{"type":"ScholarlyArticle","title":"Dynamic Dependency Awareness for QBF","authors":[{"name":"Joshua Blinkhorn","slug":"joshua-blinkhorn","given":"Joshua","family":"Blinkhorn","affiliation":"School of Computing , University of Leeds , UK"},{"name":"Olaf Beyersdorff","slug":"olaf-beyersdorff","given":"Olaf","family":"Beyersdorff","affiliation":"School of Computing , University of Leeds , UK"}],"abstract":"We provide the first proof complexity results for QBF dependency calculi. By showing that the reflexive resolution path dependency scheme admits exponentially shorter Q-resolution proofs on a known family of instances, we answer a question first posed by Slivovsky and Szeider (SAT 2014). Further, we introduce a new calculus in which a dependency scheme is applied dynamically. We demonstrate the further potential of this approach beyond that of the existing static system with an exponential separation.","doi":"10.24963/ijcai.2018/726","url":"https://ijcai.org/proceedings/2018/726","pdf":"https://ijcai.org/proceedings/2018/0726.pdf","markdown":"https://ijcai.org/proceedings/2018/726.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/726","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Sister Conferences Best Papers","track":"Best Sister Conferences","number":726,"pages":{"first":5224,"last":5228},"keywords":["Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving"],"videos":[],"references":[{"position":1,"raw":"[Benedetti and Mangassarian, 2008] Marco Benedetti and Hratch Mangassarian. QBF-based formal verification: Ex- perience and perspectives. JSAT, 5(1-4):133-191, 2008.","title":"Marco Benedetti and Hratch Mangassarian. QBF-based formal verification: Experience and perspectives","authors":"Mangassarian Benedetti","year":"2008","venue":"JSAT","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Beyersdorff and Blinkhorn, 2016] Olaf Beyersdorff and Joshua Blinkhorn. Dependency schemes in QBF calculi: Semantics and soundness. In CP, pages 96-112, 2016.","title":"Dependency schemes in QBF calculi: Semantics and soundness","authors":"Blinkhorn Beyersdorff, Olaf Beyersdorff, Joshua Blinkhorn","year":"2016","venue":"CP","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Beyersdorff et al., 2015] Olaf Beyersdorff, Leroy Chew, and Mikolás Janota. Proof complexity of resolution-based QBF calculi. In STACS, pages 76-89, 2015.","title":"Proof complexity of resolution-based QBF calculi","authors":"Beyersdorff","year":"2015","venue":"STACS","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Beyersdorff et al., 2017a] Olaf Beyersdorff, Leroy Chew, Meena Mahajan, and Anil Shukla. Feasible interpolation for QBF resolution calculi. Logical Methods in Computer Science, 13, 2017.","title":"Feasible interpolation for QBF resolution calculi","authors":"Beyersdorff","year":"2017","venue":"Logical Methods in Computer Science","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Beyersdorff et al., 2017b] Olaf Beyersdorff, Leroy Chew, and Karteek Sreenivasaiah. A game characterisation of tree-like Q-resolution size. Journal of Computer and Sys- tem Sciences, 2017. in press.","title":"A game characterisation of tree-like Q-resolution size","authors":"Beyersdorff","year":"2017","venue":"Journal of Computer and System Sciences","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Beyersdorff et al., 2018] Olaf Beyersdorff, Leroy Chew, Meena Mahajan, and Anil Shukla. Are short proofs nar- row? QBF resolution is not so simple. ACM Transactions on Computational Logic, 19(1):1:1-1:26, 2018.","title":"Are short proofs narrow? QBF resolution is not so simple","authors":"Beyersdorff","year":"2018","venue":"ACM Transactions on Computational Logic","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Buss, 2012] Samuel R. Buss. Towards NP-P via proof com- plexity and search. Annals of Pure and Applied Logic, 163(7):906-917, 2012.","title":"Towards NP-P via proof complexity and search","authors":"R Samuel, Buss","year":"2012","venue":"Annals of Pure and Applied Logic","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Cook and Nguyen, 2010] Stephen A. Cook and Phuong Nguyen. Logical Foundations of Proof Complexity. Cam- bridge University Press, Cambridge, 