{"type":"ScholarlyArticle","title":"Core-Guided Minimal Correction Set and Core Enumeration","authors":[{"name":"Nina Narodytska","slug":"nina-narodytska","given":"Nina","family":"Narodytska","affiliation":"VMware Research , USA"},{"name":"Nikolaj Bjørner","slug":"nikolaj-bj-rner","given":"Nikolaj","family":"Bjørner","affiliation":"Microsoft Research , USA"},{"name":"Maria-Cristina Marinescu","slug":"maria-cristina-marinescu","given":"Maria-Cristina","family":"Marinescu","affiliation":"Barcelona Supercomputing Center , Spain"},{"name":"Mooly Sagiv","slug":"mooly-sagiv","given":"Mooly","family":"Sagiv","affiliation":"VMware Research , USA; Tel Aviv University , Israel"}],"abstract":"A set of constraints is unsatisfiable if there is no solution that satisfies these constraints. To analyse unsatisfiable problems, the user needs to understand where inconsistencies come from and how they can be repaired. Minimal unsatisfiable cores and correction sets are important subsets of constraints that enable such analysis. In this work, we propose a new algorithm for extracting minimal unsatisfiable cores and correction sets simultaneously. Building on top of the relaxation and strengthening framework, we introduce novel techniques for extracting these sets. Our new solver significantly outperforms several state of the art algorithms on common benchmarks when it comes to extracting correction sets and compares favorably on core extraction.","doi":"10.24963/ijcai.2018/188","url":"https://ijcai.org/proceedings/2018/188","pdf":"https://ijcai.org/proceedings/2018/0188.pdf","markdown":"https://ijcai.org/proceedings/2018/188.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/188","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":"Constraints and SAT","track":"Main track","number":188,"pages":{"first":1353,"last":1361},"keywords":["Constraints and SAT: SAT","Constraints and SAT: Constraints and SAT","Constraints and SAT: MaxSAT, MinSAT"],"videos":[],"references":[{"position":1,"raw":"[Alviano et al., 2015] Mario Alviano, Carmine Dodaro, and Francesco Ricca. A maxsat algorithm using cardinality constraints of bounded size. In Proceedings of the Twenty- Fourth International Joint Conference on Artificial Intelli- gence, IJCAI 2015, pages 2677-2683. AAAI Press, 2015.","title":"A maxsat algorithm using cardinality constraints of bounded size","authors":"Mario Alviano, Carmine Dodaro, Francesco Ricca","year":"2015","venue":"Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015","doi":null,"url":null,"internal_url":"/proceedings/2015/379"},{"position":2,"raw":"[Alviano, 2017a] Mario Alviano. Circumscriptino. https://alviano.com/software/circumscriptino/, 2017.","title":"Circumscriptino","authors":"Alviano","year":"2017","venue":null,"doi":null,"url":"https://alviano.com/software/circumscriptino/","internal_url":null},{"position":3,"raw":"[Alviano, 2017b] Mario Alviano. Model enumeration in propositional circumscription via unsatisfiable core analy- sis. TPLP, 17(5-6):708-725, 2017.","title":"Model enumeration in propositional circumscription via unsatisfiable core analysis","authors":"Mario Alviano, Alviano","year":"2017","venue":"TPLP","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Andres et al., 2012] Benjamin Andres, Benjamin Kaufmann, Oliver Matheis, and Torsten Schaub. Unsatisfiability-based optimization in clasp. In Technical Communications of the 28th International Conference on Logic Programming, ICLP 2012, volume 17, pages 211-221, 2012.","title":"Unsatisfiability-based optimization in clasp","authors":"Benjamin Andres, Benjamin Kaufmann, Oliver Matheis, Torsten Schaub","year":"2012","venue":"Technical Communications of the 28th International Conference on Logic Programming, ICLP","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Bacchus and Katsirelos, 2015] Fahiem Bacchus and George Katsirelos. Using minimal correction sets to more effi- ciently compute minimal unsatisfiable sets. In Computer Aided Verification -27th