{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T04:24:22Z","timestamp":1743049462318,"version":"3.40.3"},"publisher-location":"Cham","reference-count":38,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030802226"},{"type":"electronic","value":"9783030802233"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-80223-3_10","type":"book-chapter","created":{"date-parts":[[2021,7,1]],"date-time":"2021-07-01T14:13:49Z","timestamp":1625148829000},"page":"134-151","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Weighted Model Counting Without Parameter Variables"],"prefix":"10.1007","author":[{"given":"Paulius","family":"Dilkas","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vaishak","family":"Belle","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,7,2]]},"reference":[{"key":"10_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"376","DOI":"10.1007\/978-3-319-59776-8_30","volume-title":"Integration of AI and OR Techniques in Constraint Programming","author":"M Abseher","year":"2017","unstructured":"Abseher, M., Musliu, N., Woltran, S.: htd \u2013 a free, open-source framework for\u00a0(customized) tree decompositions and\u00a0beyond. In: Salvagnin, D., Lombardi, M. (eds.) CPAIOR 2017. LNCS, vol. 10335, pp. 376\u2013386. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-59776-8_30"},{"issue":"2\/3","key":"10_CR2","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1023\/A:1008699807402","volume":"10","author":"RI Bahar","year":"1997","unstructured":"Bahar, R.I., et al.: Algebraic decision diagrams and their applications. Formal Methods Syst. Des. 10(2\/3), 171\u2013206 (1997). https:\/\/doi.org\/10.1023\/A:1008699807402","journal-title":"Formal Methods Syst. Des."},{"key":"10_CR3","doi-asserted-by":"publisher","unstructured":"Bart, A., Koriche, F., Lagniez, J., Marquis, P.: An improved CNF encoding scheme for probabilistic inference. In: Kaminka, G.A., ET AL. (eds.) ECAI 2016\u201322nd European Conference on Artificial Intelligence, 29 August-2 September 2016, The Hague, The Netherlands - Including Prestigious Applications of Artificial Intelligence (PAIS 2016). Frontiers in Artificial Intelligence and Applications, vol. 285, pp. 613\u2013621. IOS Press (2016). https:\/\/doi.org\/10.3233\/978-1-61499-672-9-613","DOI":"10.3233\/978-1-61499-672-9-613"},{"key":"10_CR4","unstructured":"Belle, V.: Open-universe weighted model counting. In: Singh, S.P., Markovitch, S. (eds.) Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, San Francisco, California, USA, 4\u20139 February 2017, pp. 3701\u20133708. AAAI Press (2017). http:\/\/aaai.org\/ocs\/index.php\/AAAI\/AAAI17\/paper\/view\/15008"},{"key":"10_CR5","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/j.ijar.2020.08.001","volume":"126","author":"V Belle","year":"2020","unstructured":"Belle, V., De Raedt, L.: Semiring programming: a semantic framework for generalized sum product problems. Int. J. Approx. Reason. 126, 181\u2013201 (2020). https:\/\/doi.org\/10.1016\/j.ijar.2020.08.001","journal-title":"Int. J. Approx. Reason."},{"key":"10_CR6","unstructured":"Belle, V., Passerini, A., Van den Broeck, G.: Probabilistic inference in hybrid domains by weighted model integration. In: Yang, Q., Wooldridge, M.J. (eds.) Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, Buenos Aires, Argentina, 25\u201331 July 2015. pp. 2770\u20132776. AAAI Press (2015). http:\/\/ijcai.org\/Abstract\/15\/392"},{"issue":"1\u20133","key":"10_CR7","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1016\/S0166-218X(01)00341-9","volume":"123","author":"E Boros","year":"2002","unstructured":"Boros, E., Hammer, P.L.: Pseudo-Boolean optimization. Discret. Appl. Math. 123(1\u20133), 155\u2013225 (2002). https:\/\/doi.org\/10.1016\/S0166-218X(01)00341-9","journal-title":"Discret. Appl. Math."},{"key":"10_CR8","unstructured":"Chavira, M., Darwiche, A.: Compiling Bayesian networks with local structure. In: Kaelbling, L.P., Saffiotti, A. (eds.) IJCAI-05, Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence, Edinburgh, Scotland, UK, 30 July\u20135 August 2005, pp. 1306\u20131312. Professional Book Center (2005). http:\/\/ijcai.org\/Proceedings\/05\/Papers\/0931.pdf"},{"key":"10_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1007\/11814948_9","volume-title":"Theory and Applications of Satisfiability Testing - SAT 2006","author":"M Chavira","year":"2006","unstructured":"Chavira, M., Darwiche, A.: Encoding CNFs to empower component analysis. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 61\u201374. Springer, Heidelberg (2006). https:\/\/doi.org\/10.1007\/11814948_9"},{"key":"10_CR10","unstructured":"Chavira, M., Darwiche, A.: Compiling Bayesian networks using variable elimination. In: Veloso, M.M. (ed.) IJCAI 2007, Proceedings of the 20th International Joint Conference on Artificial Intelligence, Hyderabad, India, 6\u201312 January 2007, pp. 2443\u20132449 (2007). http:\/\/ijcai.org\/Proceedings\/07\/Papers\/393.pdf"},{"issue":"6\u20137","key":"10_CR11","doi-asserted-by":"publisher","first-page":"772","DOI":"10.1016\/j.artint.2007.11.002","volume":"172","author":"M Chavira","year":"2008","unstructured":"Chavira, M., Darwiche, A.: On probabilistic inference by weighted model counting. Artif. Intell. 172(6\u20137), 772\u2013799 (2008). https:\/\/doi.org\/10.1016\/j.artint.2007.11.002","journal-title":"Artif. Intell."},{"issue":"1\u20132","key":"10_CR12","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1016\/j.ijar.2005.10.001","volume":"42","author":"M Chavira","year":"2006","unstructured":"Chavira, M., Darwiche, A., Jaeger, M.: Compiling relational Bayesian networks for exact inference. Int. J. Approx. Reason. 42(1\u20132), 4\u201320 (2006). https:\/\/doi.org\/10.1016\/j.ijar.2005.10.001","journal-title":"Int. J. Approx. Reason."},{"key":"10_CR13","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/978-3-642-39091-3_11","volume-title":"Symbolic and Quantitative Approaches to Reasoning with Uncertainty","author":"A Choi","year":"2013","unstructured":"Choi, A., Kisa, D., Darwiche, A.: Compiling probabilistic graphical models using sentential decision diagrams. In: van der Gaag, L.C. (ed.) ECSQARU 2013. LNCS (LNAI), vol. 7958, pp. 121\u2013132. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-39091-3_11"},{"issue":"1\u20132","key":"10_CR14","doi-asserted-by":"publisher","first-page":"11","DOI":"10.3166\/jancl.11.11-34","volume":"11","author":"A Darwiche","year":"2001","unstructured":"Darwiche, A.: On the tractable counting of theory models and its application to truth maintenance and belief revision. J. Appl. Non Class. Logics 11(1\u20132), 11\u201334 (2001). https:\/\/doi.org\/10.3166\/jancl.11.11-34","journal-title":"J. Appl. Non Class. Logics"},{"key":"10_CR15","unstructured":"Darwiche, A.: A logical approach to factoring belief networks. In: Fensel, D., Giunchiglia, F., McGuinness, D.L., Williams, M. (eds.) Proceedings of the Eights International Conference on Principles and Knowledge Representation and Reasoning (KR-02), Toulouse, France, 22\u201325 April 2002, pp. 409\u2013420. Morgan Kaufmann (2002)"},{"key":"10_CR16","unstructured":"Darwiche, A.: New advances in compiling CNF into decomposable negation normal form. In: de M\u00e1ntaras, R.L., Saitta, L. (eds.) Proceedings of the 16th Eureopean Conference on Artificial Intelligence, ECAI\u20192004, including Prestigious Applicants of Intelligent Systems, PAIS 2004, Valencia, Spain, 22\u201327 August 2004, pp. 328\u2013332. IOS Press (2004)"},{"key":"10_CR17","doi-asserted-by":"publisher","unstructured":"Darwiche, A.: SDD: a new canonical representation of propositional knowledge bases. In: Walsh, T. (ed.) IJCAI 2011, Proceedings of the 22nd International Joint Conference on Artificial Intelligence, Barcelona, Catalonia, Spain, 16\u201322 July 2011, pp. 819\u2013826. IJCAI\/AAAI (2011). https:\/\/doi.org\/10.5591\/978-1-57735-516-8\/IJCAI11-143","DOI":"10.5591\/978-1-57735-516-8\/IJCAI11-143"},{"key":"10_CR18","unstructured":"Dudek, J.M., Due\u00f1as-Osorio, L., Vardi, M.Y.: Efficient contraction of large tensor networks for weighted model counting through graph decompositions (2019). CoRR abs\/1908.04381"},{"key":"10_CR19","doi-asserted-by":"crossref","unstructured":"Dudek, J.M., Phan, V., Vardi, M.Y.: ADDMC: weighted model counting with algebraic decision diagrams. In: The Thirty-Fourth AAAI Conference on Artificial Intelligence, AAAI 2020, The Thirty-Second Innovative Applications of Artificial Intelligence Conference, IAAI 2020, The Tenth AAAI Symposium on Educational Advances in Artificial Intelligence, EAAI 2020, New York, NY, USA, 7\u201312 February 2020, pp. 1468\u20131476. AAAI Press (2020). https:\/\/aaai.org\/ojs\/index.php\/AAAI\/article\/view\/5505","DOI":"10.1609\/aaai.v34i02.5505"},{"key":"10_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1007\/978-3-030-58475-7_13","volume-title":"Principles and Practice of Constraint Programming","author":"JM Dudek","year":"2020","unstructured":"Dudek, J.M., Phan, V.H.N., Vardi, M.Y.: DPMC: weighted model counting by dynamic programming on project-join trees. In: Simonis, H. (ed.) CP 2020. LNCS, vol. 12333, pp. 211\u2013230. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-58475-7_13"},{"issue":"3","key":"10_CR21","doi-asserted-by":"publisher","first-page":"358","DOI":"10.1017\/S1471068414000076","volume":"15","author":"D Fierens","year":"2015","unstructured":"Fierens, D., et al.: Inference and learning in probabilistic logic programs using weighted Boolean formulas. Theory Pract. Log. Program. 15(3), 358\u2013401 (2015). https:\/\/doi.org\/10.1017\/S1471068414000076","journal-title":"Theory Pract. Log. Program."},{"key":"10_CR22","unstructured":"Gogate, V., Domingos, P.M.: Formula-based probabilistic inference. In: Gr\u00fcnwald, P., Spirtes, P. (eds.) UAI 2010, Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence, Catalina Island, CA, USA, 8\u201311 July 2010, pp. 210\u2013219. AUAI Press (2010)"},{"key":"10_CR23","unstructured":"Gogate, V., Domingos, P.M.: Approximation by quantization. In: Cozman, F.G., Pfeffer, A. (eds.) UAI 2011, Proceedings of the Twenty-Seventh Conference on Uncertainty in Artificial Intelligence, Barcelona, Spain, 14\u201317 July 2011, pp. 247\u2013255. AUAI Press (2011)"},{"issue":"7","key":"10_CR24","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1145\/2936726","volume":"59","author":"V Gogate","year":"2016","unstructured":"Gogate, V., Domingos, P.M.: Probabilistic theorem proving. Commun. ACM 59(7), 107\u2013115 (2016). https:\/\/doi.org\/10.1145\/2936726","journal-title":"Commun. ACM"},{"key":"10_CR25","unstructured":"Hoey, J., St-Aubin, R., Hu, A.J., Boutilier, C.: SPUDD: stochastic planning using decision diagrams. In: Laskey, K.B., Prade, H. (eds.) UAI \u201999: Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence, Stockholm, Sweden, 30 July\u20131 August 1999, pp. 279\u2013288. Morgan Kaufmann (1999)"},{"issue":"OOPSLA","key":"10_CR26","doi-asserted-by":"publisher","first-page":"140:1","DOI":"10.1145\/3428208","volume":"4","author":"S Holtzen","year":"2020","unstructured":"Holtzen, S., Van den Broeck, G., Millstein, T.D.: Scaling exact inference for discrete probabilistic programs. Proc. ACM Program. Lang. 4(OOPSLA), 140:1-140:31 (2020). https:\/\/doi.org\/10.1145\/3428208","journal-title":"Proc. ACM Program. Lang."},{"key":"10_CR27","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.jal.2016.11.031","volume":"22","author":"A Kimmig","year":"2017","unstructured":"Kimmig, A., Van den Broeck, G., De Raedt, L.: Algebraic model counting. J. Appl. Log. 22, 46\u201362 (2017). https:\/\/doi.org\/10.1016\/j.jal.2016.11.031","journal-title":"J. Appl. Log."},{"key":"10_CR28","doi-asserted-by":"publisher","unstructured":"Kolb, S., Mladenov, M., Sanner, S., Belle, V., Kersting, K.: Efficient symbolic integration for probabilistic inference. In: Lang, J. (ed.) Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, IJCAI 2018, Stockholm, Sweden, 13\u201319 July 2018, pp. 5031\u20135037. ijcai.org (2018). https:\/\/doi.org\/10.24963\/ijcai.2018\/698","DOI":"10.24963\/ijcai.2018\/698"},{"key":"10_CR29","unstructured":"Oztok, U., Darwiche, A.: A top-down compiler for sentential decision diagrams. In: Yang, Q., Wooldridge, M.J. (eds.) Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, Buenos Aires, Argentina, 25\u201331 July 2015, pp. 3141\u20133148. AAAI Press (2015). http:\/\/ijcai.org\/Abstract\/15\/443"},{"key":"10_CR30","doi-asserted-by":"crossref","unstructured":"Poon, H., Domingos, P.M.: Sum-product networks: a new deep architecture. In: Cozman, F.G., Pfeffer, A. (eds.) UAI 2011, Proceedings of the Twenty-Seventh Conference on Uncertainty in Artificial Intelligence, Barcelona, Spain, 14\u201317 July 2011, pp. 337\u2013346. AUAI Press (2011)","DOI":"10.1109\/ICCVW.2011.6130310"},{"key":"10_CR31","unstructured":"Sang, T., Bacchus, F., Beame, P., Kautz, H.A., Pitassi, T.: Combining component caching and clause learning for effective model counting. In: SAT 2004 - The Seventh International Conference on Theory and Applications of Satisfiability Testing, Vancouver, BC, Canada, 10\u201313 May 2004, Online Proceedings (2004). http:\/\/www.satisfiability.org\/SAT04\/programme\/21.pdf"},{"key":"10_CR32","unstructured":"Sang, T., Beame, P., Kautz, H.A.: Performing Bayesian inference by weighted model counting. In: Veloso, M.M., Kambhampati, S. (eds.) Proceedings, The Twentieth National Conference on Artificial Intelligence and the Seventeenth Innovative Applications of Artificial Intelligence Conference, Pittsburgh, Pennsylvania, USA, 9\u201313 July 2005, pp. 475\u2013482. AAAI Press\/The MIT Press (2005). http:\/\/www.aaai.org\/Library\/AAAI\/2005\/aaai05-075.php"},{"issue":"5\u20136","key":"10_CR33","doi-asserted-by":"publisher","first-page":"748","DOI":"10.1016\/j.artint.2008.11.003","volume":"173","author":"S Sanner","year":"2009","unstructured":"Sanner, S., Boutilier, C.: Practical solution techniques for first-order MDPs. Artif. Intell. 173(5\u20136), 748\u2013788 (2009). https:\/\/doi.org\/10.1016\/j.artint.2008.11.003","journal-title":"Artif. Intell."},{"key":"10_CR34","unstructured":"Sanner, S., Delgado, K.V., de Barros, L.N.: Symbolic dynamic programming for discrete and continuous state MDPs. In: Cozman, F.G., Pfeffer, A. (eds.) UAI 2011, Proceedings of the Twenty-Seventh Conference on Uncertainty in Artificial Intelligence, Barcelona, Spain, 14\u201317 July 2011, pp. 643\u2013652. AUAI Press (2011)"},{"key":"10_CR35","unstructured":"Sanner, S., McAllester, D.A.: Affine algebraic decision diagrams (AADDs) and their application to structured probabilistic inference. In: Kaelbling, L.P., Saffiotti, A. (eds.) IJCAI-05, Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence, Edinburgh, Scotland, UK, 30 July\u20135 August 2005, pp. 1384\u20131390. Professional Book Center (2005). http:\/\/ijcai.org\/Proceedings\/05\/Papers\/1439.pdf"},{"key":"10_CR36","doi-asserted-by":"publisher","unstructured":"Van den Broeck, G., Taghipour, N., Meert, W., Davis, J., De Raedt, L.: Lifted probabilistic inference by first-order knowledge compilation. In: Walsh, T. (ed.) IJCAI 2011, Proceedings of the 22nd International Joint Conference on Artificial Intelligence, Barcelona, Catalonia, Spain, 16\u201322 July 2011, pp. 2178\u20132185. IJCAI\/AAAI (2011). https:\/\/doi.org\/10.5591\/978-1-57735-516-8\/IJCAI11-363","DOI":"10.5591\/978-1-57735-516-8\/IJCAI11-363"},{"key":"10_CR37","unstructured":"Xu, J., Zhang, Z., Friedman, T., Liang, Y., Van den Broeck, G.: A semantic loss function for deep learning with symbolic knowledge. In: Dy, J.G., Krause, A. (eds.) Proceedings of the 35th International Conference on Machine Learning, ICML 2018, Stockholmsm\u00e4ssan, Stockholm, Sweden, 10\u201315 July 2018. Proceedings of Machine Learning Research, vol. 80, pp. 5498\u20135507. PMLR (2018). http:\/\/proceedings.mlr.press\/v80\/xu18h.html"},{"key":"10_CR38","unstructured":"Zhao, H., Melibari, M., Poupart, P.: On the relationship between sum-product networks and Bayesian networks. In: Bach, F.R., Blei, D.M. (eds.) Proceedings of the 32nd International Conference on Machine Learning, ICML 2015, Lille, France, 6\u201311 July 2015. JMLR Workshop and Conference Proceedings, vol. 37, pp. 116\u2013124. JMLR.org (2015). http:\/\/proceedings.mlr.press\/v37\/zhaoc15.html"}],"container-title":["Lecture Notes in Computer Science","Theory and Applications of Satisfiability Testing \u2013 SAT 2021"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-80223-3_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,1]],"date-time":"2021-07-01T23:31:14Z","timestamp":1625182274000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-80223-3_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030802226","9783030802233"],"references-count":38,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-80223-3_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"2 July 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"SAT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Theory and Applications of Satisfiability Testing","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Barcelona","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Spain","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"5 July 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"9 July 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"24","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"sat2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.iiia.csic.es\/sat2021\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}