2010.","title":"Logical Foundations of Proof Complexity","authors":"Stephen A Cook, Phuong Nguyen","year":"2010","venue":null,"doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Cook and Reckhow, 1979] Stephen A. Cook and Robert A. Reckhow. The relative efficiency of propositional proof systems. Journal of Symbolic Logic, 44(1):36-50, 1979.","title":"The relative efficiency of propositional proof systems","authors":"Stephen A Cook, Robert A Reckhow","year":"1979","venue":"Journal of Symbolic Logic","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Egly et al., 2017] Uwe Egly, Martin Kronegger, Florian Lonsing, and Andreas Pfandler. Conformant planning as a case study of incremental QBF solving. Annals of Mathe- matics and Artificial Intelligence, 80(1):21-45, 2017.","title":"Conformant planning as a case study of incremental QBF solving","authors":"Egly","year":"2017","venue":"Annals of Mathematics and Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Giunchiglia et al., 2006] Enrico Giunchiglia, Massimo Nar- izzano, and Armando Tacchella. Clause/term resolution and learning in the evaluation of quantified Boolean for- mulas. Journal of Artificial Intelligence Research, 26:371- 416, 2006.","title":"Clause/term resolution and learning in the evaluation of quantified Boolean formulas","authors":"Enrico Giunchiglia, Massimo Narizzano, Armando Tacchella","year":"2006","venue":"Journal of Artificial Intelligence Research","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Giunchiglia et al., 2009] Enrico Giunchiglia, Paolo Marin, and Massimo Narizzano. Reasoning with quantified Boolean formulas. In Handbook of Satisfiability, pages 761-780. IOS Press, 2009.","title":"Reasoning with quantified Boolean formulas","authors":"Enrico Giunchiglia, Paolo Marin, Massimo Narizzano","year":"2009","venue":"Handbook of Satisfiability","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Janota et al., 2016] Mikolás Janota, William Klieber, Joao Marques-Silva, and Edmund M. Clarke. Solving QBF with counterexample guided refinement. Artificial Intelligence, 234:1-25, 2016.","title":"Solving QBF with counterexample guided refinement","authors":"Janota","year":"2016","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Kleine Büning et al., 1995] Hans Kleine Büning, Marek Karpinski, and Andreas Flögel. Resolution for quanti- fied Boolean formulas. Information and Computation, 117(1):12-18, 1995.","title":"Resolution for quantified Boolean formulas","authors":"Kleine Büning","year":"1995","venue":"Information and Computation","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Kontchakov et al., 2009] Roman Kontchakov, Luca Pulina, Ulrike Sattler, Thomas Schneider, Petra Selmer, Frank Wolter, and Michael Zakharyaschev. Minimal module ex- traction from DL-lite ontologies using QBF solvers. In IJCAI, pages 836-841. AAAI Press, 2009.","title":"Minimal module extraction from DL-lite ontologies using QBF solvers","authors":"Kontchakov","year":"2009","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2009/143"},{"position":16,"raw":"[Liang et al., 2015] Jia Hui Liang, Vijay Ganesh, Ed Zulkoski, Atulan Zaman, and Krzysztof Czar- necki. Understanding VSIDS branching heuristics in conflict-driven clause-learning SAT solvers. In Haifa Verification Conference, pages 225-241, 2015.","title":"Understanding VSIDS branching heuristics in conflict-driven clause-learning SAT solvers","authors":"Jia Hui Liang, Vijay Ganesh, Ed Zulkoski, Atulan Zaman, Krzysztof Czarnecki","year":"2015","venue":"Haifa Verification Conference","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Lonsing and Biere, 2010] Florian Lonsing and Armin Biere. DepQBF: A dependency-aware QBF solver. JSAT, 7(2-3):71-76, 2010.","title":"Florian Lonsing and Armin Biere. DepQBF: A dependency-aware QBF solver","authors":"Biere Lonsing","year":"2010","venue":"JSAT","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Lonsing, 2012] Florian Lonsing. Dependency Schemes and Search-Based QBF Solving: Theory and Practice. PhD thesis, Johannes Kepler University, 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":19,"raw":"[Moskewicz et al., 2001] Matthew W. Moskewicz, Conor F. Madigan, Ying