International Conference, CAV 2015, July 18-24, 2015, volume 9207, pages 70-86, 2015.","title":"Fahiem Bacchus and George Katsirelos. Using minimal correction sets to more efficiently compute minimal unsatisfiable sets","authors":"Katsirelos Bacchus","year":"2015","venue":"Computer Aided Verification -27th International Conference","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Bacchus and Katsirelos, 2016] Fahiem Bacchus and George Katsirelos. Finding a collection of muses incrementally. In Integration of AI and OR Techniques in Constraint Pro- gramming -13th International Conference, CPAIOR 2016, volume 9676, pages 35-44, 2016.","title":"Fahiem Bacchus and George Katsirelos. Finding a collection of muses incrementally","authors":"Katsirelos Bacchus","year":"2016","venue":"Integration of AI and OR Techniques in Constraint Programming -13th International Conference","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Bacchus and Narodytska, 2014] Fahiem Bacchus and Nina Narodytska. Cores in core based maxsat algorithms: An analysis. In Theory and Applications of Satisfiability Test- ing -SAT 2014 -17th International Conference, Held as Part of the Vienna Summer of Logic, VSL 2014, volume 8561, pages 7-15, 2014.","title":"Fahiem Bacchus and Nina Narodytska. Cores in core based maxsat algorithms: An analysis","authors":"Narodytska Bacchus","year":"2014","venue":"Theory and Applications of Satisfiability Testing -SAT 2014 -17th International Conference, Held as Part of the Vienna Summer of Logic","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Bacchus et al., 2014] Fahiem Bacchus, Jessica Davies, Maria Tsimpoukelli, and George Katsirelos. Relaxation search: A simple way of managing optional clauses. In Proceedings of the Twenty-Eighth AAAI Conference on Ar- tificial Intelligence, 2014, pages 835-841, 2014.","title":"Relaxation search: A simple way of managing optional clauses","authors":"Bacchus","year":"2014","venue":"Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Belov and Marques-Silva, 2011] Anton Belov and Joao Marques-Silva. Accelerating MUS extraction with recur- sive model rotation. In International Conference on Formal Methods in Computer-Aided Design, FMCAD '11, 2011, pages 37-40. FMCAD Inc., 2011.","title":"Accelerating MUS extraction with recursive model rotation","authors":"Marques-Silva ; Belov, Anton Belov, Joao Marques-Silva","year":"2011","venue":"International Conference on Formal Methods in Computer-Aided Design","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Belov and Marques-Silva, 2012] Anton Belov and Joao Marques-Silva. Muser2: An efficient MUS extractor. JSAT, 8(3/4):123-128, 2012.","title":"Muser2: An efficient MUS extractor","authors":"Marques-Silva ; Belov, Anton Belov, Joao Marques-Silva","year":"2012","venue":"JSAT","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Belov et al., 2012] Anton Belov, Ines Lynce, and Joao Marques-Silva. Towards efficient MUS extraction. AI Commun., 25(2):97-116, 2012.","title":"Towards efficient MUS extraction","authors":"Anton Belov, Ines Lynce, Joao Marques-Silva","year":"2012","venue":"AI Commun","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Fu and Malik, 2006] Zhaohui Fu and Sharad Malik. On solv- ing the partial MAX-SAT problem. In Theory and Applica- tions of Satisfiability Testing -SAT 2006, 9th International Conference, 2006, volume 4121, pages 252-265, 2006.","title":"On solving the partial MAX-SAT problem","authors":"Zhaohui Fu, Sharad Malik","year":"2006","venue":"Theory and Applications of Satisfiability Testing -SAT 2006, 9th International Conference","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Janota, 2013] Mikoas Janota. The MiFuMaX solver. http://sat.inesc-id.pt/ mikolas/sw/mifumax/, 2013.","title":"Mikoas Janota. The MiFuMaX solver","authors":"Janota","year":"2013","venue":null,"doi":null,"url":"http://sat.inesc-id.pt/mikolas/sw/mifumax/,2013","internal_url":null},{"position":14,"raw":"[Jarvisalo et