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On the Relative Efficiency of Dynamic and Static Top-Down Compilation to Decision-DNNF

Author Alexis de Colnet

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LIPIcs.SAT.2024.11.pdf
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Alexis de Colnet
  • Algorithms and Complexity Group, TU Wien, Austria

Funding

This work has been supported by the Austrian Science Fund (FWF), ESPRIT project FWF ESP 235.

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Alexis de Colnet. On the Relative Efficiency of Dynamic and Static Top-Down Compilation to Decision-DNNF. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 11:1-11:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.SAT.2024.11

Abstract

Top-down compilers of CNF formulas to circuits in decision-DNNF (Decomposable Negation Normal Form) have proved to be useful for model counting. These compilers rely on a common set of techniques including DPLL-style exploration of the set of models, caching of residual formulas, and connected components detection. Differences between compilers lie in the variable selection heuristics and in the additional processing techniques they may use. We investigate, from a theoretical perspective, the ability of top-down compilation algorithms to find small decision-DNNF circuits for two different variable selection strategies. Both strategies are guided by a graph of the CNF formula and are inspired by what is done in practice. The first uses a dynamic graph-partitioning approach while the second works with a static tree decomposition. We show that the dynamic approach performs significantly better than the static approach for some formulas, and that the opposite also holds for other formulas. Our lower bounds are proved despite loose settings where the compilation algorithm is only forced to follow its designed variable selection strategy and where everything else, including the many opportunities for tie-breaking, can be handled non-deterministically.

Subject Classification

ACM Subject Classification
  • Theory of computation → Dynamic programming
Keywords
  • Knowledge compilation
  • top-down compilation
  • decision-DNNF Circuits