Zhao, Lintao Zhang, and Sharad Malik. Chaff: Engineering an efficient SAT solver. In Design Au- tomation Conference, pages 530-535, 2001.","title":"Chaff: Engineering an efficient SAT solver","authors":"Matthew W Moskewicz, F Conor, Ying Madigan, Lintao Zhao, Sharad Zhang, Malik","year":"2001","venue":"Design Automation Conference","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Peitl et al., 2016] Tomás Peitl, Friedrich Slivovsky, and Ste- fan Szeider. Long distance Q-resolution with dependency schemes. In SAT, pages 500-518, 2016.","title":"Long distance Q-resolution with dependency schemes","authors":"Tomás Peitl, Friedrich Slivovsky, Stefan Szeider","year":"2016","venue":"SAT","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Rintanen, 2007] Jussi Rintanen. Asymptotically optimal en- codings of conformant planning in QBF. In AAAI, pages 1045-1050. AAAI Press, 2007.","title":"Asymptotically optimal encodings of conformant planning in QBF","authors":"Jussi Rintanen","year":"2007","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Samer and Szeider, 2009] Marko Samer and Stefan Szeider. Backdoor sets of quantified Boolean formulas. Journal of Automated Reasoning, 42(1):77-97, 2009.","title":"Backdoor sets of quantified Boolean formulas","authors":"Marko Samer, Stefan Szeider","year":"2009","venue":"Journal of Automated Reasoning","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Samulowitz and Bacchus, 2005] Horst Samulowitz and Fahiem Bacchus. Using SAT in QBF. In CP, pages 578-592, 2005.","title":"Horst Samulowitz and Fahiem Bacchus. Using SAT in QBF","authors":"Bacchus Samulowitz","year":"2005","venue":"CP","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Shacham and Zarpas, 2003] Ohad Shacham and Emmanuel Zarpas. Tuning the VSIDS decision heuristic for bounded model checking. In International Workshop on Micropro- cessor Test and Verification, page 75, 2003.","title":"Tuning the VSIDS decision heuristic for bounded model checking","authors":"Zarpas Shacham, Ohad Shacham, Emmanuel Zarpas","year":"2003","venue":"International Workshop on Microprocessor Test and Verification","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Silva and Sakallah, 1996] João P. Marques Silva and Karem A. Sakallah. GRASP -a new search algorithm for satisfiability. In ICCAD, pages 220-227, 1996.","title":"GRASP -a new search algorithm for satisfiability","authors":"P Marques João, Karem A Silva, Sakallah","year":"1996","venue":"ICCAD","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Silva, 1999] João P. Marques Silva. The impact of branch- ing heuristics in propositional satisfiability algorithms. In EPIA, pages 62-74, 1999.","title":"The impact of branching heuristics in propositional satisfiability algorithms","authors":"P Marques João, Silva","year":"1999","venue":"EPIA","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Slivovsky and Szeider, 2016] Friedrich Slivovsky and Ste- fan Szeider. Soundness of Q-resolution with dependency schemes. Theoretical Computer Science, 612:83-101, 2016.","title":"Friedrich Slivovsky and Stefan Szeider. Soundness of Q-resolution with dependency schemes","authors":"Szeider Slivovsky","year":"2016","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Slivovsky, 2015] Friedrich Slivovsky. Structure in #SAT and QBF. PhD thesis, Vienna University of Technology, 2015.","title":"Structure in #SAT and QBF","authors":"Slivovsky","year":"2015","venue":null,"doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Van Gelder, 2011] Allen Van Gelder. Variable indepen- dence and resolution paths for quantified Boolean formu- las. In CP, pages 789-803, 2011.","title":"Variable independence and resolution paths for quantified Boolean formulas","authors":"Allen Van Gelder","year":"2011","venue":"CP","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Zhang and Malik, 2002] Lintao Zhang and Sharad Malik. Conflict driven learning in a quantified Boolean satisfia- bility solver. In ICCAD, pages 442-449, 2002.","title":"Conflict driven learning in a quantified Boolean satisfiability solver","authors":"Lintao Zhang, Sharad Malik","year":"2002","venue":"ICCAD","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}