{"type":"ScholarlyArticle","title":"Lower Bounds for Approximate Knowledge Compilation","authors":[{"name":"Alexis de Colnet","slug":"alexis-de-colnet","given":"Alexis","family":"de Colnet","affiliation":"CNRS & Univ Artois"},{"name":"Stefan Mengel","slug":"stefan-mengel","given":"Stefan","family":"Mengel","affiliation":"CNRS & Univ Artois"}],"abstract":"Knowledge compilation studies the trade-off between succinctness and efficiency of different representation languages. For many languages, there are known strong lower bounds on the representation size, but recent work shows that, for some languages, one can bypass these bounds using approximate compilation. The idea is to compile an approximation of the knowledge for which the number of errors can be controlled. We focus on circuits in deterministic decomposable negation normal form (d-DNNF), a compilation language suitable in contexts such as probabilistic reasoning, as it supports efficient model counting and probabilistic inference. Moreover, there are known size lower bounds for d-DNNF which by relaxing to approximation one might be able to avoid. In this paper we formalize two notions of approximation: weak approximation which has been studied before in the decision diagram literature and strong approximation which has been used in recent algorithmic results. We then show lower bounds for approximation by d-DNNF, complementing the positive results from the literature.","doi":"10.24963/ijcai.2020/254","url":"https://ijcai.org/proceedings/2020/254","pdf":"https://ijcai.org/proceedings/2020/0254.pdf","markdown":"https://ijcai.org/proceedings/2020/254.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/254","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Knowledge Representation and Reasoning","track":"Main track","number":254,"pages":{"first":1834,"last":1840},"keywords":["Knowledge Representation and Reasoning: Automated Reasoning; Tractable Languages and Knowledge compilation"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/24707/file_24707.m3u8","length_sec":291,"provider":"hls"}],"references":[{"position":1,"raw":"[Beame and Liew, 2015] Paul Beame and Vincent Liew. New Limits for Knowledge Compilation and Applications to Exact Model Counting. In Conference on Uncertainty in Artificial Intelligence, UAI, pages 131-140, 2015.","title":"New Limits for Knowledge Compilation and Applications to Exact Model Counting","authors":"Liew Beame, Paul Beame, Vincent Liew","year":"2015","venue":"Conference on Uncertainty in Artificial Intelligence, UAI","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Beame et al., 2017] Paul Beame, Jerry Li, Sudeepa Roy, and Dan Suciu. Exact Model Counting of Query Expres- sions: Limitations of Propositional Methods. ACM Trans. Database Syst., 42(1):1:1-1:46, 2017.","title":"Exact Model Counting of Query Expressions: Limitations of Propositional Methods","authors":"Paul Beame, Jerry Li, Sudeepa Roy, Dan Suciu","year":"2017","venue":"ACM Trans. Database Syst","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Biere et al., 2009] Armin Biere, Marijn Heule, Hans van Maaren, and Toby Walsh, editors. Handbook of Satisfi- ability, volume 185 of Frontiers in Artificial Intelligence and Applications. IOS Press, 2009.","title":"Handbook of Satisfiability","authors":"Biere","year":"2009","venue":"Frontiers in Artificial Intelligence and Applications","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Bollig et al., 2002] Beate Bollig, Martin Sauerhoff, and Ingo Wegener. On the Nonapproximability of Boolean Functions by OBDDs and Read-k-Times Branching Pro- grams. Inf. Comput., 178(1):263-278, 2002.","title":"On the Nonapproximability of Boolean Functions by OBDDs and Read-k-Times Branching Programs","authors":"Bollig","year":"2002","venue":"Inf. Comput","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Bova et al., 2016] Simone Bova, Florent Capelli, Stefan Mengel, and Friedrich Slivovsky. Knowledge Compilation Meets Communication Complexity. In International Joint Conference on Artificial Intelligence, IJCAI, pages 1008- 1014, 2016.","title":"Knowledge Compilation Meets Communication Complexity","authors":"Simone Bova, Florent Capelli, Stefan Mengel, Friedrich Slivovsky","year":"2016","venue":"International Joint Conference on Artificial Intelligence, IJCAI","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Bryant, 1986] Randal E. Bryant. Graph-Based Algorithms for Boolean Function Manipulation. IEEE Trans. Comput- ers, 35(8):677-691, 1986.","title":"Graph-Based