al., 2011] Matti Jarvisalo, Daniel Le Berre, Joao Marques-Silva, and Olivier Rous- sel. The MUS track of the 2011 SAT competition. http://www.satcompetition.org/2011/, 2011.","title":"The MUS track of the 2011 SAT competition","authors":"Matti Jarvisalo, Daniel Le Berre, Joao Marques-Silva, Olivier Roussel","year":null,"venue":null,"doi":null,"url":"http://www.satcompetition.org/2011/,2011","internal_url":null},{"position":15,"raw":"[Junker, 2004] Ulrich Junker. QUICKXPLAIN: preferred explanations and relaxations for over-constrained problems. In Proceedings of the Nineteenth National Conference on Artificial Intelligence, pages 167-172, 2004.","title":"QUICKXPLAIN: preferred explanations and relaxations for over-constrained problems","authors":"Ulrich Junker, Junker","year":"2004","venue":"Proceedings of the Nineteenth National Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Liffiton and Sakallah, 2008a] Mark H. Liffiton and Karem A. Sakallah. Algorithms for computing minimal unsatisfiable subsets of constraints. J. Autom. Reasoning, 40(1):1-33, 2008.","title":"Algorithms for computing minimal unsatisfiable subsets of constraints","authors":"Liffiton, H Sakallah ; Mark, Karem A Liffiton, Sakallah","year":"2008","venue":"J. Autom. Reasoning","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Liffiton and Sakallah, 2008b] Mark H. Liffiton and Karem A. Sakallah. Reveal: A formal verification tool for verilog designs. In Logic for Programming, Artificial Intelligence, and Reasoning, 15th International Conference, LPAR 2008, Doha, Qatar, November 22-27, 2008, volume 5330, pages 343-352, 2008.","title":"Reveal: A formal verification tool for verilog designs","authors":"Liffiton, H Sakallah ; Mark, Karem A Liffiton, Sakallah","year":"2008","venue":"Logic for Programming, Artificial Intelligence, and Reasoning, 15th International Conference, LPAR 2008","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Liffiton and Sakallah, 2009] Mark H. Liffiton and Karem A. Sakallah. Generalizing core-guided max-sat. In Theory and Applications of Satisfiability Testing -SAT 2009, 12th International Conference, SAT 2009, volume 5584, pages 481-494. Springer, 2009.","title":"Generalizing core-guided max-sat","authors":"H Mark, Karem A Liffiton, Sakallah","year":"2009","venue":"Theory and Applications of Satisfiability Testing -SAT 2009, 12th International Conference","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Liffiton et al., 2016] Mark H. Liffiton, Alessandro Previti, Ammar Malik, and Joao Marques-Silva. Fast, flexible MUS enumeration. Constraints, 21(2):223-250, 2016.","title":"Fast, flexible MUS enumeration","authors":"H Mark, Alessandro Liffiton, Ammar Previti, Joao Malik, Marques-Silva","year":"2016","venue":"Constraints","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Marques-Silva and Planes, 2008] Joao Marques-Silva and Jordi Planes. Algorithms for maximum satisfiability us- ing unsatisfiable cores. In Design, Automation and Test in Europe, DATE 2008, Munich, Germany, March 10-14, 2008, pages 408-413. ACM, 2008.","title":"Algorithms for maximum satisfiability using unsatisfiable cores","authors":"Joao Marques, - Silva, Jordi Planes","year":"2008","venue":"Design, Automation and Test in Europe, DATE 2008","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Marques-Silva et al., 2013] Joao Marques-Silva, Federico Heras, Mikolas Janota, Alessandro Previti, and Anton Belov. On computing minimal correction subsets. In IJCAI 2013, Proceedings of the 23rd International Joint Confer- ence on Artificial Intelligence 2013, pages 615-622, 2013.","title":"On computing minimal correction subsets","authors":"Joao Marques-Silva, Federico Heras, Mikolas Janota, Alessandro Previti, Anton Belov","year":"2013","venue":"Proceedings of the 23rd International Joint Conference on Artificial Intelligence 2013","doi":null,"url":null,"internal_url":"/proceedings/2013/98"},{"position":22,"raw":"[Morgado et al., 2012] Antonio Morgado, Mark