{"type":"ScholarlyArticle","title":"QCDCL with Cube Learning or Pure Literal Elimination - What is Best?","authors":[{"name":"Benjamin Böhm","slug":"benjamin-bohm","given":"Benjamin","family":"Böhm","affiliation":"Friedrich Schiller University Jena , Germany"},{"name":"Tomáš Peitl","slug":"tomas-peitl","given":"Tomáš","family":"Peitl","affiliation":"TU Wien , Vienna , Austria"},{"name":"Olaf Beyersdorff","slug":"olaf-beyersdorff","given":"Olaf","family":"Beyersdorff","affiliation":"Friedrich Schiller University Jena , Germany"}],"abstract":"Quantified conflict-driven clause learning (QCDCL) is one of the main approaches for solving quantified Boolean formulas (QBF). We formalise and investigate several versions of QCDCL that include cube learning and/or pure-literal elimination, and formally compare the resulting solving models via proof complexity techniques. Our results show that almost all of the QCDCL models are exponentially incomparable with respect to proof size (and hence solver running time), pointing towards different orthogonal ways how to practically implement QCDCL.","doi":"10.24963/ijcai.2022/248","url":"https://ijcai.org/proceedings/2022/248","pdf":"https://ijcai.org/proceedings/2022/0248.pdf","markdown":"https://ijcai.org/proceedings/2022/248.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/248","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Constraint Satisfaction and Optimization","track":"Main Track","number":248,"pages":{"first":1781,"last":1787},"keywords":["Constraint Satisfaction and Optimization: Solvers and Tools","Constraint Satisfaction and Optimization: Satisfiabilty"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38987013","length_sec":81,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38985156","length_sec":716,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Atserias et al., 2011] Albert Atserias, Johannes Klaus Fichte, and Marc Thurley. Clause-learning algorithms with many restarts and bounded-width resolution. J. Artif. Intell. Res., 40:353-373, 2011.","title":"Clause-learning algorithms with many restarts and bounded-width resolution","authors":"Atserias","year":"2011","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Balabanov and Jiang, 2012] Valeriy Balabanov and Jie- Hong R. Jiang. Unified QBF certification and its appli- cations. Form. Methods Syst. Des., 41(1):45-65, 2012.","title":"Unified QBF certification and its applications","authors":"Valeriy Balabanov, R Jie-Hong, Jiang","year":"2012","venue":"Form. Methods Syst. Des","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Beame et al., 2004] Paul Beame, Henry A. Kautz, and Ashish Sabharwal. Towards understanding and harness- ing the potential of clause learning. J. Artif. Intell. Res. (JAIR), 22:319-351, 2004.","title":"Towards understanding and harnessing the potential of clause learning","authors":"Paul Beame, Henry A Kautz, Ashish Sabharwal","year":"2004","venue":"J. Artif. Intell. Res. (JAIR)","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Beyersdorff and Böhm, 2021] Olaf Beyersdorff and Ben- jamin Böhm. Understanding the Relative Strength of QBF CDCL Solvers and QBF Resolution. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021), volume 185 of Leibniz International Proceedings in Infor- matics (LIPIcs), pages 12:1-12:20, 2021.","title":"Understanding the Relative Strength of QBF CDCL Solvers and QBF Resolution","authors":"Böhm Beyersdorff, Olaf Beyersdorff, Benjamin Böhm","year":"2021","venue":"12th Innovations in Theoretical Computer Science Conference (ITCS 2021","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Beyersdorff et al., 2019a] Olaf Beyersdorff, Joshua Blinkhorn, and Luke Hinde. Size, cost, and capacity: A semantic technique for hard random QBFs. Logical Methods in Computer Science, 15(1), 2019.","title":"Size, cost, and capacity: A semantic technique for hard random QBFs","authors":"Beyersdorff","year":"2019","venue":"Logical Methods in Computer Science","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Beyersdorff