Algorithms for Boolean Function Manipulation","authors":"Randal E Bryant","year":"1986","venue":"IEEE Trans. Computers","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Capelli, 2017] Florent Capelli. Understanding the complex- ity of #SAT using knowledge compilation. In ACM/IEEE Symposium on Logic in Computer Science, LICS, pages 1-10, 2017.","title":"Understanding the complexity of #SAT using knowledge compilation","authors":"Florent Capelli","year":"2017","venue":"ACM/IEEE Symposium on Logic in Computer Science, LICS","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Chan and Darwiche, 2003] Hei Chan and Adnan Darwiche. Reasoning about Bayesian Network Classifiers. In Confer- ence in Uncertainty in Artificial Intelligence, UAI, pages 107-115, 2003.","title":"Reasoning about Bayesian Network Classifiers","authors":"Chan, Darwiche ;, Hei Chan, Adnan Darwiche","year":"2003","venue":"Conference in Uncertainty in Artificial Intelligence, UAI","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Choi et al., 2013] Arthur Choi, Doga Kisa, and Adnan Dar- wiche. Compiling Probabilistic Graphical Models Using Sentential Decision Diagrams. In Symbolic and Quan- titative Approaches to Reasoning with Uncertainty, EC- SQARU, volume 7958, pages 121-132, 2013.","title":"Compiling Probabilistic Graphical Models Using Sentential Decision Diagrams","authors":"Arthur Choi, Doga Kisa, Adnan Darwiche","year":"2013","venue":"Symbolic and Quantitative Approaches to Reasoning with Uncertainty","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Chubarian and Turán, 2020] Karine Chubarian and György Turán. Interpretability of Bayesian Network Classifiers: OBDD Approximation and Polynomial Threshold Func- tions. In International Symposium on Artificial Intelli- gence and Mathematics, ISAIM, 2020.","title":"Interpretability of Bayesian Network Classifiers: OBDD Approximation and Polynomial Threshold Functions","authors":"Turán Chubarian, Karine Chubarian, György Turán","year":"2020","venue":"International Symposium on Artificial Intelligence and Mathematics","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Darwiche and Marquis, 2002] Adnan Darwiche and Pierre Marquis. A Knowledge Compilation Map. J. Artif. Intell. Res., 17:229-264, 2002.","title":"A Knowledge Compilation Map","authors":"Adnan Darwiche, Pierre Marquis","year":"2002","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Darwiche, 2001] Adnan Darwiche. On the Tractable Count- ing of Theory Models and its Application to Truth Main- tenance and Belief Revision. Journal of Applied Non- Classical Logics, 11(1-2):11-34, 2001.","title":"On the Tractable Counting of Theory Models and its Application to Truth Maintenance and Belief Revision","authors":"Adnan Darwiche","year":"2001","venue":"Journal of Applied Non-Classical Logics","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Darwiche, 2004] Adnan Darwiche. New Advances in Com- piling CNF into Decomposable Negation Normal Form. In European Conference on Artificial Intelligence, ECAI, pages 328-332, 2004.","title":"New Advances in Compiling CNF into Decomposable Negation Normal Form","authors":"Adnan Darwiche","year":"2004","venue":"European Conference on Artificial Intelligence, ECAI","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Darwiche, 2011] Adnan Darwiche. SDD: A New Canoni- cal Representation of Propositional Knowledge Bases. In International Joint Conference on Artificial Intelligence, IJCAI, pages 819-826, 2011.","title":"SDD: A New Canonical Representation of Propositional Knowledge Bases","authors":"Adnan Darwiche, Darwiche","year":"2011","venue":"International Joint Conference on Artificial Intelligence, IJCAI","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Duris et al., 2004] Pavol Duris, Juraj Hromkovic, Stasys Jukna, Martin Sauerhoff, and Georg Schnitger. On multi-partition communication complexity. Inf. Comput., 194(1):49-75, 2004.","title":"On multi-partition communication complexity","authors":"Duris","year":"2004","venue":"Inf. Comput","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Gopalan et al., 2011] Parikshit Gopalan, Adam R. Klivans, Raghu Meka, Daniel Stefankovic, Santosh S. Vempala, and Eric Vigoda. An FPTAS for #Knapsack and Related Counting Problems. In IEEE Symposium on Foundations of Computer Science, FOCS, pages 817-826, 2011.","title":"An FPTAS for #Knapsack and Related Counting Problems","authors":"Parikshit Gopalan, Adam R Klivans, Raghu Meka, Daniel Stefankovic, Santosh S Vempala, Eric