective Learnt Clause Minimization Approach for CDCL SAT Solvers. In Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI-17, Melbourne, Australia 19–25 August 2017; pp. 703–711. [B13] Liang, J.H.; Ganesh, V.; Poupart, P.; Czarnecki, K. Exponential Recency Weighted Average Branching Heuristic for SAT Solvers. In Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, Phoenix, AZ, USA, 12–17 February 2016; AAAI’16. pp. 3434–3440. [B14] Liang, J.H.; Ganesh, V.; Poupart, P.; Czarnecki, K. Learning Rate Based Branching Heuristic for SAT Solvers. In Proceedings of the Theory and Applications of Satisfiability Testing—SAT 2016—19th International Conference, Bordeaux, France, 5–8 July 2016; Creignou, N., Berre, D.L., Eds.; Springer: Berlin/Heidelberg, Germany, 2016; Volume 9710, pp. 123–140. [B15] Zhang, X.; Cai, S. Relaxed Backtracking with Rephasing. In Proceedings of the SAT Competition 2020, Alghero, Italy, 3–10 July 2020; Solver and Benchmark Descriptions. University of Helsinki, Department of Computer Science: Helsinki, Finland, 2020; Volume B-2020-1, pp. 15–16.
	Non-Chronological Backtracking (NCB)、Conflict Analysis, 2 Watched-Literal, restarts, phase caching scheme, managing the learnt clause database, integrate inprocessing and sophisticated preprocessing techniques and VSIDS are still the most important ingredients of any CDCL implementation. Even if the theoretical reasons behind the practical success of SAT solvers are largely unclear,虽然是不明确的，许多模块作为组件ingredients are needed and   must be incorporated in any SAT solver for 发挥CDCL的潜在能力。
	SAT的应用场合及其来源文献 The task of computing the number of models of a propositional formula, also referred to as #SAT, has various applications in hardware and software verification [5, 4, 12, 15, 11] as well as cryptography[16]. Classical applications are found in the area of probabilistic reasoning [24] as well as Bayesian networks [2, 19, 27] which are adopted in medical diagnosis and planning. A counting characterization of diagnoses is presented in [18]. Propositional model counting finds further applications in product configuration [32, 17] and planning [1, 31].   [4] Fabrizio Biondi, Michael A. Enescu, Annelie Heuser, Axel Legay, Kuldeep S. Meel, and Jean Quilbeuf.Scalable approximation of quantitative information flow in programs.In VMCAI,volume 10747 of Lecture Notes in Computer Science, pages 71–93. Springer, 2018. [5] Jan Burchard, Dominik Erb, and Bernd Becker. Characterization of possibly detected faults by accurately computing their detection probability. In DATE, pages 385–390. IEEE, 2018. [11] Linus Feiten, Matthias Sauer, Tobias Schubert, Alexander Czutro, Eberhard B¨ohl, Ilia Polian, and Bernd Becker. #SAT-based vulnerability analysis of security components - A case study. In DFT, pages 49–54. IEEE Computer Society, 2012. [12] Linus Feiten, Matthias Sauer, Tobias Schubert, Victor Tomashevich, Ilia Polian, and Bernd Becker. Formal vulnerability analysis of security components. IEEE Trans. on CAD of Integrated Circuits and Systems, 34(8):1358–1369, 2015. [15] Vladimir Klebanov, Norbert Manthey, and Christian J. Muise. SAT-based analysis and quantifi- cation of information flow in programs. In QEST, volume 8054 of Lecture Notes in Computer Science, pages 177–192. Springer, 2013. [16] Stefan K¨olbl, Gregor Leander, and Tyge Tiessen. Observations on the SIMON block cipher family. In CRYPTO (1), volume 9215 of Lecture Notes in Computer Science, pages 161–185. Springer, 2015. [17] Andreas K¨ubler, Christoph Zengler, and Wolfgang K¨uchlin. Model counting in product configu- ration. In LoCoCo, volume 29 of EPTCS, pages 44–53, 2010. [18] T.K. Satish Kumar. A model counting characterization of diagnoses. In DX 02, pages 70–76, 2002.   [19] Wei Li, Peter van Beek, and Pascal Poupart. Performing incremental Bayesian inference by dynamic model counting. In AAAI, pages 1173–1179. AAAI Press, 2006. [20] Sibylle M¨ohle and Armin Biere. Dualizing projected model counting. In ICTAI, pages 702–709. IEEE, 2018. [21] Sibylle M¨ohle and Armin Biere. Backing backtracking. In SAT, volume 11628 of Lecture Notes in 125 On Backtracking Chronologically in Propositional Model Counting M¨ohle and Biere Computer Science, pages 250–266. Springer, 2019. [22] Matthew W. Moskewicz, Conor F. Madigan, Ying Zhao, Lintao Zhang, and Sharad Malik. Chaff: Engineering an efficient SAT solver. In DAC, pages 530–535. ACM, 2001. [23] Alexander Nadel and Vadim Ryvchin. Chronological backtracking. In SAT, volume 10929 of Lecture Notes in Computer Science, pages 111–121. Springer, 2018. [24] Dan Roth. On the hardness of approximate reasoning. Artif. Intell., 82(1-2):273–302, 1996. [25] Tian Sang, Fahiem Bacchus, Paul Beame, Henry A. Kautz, and Toniann Pitassi. Combining component caching and clause learning for effective model counting. In SAT, 2004. [26] Tian Sang, Paul Beame, and Henry A. Kautz. Heuristics for fast exact model counting. In SAT, volume 3569 of Lecture Notes in Computer Science, pages 226–240. Springer, 2005. [27] Tian Sang, Paul Beame, and Henry A. Kautz. Performing Bayesian inference by weighted model counting. In AAAI, pages 475–482. AAAI Press / The MIT Press, 2005. [28] Jo˜ao P. Marques Silva and Karem A. Sakallah. GRASP: A search algorithm for propositional satisfiability. IEEE Trans. Computers, 48(5):506–521, 1999. [29] Marc Thurley. sharpSAT – counting models with advanced component caching and implicit BCP. In SAT, volume 4121 of Lecture Notes in Computer Science, pages 424–429. Springer, 2006. [30] Peter van der Tak, Antonio Ramos, and Marijn Heule. Reusing the assignment trail in CDCL solvers. JSAT, 7(4):133–138, 2011. [31] Erik Peter Zawadzki, Andr´e Platzer, and Geoffrey J. Gordon. A generalization of SAT and #SAT for robust policy evaluation. In IJCAI, pages 2583–2590. IJCAI/AAAI, 2013. [32] Christoph Zengler and Wolfgang K¨uchlin. Boolean quantifier elimination for automotive configu- ration - A case study. In FMICS, volume 8187 of Lecture Notes in Computer Science, pages 48–62. Springer, 2013.
	标准符号表示——参见以下文献： [1]. Sibylle M¨ohle and Armin Biere. Backing backtracking. In SAT, volume 11628 of Lecture Notes in Computer Science, pages 250–266. Springer, 2019.