et al., 2019b] Olaf Beyersdorff, Leroy Chew, and Mikolás Janota. New resolution-based QBF calculi and their proof complexity. ACM Transactions on Compu- tation Theory, 11(4):26:1-26:42, 2019.","title":"New resolution-based QBF calculi and their proof complexity","authors":"Beyersdorff","year":"2019","venue":"ACM Transactions on Computation Theory","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Beyersdorff et al., 2021] Olaf Beyersdorff, Mikolás Janota, Florian Lonsing, and Martina Seidl. Quantified boolean formulas. In Armin Biere, Marijn Heule, Hans van Maaren, and Toby Walsh, editors, Handbook of Satisfia- bility, Frontiers in Artificial Intelligence and Applications, pages 1177-1221. IOS Press, 2021.","title":"Quantified boolean formulas","authors":"Beyersdorff","year":"2021","venue":"Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Biere et al., 2021a] Armin Biere, Marijn Heule, Hans van Maaren, and Toby Walsh, editors. Handbook of Satisfia- bility, Frontiers in Artificial Intelligence and Applications. IOS Press, 2021.","title":"Handbook of Satisfiability","authors":"Biere","year":"2021","venue":"Frontiers in Artificial Intelligence and Applications","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Biere et al., 2021b] Armin Biere, Matti Järvisalo, and Ben- jamin Kiesl. Preprocessing in sat solving. In Armin Biere, Marijn Heule, Hans van Maaren, and Toby Walsh, editors, Handbook of Satisfiability, Frontiers in Artificial Intelli- gence and Applications, pages 291-436. IOS Press, 2021.","title":"Preprocessing in sat solving","authors":"Biere","year":"2021","venue":"Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Böhm and Beyersdorff, 2021] Benjamin Böhm and Olaf Beyersdorff. Lower bounds for QCDCL via formula gauge. In Theory and Applications of Satisfiability Test- ing (SAT 2021), pages 47-63. Springer, 2021.","title":"Lower bounds for QCDCL via formula gauge","authors":"Beyersdorff Böhm, Benjamin Böhm, Olaf Beyersdorff","year":"2021","venue":"Theory and Applications of Satisfiability Testing (SAT 2021)","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Buss and Nordström, 2021] Sam Buss and Jakob Nord- ström. Proof complexity and sat solving. In Armin Biere, Marijn Heule, Hans van Maaren, and Toby Walsh, editors, Handbook of Satisfiability, Frontiers in Artificial Intelli- gence and Applications, pages 233-350. IOS Press, 2021. Elffers et al., 2018] Jan Elffers, Jesús Giráldez-Cru, Stephan Gocht, Jakob Nordström, and Laurent Simon. Seeking practical CDCL insights from theoretical SAT benchmarks. In Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence (IJCAI), pages 1300-1308. ijcai.org, 2018.","title":"Seeking practical CDCL insights from theoretical SAT benchmarks","authors":"Nordström ; Buss, Elffers","year":"2018","venue":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence (IJCAI)","doi":null,"url":null,"internal_url":"/proceedings/2018/181"},{"position":12,"raw":"[Janota, 2016] Mikolás Janota. On Q-Resolution and CDCL QBF solving. In Proc. International Conference on The- ory and Applications of Satisfiability Testing (SAT), pages 402-418, 2016.","title":"Mikolás Janota. On Q-Resolution and CDCL QBF solving","authors":"Janota","year":"2016","venue":"Proc. International Conference on Theory and Applications of Satisfiability Testing (SAT)","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Kleine Büning et al., 1995] Hans Kleine Büning, Marek Karpinski, and Andreas Flögel. Resolution for quantified Boolean formulas. Inf. Comput., 117(1):12-18, 1995.","title":"Resolution for quantified Boolean formulas","authors":"Kleine Büning","year":"1995","venue":"Inf. Comput","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Kokkala and Nordström, 2020] Janne I. Kokkala and Jakob Nordström. Using resolution proofs to analyse CDCL solvers. In Principles and Practice of Constraint Program- ming -26th International Conference (CP), pages 427- 444. Springer, 2020.","title":"Using resolution proofs to