H. Liffiton, and Joao Marques-Silva. Maxsat-based MCS enumeration. In HVC 2012, Haifa, Israel, November 6-8, 2012. Revised Selected Papers, volume 7857, pages 86-101. Springer, 2012.","title":"Maxsat-based MCS enumeration","authors":"Antonio Morgado, Mark H Liffiton, Joao Marques-Silva","year":"2012","venue":"HVC 2012","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Narodytska and Bacchus, 2014] Nina Narodytska and Fahiem Bacchus. Maximum satisfiability using core- guided maxsat resolution. In Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence, 2014., pages 2717-2723. AAAI Press, 2014.","title":"Nina Narodytska and Fahiem Bacchus. Maximum satisfiability using coreguided maxsat resolution","authors":"Bacchus Narodytska","year":"2014","venue":"Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Previti et al., 2017] Alessandro Previti, Carlos Mencia, Matti Jarvisalo, and Joao Marques-Silva. Improving MCS enumeration via caching. In Theory and Applications of Satisfiability Testing -SAT 2017 -20th International Con- ference, 2017, volume 10491, pages 184-194, 2017.","title":"Improving MCS enumeration via caching","authors":"Alessandro Previti, Carlos Mencia, Matti Jarvisalo, Joao Marques-Silva","year":"2017","venue":"Theory and Applications of Satisfiability Testing -SAT 2017 -20th International Conference","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Previti et al., 2018] Alessandro Previti, Carlos Mencia, Matti Jarvisalo, and Joao Marques-Silva. Premise set caching for enumerating minimal correction subsets. In Proceedings of the Thirty-Second AAAI Conference on Ar- tificial Intelligence, 2018, 2018.","title":"Premise set caching for enumerating minimal correction subsets","authors":"Alessandro Previti, Carlos Mencia, Matti Jarvisalo, Joao Marques-Silva","year":"2018","venue":"Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Reiter, 1987] Raymond Reiter. A theory of diagnosis from first principles. Artif. Intell., 32(1):57-95, 1987.","title":"A theory of diagnosis from first principles","authors":"Raymond Reiter","year":"1987","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Schulz, 2013] Stephan Schulz. Simple and efficient clause subsumption with feature vector indexing. In Automated Reasoning and Mathematics -Essays in Memory of William W. McCune, volume 7788, pages 45-67, 2013.","title":"Simple and efficient clause subsumption with feature vector indexing","authors":"Stephan Schulz","year":"2013","venue":"Automated Reasoning and Mathematics -Essays in Memory of William W. McCune","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Tessil, 2017] Thibaut Tessil. A C++ implemen- tation of a fast and memory efficient HAT-trie. https://github.com/Tessil/hat-trie/, 2017.","title":"A C++ implementation of a fast and memory efficient HAT-trie","authors":"Thibaut Tessil","year":null,"venue":null,"doi":null,"url":"https://github.com/Tessil/hat-trie/,2017","internal_url":null},{"position":29,"raw":"[Zhao and Liffiton, 2016] Wenting Zhao and Mark H. Liffi- ton. Parallelizing partial MUS enumeration. In 28th IEEE International Conference on Tools with Artificial Intelli- gence, ICTAI 2016, pages 464-471. IEEE Computer Soci- ety, 2016.","title":"Parallelizing partial MUS enumeration","authors":"Wenting Zhao, H Mark","year":"2016","venue":"28th IEEE International Conference on Tools with Artificial Intelligence, ICTAI 2016","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Zielke and Kaufmann, 2015] Christian Zielke and Michael Kaufmann. A new approach to partial MUS enumeration. In Theory and Applications of Satisfiability Testing -SAT 2015 -18th International Conference, 2015, volume 9340, pages 387-404, 2015.","title":"Christian Zielke and Michael Kaufmann. A new approach to partial MUS enumeration","authors":"Kaufmann Zielke","year":"2015","venue":"Theory and Applications of Satisfiability Testing -SAT 2015 -18th International Conference","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}