Encyclopedia of Algorithms

2008 Edition
| Editors: Ming-Yang Kao

Learning Constant-Depth Circuits

1993; Linial, Mansour, Nisan
  • Rocco Servedio
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_195

Keywords and Synonyms

Learning AC0 circuits          

Problem Definition

This problem deals with learning “simple” Boolean functions \( { f: \{0,1\}^n \rightarrow \{-1,1\} } \)

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Recommended Reading

  1. 1.
    Blum, A.: Learning a function of r relevant variables (open problem). In: Proceedings of the 16th Annual Conference on Learning Theory, pp. 731–733, Washington, 24–27 August 2003Google Scholar
  2. 2.
    Furst, M., Jackson, J., Smith, S.: Improved learning of AC0 functions. In: Proceedings of the Fourth Annual Workshop on Computational Learning Theory, pp. 317–325, Santa Cruz, (1991)Google Scholar
  3. 3.
    Håstad, J.: A slight sharpening of LMN. J. Comput. Syst. Sci. 63(3), 498–508 (2001)MATHCrossRefGoogle Scholar
  4. 4.
    Jackson, J.: An efficient membership-query algorithm for learning DNF with respect to the uniform distribution. J. Comput. Syst. Sci. 55, 414–440 (1997)MATHCrossRefGoogle Scholar
  5. 5.
    Jackson, J., Klivans, A., Servedio, R.: Learnability beyond \( { {AC^0} } \). In: Proceedings of the 34th ACM Symposium on Theory of Computing, pp. 776–784, Montréal, 23–25 May 2002Google Scholar
  6. 6.
    Kalai, A., Klivans, A., Mansour, Y., Servedio, R.: Agnostically learning halfspaces. In: Proceedings of the 46th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 11–20, Pittsburgh, PA, USA, 23–25 October 2005Google Scholar
  7. 7.
    Kharitonov, M.: Cryptographic hardness of distribution-specific learning. In: Proceedings of the 25th Annual Symposium on Theory of Computing, pp. 372–381. (1993)Google Scholar
  8. 8.
    Klivans, A., O'Donnell, R., Servedio, R.: Learning intersections and thresholds of halfspaces. J. Comput. Syst. Sci. 68(4), 808–840 (2004)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Klivans, A., Servedio, R.: Learning DNF in time \( { 2^{\tilde{O}(n^{1/3})} } \). J. Comput. Syst. Sci. 68(2), 303–318 (2004)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Klivans, A., Sherstov, A.: Cryptographic hardness results for learning intersections of halfspaces. In: Proceedings of the 47th Annual Symposium on Foundations of Computer Science, pp. 553–562, Berkeley, 22–24 October 2006Google Scholar
  11. 11.
    Kushilevitz, E., Mansour, Y.: Learning decision trees using the Fourier spectrum. SIAM J. Comput. 22(6), 1331–1348 (1993)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Linial, N., Mansour, Y., Nisan, N.: Constant depth circuits, Fourier transform and learnability. J. ACM 40(3), 607–620 (1993)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Mansour, Y., Sahar, S.: Implementation Issues in the Fourier Transform Algorithm. Mach. Learn. 40(1), 5–33 (2000)MATHCrossRefGoogle Scholar
  14. 14.
    Naor, M., Reingold, O.: Number-theoretic constructions of efficient pseudo-random functions. J. ACM 51(2), 231–262 (2004)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    O'Donnell, R., Servedio, R.: Learning monotone decision trees in polynomial time. In: Proceedings of the 21st Conference on Computational Complexity (CCC), pp. 213–225, Prague, 16–20 July 2006Google Scholar
  16. 16.
    Servedio, R.: On learning monotone DNF under product distributions. Inform Comput 193(1), 57–74 (2004)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Stefankovic, D.: Fourier transforms in computer science. Masters thesis, TR-2002-03, University of Chicago (2002)Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Rocco Servedio
    • 1
  1. 1.Department of Computer ScienceColumbia UniversityNew YorkUSA