Nucleus-Satellites Systems of OMDDs for Reducing the Size of Compiled Forms

Authors Hélène Fargier, Jérôme Mengin, Nicolas Schmidt

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Hélène Fargier
  • IRIT, Université de Toulouse, CNRS, Toulouse INP, UT3, France
Jérôme Mengin
  • IRIT, Université de Toulouse, CNRS, Toulouse INP, UT3, France
Nicolas Schmidt
  • IRIT, Université de Toulouse, CNRS, Toulouse INP, UT3, France


We thank anonymous reviewers for the CPAIOR and CP conferences for their numerous comments and suggestions that helped improve the paper.

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Hélène Fargier, Jérôme Mengin, and Nicolas Schmidt. Nucleus-Satellites Systems of OMDDs for Reducing the Size of Compiled Forms. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


In order to reduce the size of compiled forms in knowledge compilation, we propose a new approach based on a splitting of the main representation into a nucleus representation and satellite representations. Nucleus representation is the projection of the original representation onto the "main" variables and satellite representations define the other variables according to the nucleus. We propose a language and a method, aimed at OBDD/OMDD representations, to compile into this split form. Our experimental study shows major size reductions on configuration- and diagnosis- oriented benchmarks.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Constraint and logic programming
  • Knowledge representation
  • knowledge compilation
  • ordered multivalued decision diagram


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  1. Jérôme Amilhastre, Hélène Fargier, and Pierre Marquis. Consistency restoration and explanations in dynamic CSPs - Application to configuration. Artificial Intellligence, 135(1-2):199-234, 2002. Google Scholar
  2. Jean-Marc Astesana, Laurent Cosserat, and Hélène Fargier. Constraint-based vehicle configuration: A case study. In ICTAI 2010, pages 68-75. IEEE Computer Society, 2010. Google Scholar
  3. Randall E. Bryant. Graph-Based Algorithms for Boolean Function Manipulation. IEEE Transactions on Computers (TC), 38.8:677-691, 1986. Google Scholar
  4. Marco Cadoli and Francesco M. Donini. A survey on knowledge compilation. AI Communications, 10(3-4):137-150, 1997. Google Scholar
  5. Arthur Choi and Adnan Darwiche. Dynamic minimization of sentential decision diagrams. In AAAI'2013, pages 187-194, 2013. Google Scholar
  6. A. Darwiche. SDD: A new canonical representation of propositional knowledge bases. In IJCAI'2011, pages 819-826, 2011. Google Scholar
  7. Adnan Darwiche. New Advances in Compiling CNF into Decomposable Negation Normal Form. In ECAI 2004, pages 328-332, 2004. Google Scholar
  8. Adnan Darwiche and Pierre Marquis. A Knowledge Compilation Map. Journal of Artificial Intelligence Research (JAIR), 17:229-264, 2002. Google Scholar
  9. Hélène Fargier and Pierre Marquis. Knowledge Compilation Properties of Trees-of-BDDs, Revisited. In IJCAI 2009, pages 772-777, 2009. Google Scholar
  10. Hélène Fargier, Pierre Marquis, and Nicolas Schmidt. Semiring Labelled Decision Diagrams, Revisited: Canonicity and Spatial Efficiency Issues. In IJCAI 2013, pages 884-890, 2013. URL:
  11. Goran Gogic, Henry Kautz, Christos Papadimitriou, and Bart Selman. The Comparative Linguistics of Knowledge Representation. In IJCAI'1995, pages 862-869, 1995. Google Scholar
  12. Tarik Hadzic, Henrik Reif Andersen, John N. Hooker, and Peter Tiedemann. A constraint store based on multivalued decision diagrams. In CP 2007, pages 118-132, 2007. Google Scholar
  13. Tarik Hadzic, Rune Jensen, and Henrik Reif Andersen. Calculating Valid Domains for BDD-Based Interactive Configuration. Computing Research Repository (CoRR), 0704.1394, 2007. URL:
  14. Toshihide Ibaraki, Alexander Kogan, and Kazuhisa Makino. Functional dependencies in horn theories. Artificial Intelligence, 108(1-2):1-30, 1999. Google Scholar
  15. Toshihide Ibaraki, Alexander Kogan, and Kazuhisa Makino. On functional dependencies in q-horn theories. Artificial Intelligence, 131(1-2):171-187, 2001. Google Scholar
  16. Toshihide Ibaraki, Alexander Kogan, and Kazuhisa Makino. Inferring minimal functional dependencies in horn and q-horn theories. Annals of Mathematics and Artificial Intelligence, 38(4):233-255, 2003. Google Scholar
  17. T. Kam, T.Villa, R.K. Brayton, and A.L Sangiovanni-Vincentelli. Multi-valued decision diagrams: Theory and applications. International Journal of Multiple-Valued Logic, 4:9-12, 1998. Google Scholar
  18. Frédéric Koriche, Jean-Marie Lagniez, Pierre Marquis, and Samuel Thomas. Compiling constraint networks into multivalued decomposable decision graphs. In IJCAI 2015, 2015. Google Scholar
  19. Jean-Marie Lagniez, Emmanuel Lonca, and Pierre Marquis. Definability for model counting. Artificial Intelligence, 281:103229, 2020. Google Scholar
  20. Jean-Marie Lagniez and Pierre Marquis. An improved decision-DNNF compiler. In IJCAI'2017, volume 17, pages 667-673, 2017. Google Scholar
  21. Jean-Marie Lagniez, Pierre Marquis, and Anastasia Paparrizou. Defining and evaluating heuristics for the compilation of constraint networks. In CP 2017, pages 172-188. Springer, 2017. Google Scholar
  22. Jérôme Lang and Pierre Marquis. On propositional definability. Artificial Intelligence, 172(8):991-1017, 2008. Google Scholar
  23. Robert Mateescu and Rina Dechter. Compiling Constraint Networks into AND/OR Multi-valued Decision Diagrams (AOMDDs). In CP 2006, pages 329-343, 2006. Google Scholar
  24. Christian Muise, Sheila A McIlraith, J Christopher Beck, and Eric I Hsu. D sharp: fast d-DNNF compilation with sharpsat. In CCAI'12, pages 356-361, 2012. Google Scholar
  25. Knot Pipatsrisawat and Adnan Darwiche. New compilation languages based on structured decomposability. In AAAI 2008, pages 517-522, 2008. Google Scholar
  26. Carsten Sinz. Knowledge compilation for product configuration. In Proceedings of the Workshop on Configuration at the 15th European Conference on Artificial Intelligence (ECAI), pages 23-26, 2002. Google Scholar
  27. Takahisa Toda and Takehide Soh. Implementing efficient all solutions SAT solvers. ACM Journal of Experimental Algorithmics, 21(1):1.12:1-1.12:44, 2016. Google Scholar
  28. Nageshwara Rao Vempaty. Solving Constraint Satisfaction Problems Using Finite State Automata. In AAAI'92, pages 453-458, 1992. Google Scholar
  29. Bwolen Yang, Reid G. Simmons, Randal E. Bryant, and David R. O'Hallaron. Optimizing symbolic model checking for constraint-rich models. In Nicolas Halbwachs and Doron A. Peled, editors, Proceedings of the 11th International Conference on Computer Aided Verification (CAV'99), volume 1633 of Lecture Notes in Computer Science, pages 328-340. Springer, 1999. URL: