Papers
Topics
Authors
Recent
Search
2000 character limit reached

A Circus of Circuits: Connections Between Decision Diagrams, Circuits, and Automata

Published 15 Apr 2024 in cs.DS, cs.DB, and cs.FL | (2404.09674v1)

Abstract: This document is an introduction to two related formalisms to define Boolean functions: binary decision diagrams, and Boolean circuits. It presents these formalisms and several of their variants studied in the setting of knowledge compilation. Last, it explains how these formalisms can be connected to the notions of automata over words and trees.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (45)
  1. Provenance circuits for trees and treelike instances. In ICALP, 2015. doi: 10.1007/978-3-662-47666-6˙5.
  2. A circuit-based approach to efficient enumeration. In ICALP, 2017. doi: 10.4230/LIPIcs.ICALP.2017.111.
  3. Connecting knowledge compilation classes and width parameters. Theory Comput. Syst., 64(5), 2020. doi: 10.1007/s00224-019-09930-2.
  4. Efficient enumeration algorithms for annotated grammars. In PODS, 2022. doi: 10.1145/3517804.3526232.
  5. Learning read-once formulas with queries. JACM, 40(1), 1993. doi: 10.1145/138027.138061.
  6. On the complexity of SHAP-score-based explanations: Tractability via knowledge compilation and non-approximability results. Journal of Machine Learning Research, 24(63), 2023.
  7. Lower bounds for exact model counting and applications in probabilistic databases. In UAI, 2013.
  8. Equivalence of free boolean graphs can be decided probabilistically in polynomial time. Inf. Process. Lett., 10(2), 1980. doi: 10.1016/S0020-0190(80)90078-2.
  9. Beate Bollig. On the minimization of (complete) ordered binary decision diagrams. Theory of Computing Systems, 59, 2016. doi: 10.1007/s00224-015-9657-x.
  10. Complexity theoretical results on partitioned (nondeterministic) binary decision diagrams. In MFCS, 1997. doi: 10.1007/s002240000128.
  11. Binary decision diagrams. In Yves Crama and Peter L. Hammer, editors, Boolean Models and Methods in Mathematics, Computer Science, and Engineering. Cambridge University Press, 2010. ISBN 978-0-521-84752-0.
  12. Randal E. Bryant. Graph-based algorithms for boolean function manipulation. IEEE Trans. Computers, 35(8), 1986. doi: 10.1109/TC.1986.1676819.
  13. Tractable QBF by knowledge compilation. In STACS, 2019. doi: 10.4230/LIPIcs.STACS.2019.18.
  14. Probabilistic circuits: A unifying framework for tractable probabilistic models. 2020. URL http://starai.cs.ucla.edu/papers/ProbCirc20.pdf.
  15. Adnan Darwiche. On the tractable counting of theory models and its application to truth maintenance and belief revision. Journal of Applied Non-Classical Logics, 11(1-2), 2001. doi: 10.3166/jancl.11.11-34.
  16. Adnan Darwiche. A differential approach to inference in bayesian networks. Journal of the ACM (JACM), 50(3), 2003. doi: 10.1145/765568.765570.
  17. Adnan Darwiche. SDD: A new canonical representation of propositional knowledge bases. In IJCAI, 2011.
  18. A knowledge compilation map. Journal of Artificial Intelligence Research, 17, 2002. doi: 10.1613/jair.989.
  19. AND/OR search spaces for graphical models. Artificial intelligence, 171(2-3), 2007. doi: 10.1016/j.artint.2006.11.003.
  20. Circuits for Datalog Provenance. In ICDT, 2014. doi: 10.5441/002/ICDT.2014.22.
  21. The complexity of equivalence and containment for free single variable program schemes. In ICALP, 1978. doi: 10.1007/3-540-08860-1˙17.
  22. Provenance semirings. In PODS, 2007. doi: 10.1145/1265530.1265535.
  23. Knowledge compilation meets database theory: Compiling queries to decision diagrams. Theory of Computing Systems, 52, 2013. doi: 10.1145/1938551.1938574.
  24. A unifying perspective on succinct data representations. arXiv preprint arXiv:2309.11663, 2023. doi: 10.48550/arXiv.2309.11663.
  25. Algebraic model counting. Journal of Applied Logic, 22, 2017. doi: 10.1016/j.jal.2016.11.031.
  26. Probabilistic sentential decision diagrams. In KR, 2014.
  27. Eyal Kushilevitz. Communication complexity. In Advances in Computers, volume 44. 1997. doi: 10.1016/S0065-2458(08)60342-3.
  28. An improved decision-DNNF compiler. In IJCAI, volume 17, 2017.
  29. Chang-Yeong Lee. Representation of switching circuits by binary-decision programs. The Bell System Technical Journal, 38(4), 1959. doi: 10.1002/j.1538-7305.1959.tb01585.x.
  30. Shin-ichi Minato. Zero-suppressed BDDs for set manipulation in combinatorial problems. In IDAC, 1993. doi: 10.1145/157485.164890.
  31. Size bounds for factorised representations of query results. ACM Transactions on Database Systems (TODS), 40(1), 2015. doi: 10.1145/2656335.
  32. A lower bound on the size of decomposable negation normal form. In AAAI, volume 24, 2010. doi: 10.1609/AAAI.V24I1.7600.
  33. Sum-product networks: A new deep architecture. In ICCV workshops, 2011.
  34. Cutset networks: A simple, tractable, and scalable approach for improving the accuracy of Chow-Liu trees. In ECML/PKDD, 2014. doi: 10.1007/978-3-662-44851-9˙40.
  35. Alexander A Razborov. Lower bounds for deterministic and nondeterministic branching programs. In FCT, 1991. doi: 10.1007/3-540-54458-5˙49.
  36. Igor Razgon. No small nondeterministic read-once branching programs for CNFs of bounded treewidth. In IPEC, 2014. doi: 10.1007/978-3-319-13524-3˙27.
  37. A survey of decision tree classifier methodology. IEEE Trans. Syst. Man Cybern., 21(3), 1991.
  38. Smoothing structured decomposable circuits. In NeurIPS, 2019.
  39. Arithmetic circuits: A survey of recent results and open questions. Foundations and Trends in Theoretical Computer Science, 5(3–4), 2010. doi: 10.1561/0400000039.
  40. Fast parallel computation of polynomials using few processors. SIAM Journal on Computing, 12(4), 1983. doi: 10.1007/3-540-10856-4˙79.
  41. Heribert Vollmer. Introduction to circuit complexity: a uniform approach. Springer Science & Business Media, 1999. ISBN 978-3-540-64310-4.
  42. Ingo Wegener. The complexity of Boolean functions. John Wiley & Sons, Inc., 1987. ISBN 0-471-91555-6.
  43. Ingo Wegener. Branching programs and binary decision diagrams: Theory and applications. SIAM, 2000. ISBN 978-0-89871-458-6.
  44. Ingo Wegener. BDDs–design, analysis, complexity, and applications. Discret. Appl. Math., 138(1-2), 2004. doi: 10.1016/S0166-218X(03)00297-X.
  45. Top 10 algorithms in data mining. Knowl. Inf. Syst., 14(1), 2008. doi: 10.1007/s10115-007-0114-2.
Citations (3)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up