analyse CDCL solvers","authors":"I Janne, Jakob Kokkala, Nordström","year":"2020","venue":"Principles and Practice of Constraint Programming -26th International Conference (CP)","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Krajíček, 2019] Jan Krajíček. Proof complexity, volume 170 of Encyclopedia of Mathematics and Its Applications. Cambridge University Press, 2019.","title":"Encyclopedia of Mathematics and Its Applications","authors":null,"year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Lonsing and Egly, 2017] Florian Lonsing and Uwe Egly. DepQBF 6.0: A search-based QBF solver beyond tradi- tional QCDCL. In Proc. International Conference on Au- tomated Deduction (CADE), pages 371-384, 2017.","title":"Florian Lonsing and Uwe Egly. DepQBF 6.0: A search-based QBF solver beyond traditional QCDCL","authors":"Egly Lonsing","year":"2017","venue":"Proc. International Conference on Automated Deduction (CADE)","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Lonsing, 2012] Florian Lonsing. Dependency Schemes and Search-Based QBF Solving: Theory and Practice. PhD thesis, Johannes Kepler University Linz, 2012.","title":"Dependency Schemes and Search-Based QBF Solving: Theory and Practice","authors":"Florian Lonsing","year":"2012","venue":null,"doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Marques Silva et al., 2021] João P. Marques Silva, Inês Lynce, and Sharad Malik. Conflict-driven clause learn- ing SAT solvers. In Armin Biere, Marijn Heule, Hans van Maaren, and Toby Walsh, editors, Handbook of Satisfia- bility, Frontiers in Artificial Intelligence and Applications. IOS Press, 2021.","title":"Conflict-driven clause learning SAT solvers","authors":"P Marques João, Inês Silva, Sharad Lynce, Malik","year":"2021","venue":"Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Peitl et al., 2019] Tomás Peitl, Friedrich Slivovsky, and Ste- fan Szeider. Dependency learning for QBF. J. Artif. Intell. Res., 65:180-208, 2019.","title":"Dependency learning for QBF","authors":"Tomás Peitl, Friedrich Slivovsky, Stefan Szeider","year":"2019","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Pipatsrisawat and Darwiche, 2011] Knot Pipatsrisawat and Adnan Darwiche. On the power of clause-learning SAT solvers as resolution engines. Artif. Intell., 175(2):512- 525, 2011.","title":"Knot Pipatsrisawat and Adnan Darwiche. On the power of clause-learning SAT solvers as resolution engines","authors":"Darwiche Pipatsrisawat","year":"2011","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Sakallah and Marques-Silva, 2011] Karem A. Sakallah and João Marques-Silva. Anatomy and empirical evaluation of modern SAT solvers. Bull. EATCS, 103:96-121, 2011.","title":"Anatomy and empirical evaluation of modern SAT solvers","authors":"A Karem, João Sakallah, Marques-Silva","year":"2011","venue":"Bull. EATCS","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Tange, 2011] Ole Tange. GNU parallel: The command-line power tool. login Usenix Mag., 36(1), 2011.","title":"GNU parallel: The command-line power tool","authors":"Ole Tange","year":"2011","venue":"login Usenix Mag","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Vinyals, 2020] Marc Vinyals. Hard examples for common variable decision heuristics. In Proceedings of the AAAI Conference on Artificial Intelligence (AAAI), 2020.","title":"Hard examples for common variable decision heuristics","authors":"Marc Vinyals","year":"2020","venue":"Proceedings of the AAAI Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Zhang and Malik, 2002] Lintao Zhang and Sharad Malik. Conflict driven learning in a quantified Boolean satisfi- ability solver. In Proc. IEEE/ACM International Con- ference on Computer-aided Design (ICCAD), pages 442- 449, 2002.","title":"Conflict driven learning in a quantified Boolean satisfiability solver","authors":"Lintao Zhang, Sharad Malik","year":"2002","venue":"Proc. IEEE/ACM International Conference on Computer-aided Design (ICCAD)","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}