Vigoda","year":"2011","venue":"IEEE Symposium on Foundations of Computer Science, FOCS","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Krause et al., 1999] Matthias Krause, Petr Savický, and Ingo Wegener. Approximations by OBDDs and the Vari- able Ordering Problem. In International Colloquium Au- tomata, Languages and Programming, ICALP, pages 493- 502, 1999.","title":"Approximations by OBDDs and the Variable Ordering Problem","authors":"Krause","year":"1999","venue":"International Colloquium Automata, Languages and Programming, ICALP","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Kushilevitz and Nisan, 1997] Eyal Kushilevitz and Noam Nisan. Communication complexity. Cambridge University Press, 1997.","title":"Communication complexity","authors":"Eyal Kushilevitz, Noam Nisan","year":"1997","venue":null,"doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Lagniez and Marquis, 2017] Jean-Marie Lagniez and Pierre Marquis. An Improved Decision-DNNF Compiler. In In- ternational Joint Conference on Artificial Intelligence, IJ- CAI, pages 667-673, 2017.","title":"An Improved Decision-DNNF Compiler","authors":"Marquis ; Jean-Marie Lagniez, Pierre Lagniez, Marquis","year":"2017","venue":"ternational Joint Conference on Artificial Intelligence, IJ-CAI","doi":null,"url":null,"internal_url":"/proceedings/2017/93"},{"position":20,"raw":"[Mengel, 2016] Stefan Mengel. Parameterized Compilation Lower Bounds for Restricted CNF-Formulas. In Interna- tional Conference Theory and Applications of Satisfiability Testing, SAT, pages 3-12, 2016.","title":"Parameterized Compilation Lower Bounds for Restricted CNF-Formulas","authors":"Stefan Mengel","year":"2016","venue":"International Conference Theory and Applications of Satisfiability Testing","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Muise et al., 2012] Christian J. Muise, Sheila A. McIlraith, J. Christopher Beck, and Eric I. Hsu. Dsharp: Fast d- DNNF Compilation with sharpSAT. In Canadian Confer- ence on Artificial Intelligence, pages 356-361, 2012.","title":"Dsharp: Fast d-DNNF Compilation with sharpSAT","authors":"Christian J Muise, Sheila A Mcilraith, J Christopher Beck, Eric I Hsu","year":"2012","venue":"Canadian Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Oztok and Darwiche, 2015] Umut Oztok and Adnan Dar- wiche. A Top-Down Compiler for Sentential Decision Di- agrams. In International Joint Conference on Artificial In- telligence, IJCAI, pages 3141-3148, 2015.","title":"Umut Oztok and Adnan Darwiche. A Top-Down Compiler for Sentential Decision Diagrams","authors":"Darwiche Oztok","year":"2015","venue":"International Joint Conference on Artificial Intelligence, IJCAI","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Pipatsrisawat and Darwiche, 2010] Thammanit Pipatsri- sawat and Adnan Darwiche. A Lower Bound on the Size of Decomposable Negation Normal Form. In AAAI Con- ference on Artificial Intelligence, AAAI, pages 345-350, 2010.","title":"Thammanit Pipatsrisawat and Adnan Darwiche. A Lower Bound on the Size of Decomposable Negation Normal Form","authors":"Darwiche Pipatsrisawat","year":"2010","venue":"AAAI Conference on Artificial Intelligence, AAAI","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Selman and Kautz, 1996] Bart Selman and Henry A. Kautz. Knowledge Compilation and Theory Approximation. J. ACM, 43(2):193-224, 1996.","title":"Knowledge Compilation and Theory Approximation","authors":"Kautz Selman, Bart Selman, Henry A Kautz","year":"1996","venue":"J. ACM","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Shih et al., 2019] Andy Shih, Arthur Choi, and Adnan Dar- wiche. Compiling Bayesian Network Classifiers into De- cision Graphs. In AAAI Conference on Artificial Intelli- gence, AAAI, pages 7966-7974, 2019.","title":"Compiling Bayesian Network Classifiers into Decision Graphs","authors":"Andy Shih, Arthur Choi, Adnan Darwiche","year":"2019","venue":"AAAI Conference on Artificial Intelligence, AAAI","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Takenaga et al., 1997] Yasuhiko Takenaga, Mitsushi Nouzoe, and Shuzo Yajima. Size and Variable Ordering of OBDDs Representing Treshold Functions. In Inter- national Conference on Computing and Combinatorics, COCOON, pages 91-100, 1997.","title":"Size and Variable Ordering of OBDDs Representing Treshold Functions","authors":"Yasuhiko Takenaga, Mitsushi Nouzoe, Shuzo Yajima","year":"1997","venue":"International Conference on Computing and Combinatorics, COCOON","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}