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References

  1. Fahiem Bacchus, Shannon Dalmao, and Toniann Pitassi. Algorithms and complexity results for #sat and bayesian inference. In 44th Symposium on Foundations of Computer Science (FOCS 2003), 11-14 October 2003, Cambridge, MA, USA, Proceedings, pages 340-351. IEEE Computer Society, 2003. URL: https://doi.org/10.1109/SFCS.2003.1238208.
  2. Paul Beame, Jerry Li, Sudeepa Roy, and Dan Suciu. Lower bounds for exact model counting and applications in probabilistic databases. In Ann E. Nicholson and Padhraic Smyth, editors, Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence, UAI 2013, Bellevue, WA, USA, August 11-15, 2013. AUAI Press, 2013. URL: https://dslpitt.org/uai/displayArticleDetails.jsp?mmnu=1&smnu=2&article_id=2366&proceeding_id=29.
  3. Béla Bollobás and Imre Leader. Edge-isoperimetric inequalities in the grid. Comb., 11(4):299-314, 1991. URL: https://doi.org/10.1007/BF01275667.
  4. Marco Cadoli, Francesco M. Donini, Paolo Liberatore, and Marco Schaerf. Preprocessing of intractable problems. Inf. Comput., 176(2):89-120, 2002. URL: https://doi.org/10.1006/INCO.2001.3043.
  5. Andrea Calì, Florent Capelli, and Igor Razgon. Non-fpt lower bounds for structural restrictions of decision DNNF. CoRR, abs/1708.07767, 2017. URL: https://arxiv.org/abs/1708.07767.
  6. Hubie Chen. Parameterized compilability. In Leslie Pack Kaelbling and Alessandro Saffiotti, editors, IJCAI-05, Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence, Edinburgh, Scotland, UK, July 30 - August 5, 2005, pages 412-417. Professional Book Center, 2005. URL: http://ijcai.org/Proceedings/05/Papers/0644.pdf.
  7. Adnan Darwiche. Recursive conditioning. Artif. Intell., 126(1-2):5-41, 2001. URL: https://doi.org/10.1016/S0004-3702(00)00069-2.
  8. Adnan Darwiche. A compiler for deterministic, decomposable negation normal form. In Rina Dechter, Michael J. Kearns, and Richard S. Sutton, editors, Proceedings of the Eighteenth National Conference on Artificial Intelligence and Fourteenth Conference on Innovative Applications of Artificial Intelligence, July 28 - August 1, 2002, Edmonton, Alberta, Canada, pages 627-634. AAAI Press / The MIT Press, 2002. URL: http://www.aaai.org/Library/AAAI/2002/aaai02-094.php.
  9. Adnan Darwiche. New advances in compiling CNF into decomposable negation normal form. In Ramón López de Mántaras and Lorenza Saitta, editors, Proceedings of the 16th Eureopean Conference on Artificial Intelligence, ECAI'2004, including Prestigious Applicants of Intelligent Systems, PAIS 2004, Valencia, Spain, August 22-27, 2004, pages 328-332. IOS Press, 2004. Google Scholar
  10. Adnan Darwiche and Pierre Marquis. A knowledge compilation map. J. Artif. Intell. Res., 17:229-264, 2002. URL: https://doi.org/10.1613/JAIR.989.
  11. Hélène Fargier, Pierre Marquis, Alexandre Niveau, and Nicolas Schmidt. A knowledge compilation map for ordered real-valued decision diagrams. In Carla E. Brodley and Peter Stone, editors, Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence, July 27 -31, 2014, Québec City, Québec, Canada, pages 1049-1055. AAAI Press, 2014. URL: https://doi.org/10.1609/AAAI.V28I1.8853.
  12. Hélène Fargier and Jérôme Mengin. A knowledge compilation map for conditional preference statements-based languages. In Frank Dignum, Alessio Lomuscio, Ulle Endriss, and Ann Nowé, editors, AAMAS '21: 20th International Conference on Autonomous Agents and Multiagent Systems, Virtual Event, United Kingdom, May 3-7, 2021, pages 492-500. ACM, 2021. URL: https://doi.org/10.5555/3463952.3464014.
  13. Jinbo Huang and Adnan Darwiche. DPLL with a trace: From SAT to knowledge compilation. In Leslie Pack Kaelbling and Alessandro Saffiotti, editors, IJCAI-05, Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence, Edinburgh, Scotland, UK, July 30 - August 5, 2005, pages 156-162. Professional Book Center, 2005. URL: http://ijcai.org/Proceedings/05/Papers/0876.pdf.
  14. Roberto J. Bayardo Jr. and Joseph Daniel Pehoushek. Counting models using connected components. In Henry A. Kautz and Bruce W. Porter, editors, Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on on Innovative Applications of Artificial Intelligence, July 30 - August 3, 2000, Austin, Texas, USA, pages 157-162. AAAI Press / The MIT Press, 2000. URL: http://www.aaai.org/Library/AAAI/2000/aaai00-024.php.
  15. Rafael Kiesel and Thomas Eiter. Knowledge compilation and more with sharpsat-td. In Pierre Marquis, Tran Cao Son, and Gabriele Kern-Isberner, editors, Proceedings of the 20th International Conference on Principles of Knowledge Representation and Reasoning, KR 2023, Rhodes, Greece, September 2-8, 2023, pages 406-416, 2023. URL: https://doi.org/10.24963/KR.2023/40.
  16. Tuukka Korhonen and Matti Järvisalo. Integrating tree decompositions into decision heuristics of propositional model counters (short paper). In Laurent D. Michel, editor, 27th International Conference on Principles and Practice of Constraint Programming, CP 2021, Montpellier, France (Virtual Conference), October 25-29, 2021, volume 210 of LIPIcs, pages 8:1-8:11. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPICS.CP.2021.8.
  17. Jean-Marie Lagniez and Pierre Marquis. An improved decision-dnnf compiler. In Carles Sierra, editor, Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI 2017, Melbourne, Australia, August 19-25, 2017, pages 667-673. ijcai.org, 2017. URL: https://doi.org/10.24963/IJCAI.2017/93.
  18. Jean-Marie Lagniez, Pierre Marquis, and Anastasia Paparrizou. Defining and evaluating heuristics for the compilation of constraint networks. In J. Christopher Beck, editor, Principles and Practice of Constraint Programming - 23rd International Conference, CP 2017, Melbourne, VIC, Australia, August 28 - September 1, 2017, Proceedings, volume 10416 of Lecture Notes in Computer Science, pages 172-188. Springer, 2017. URL: https://doi.org/10.1007/978-3-319-66158-2_12.
  19. Christian Muise, Sheila A. McIlraith, J. Christopher Beck, and Eric Hsu. DSHARP: Fast d-DNNF Compilation with sharpSAT. In Canadian Conference on Artificial Intelligence, 2012. Google Scholar
  20. Umut Oztok and Adnan Darwiche. On compiling CNF into decision-dnnf. In Barry O'Sullivan, editor, Principles and Practice of Constraint Programming - 20th International Conference, CP 2014, Lyon, France, September 8-12, 2014. Proceedings, volume 8656 of Lecture Notes in Computer Science, pages 42-57. Springer, 2014. URL: https://doi.org/10.1007/978-3-319-10428-7_7.
  21. Cédric Piette, Youssef Hamadi, and Lakhdar Sais. Vivifying propositional clausal formulae. In Malik Ghallab, Constantine D. Spyropoulos, Nikos Fakotakis, and Nikolaos M. Avouris, editors, ECAI 2008 - 18th European Conference on Artificial Intelligence, Patras, Greece, July 21-25, 2008, Proceedings, volume 178 of Frontiers in Artificial Intelligence and Applications, pages 525-529. IOS Press, 2008. URL: https://doi.org/10.3233/978-1-58603-891-5-525.
  22. Knot Pipatsrisawat and Adnan Darwiche. New compilation languages based on structured decomposability. In Dieter Fox and Carla P. Gomes, editors, Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligence, AAAI 2008, Chicago, Illinois, USA, July 13-17, 2008, pages 517-522. AAAI Press, 2008. URL: http://www.aaai.org/Library/AAAI/2008/aaai08-082.php.
  23. Tian Sang, Fahiem Bacchus, Paul Beame, Henry A. Kautz, and Toniann Pitassi. Combining component caching and clause learning for effective model counting. In SAT 2004 - The Seventh International Conference on Theory and Applications of Satisfiability Testing, 10-13 May 2004, Vancouver, BC, Canada, Online Proceedings, 2004. URL: http://www.satisfiability.org/SAT04/programme/21.pdf.
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