Advertisement

Learning orthogonal F-Horn formulas

  • Akira Miyashiro
  • Eiji Takimoto
  • Yoshifumi Sakai
  • Akira Maruoka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 997)

Abstract

In the PAC-learning, or the query learning model, it has been an important open problem to decide whether the class of DNF and CNF formulas is learnable. Recently, it was pointed out that the problem of PAC-learning for these classes with membership queries can be reduced to that of query learning for the class of k-quasi Horn formulas with membership and equivalence queries. A k-quasi Horn formula is a CNF formula with each clause containing at most k unnegated literals. In this paper, notions of F-Horn formulas and l-F-Horn formulas, which are extensions of k-quasi formulas, are introduced, and it is shown that the problem of PAC-learning for DNF and CNF formulas with membership queries can be reduced to that of query learning for l-F-Horn formulas with membership and equivalence queries for an appropriate choice of F. It is shown that under some condition, the class of orthogonal F-Horn formulas is learnable with membership, equivalence and subset queries. Moreover, it is shown that under some condition the class of orthogonal l-F-Horn formulas is learnable with membership and equivalence queries.

Keywords

Horn Clause Monotone Formula Membership Query Equivalence Query Horn Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AFP92]
    Dana Angluin, Michael Frazier, and Leonard Pitt. Learning conjunctions of Horn clauses. Machine Learning, 9:147–164, 1992.Google Scholar
  2. [AK91]
    Dana Angluin and Michael Kharitonov. When won't membership queries help? In Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, pages 444–454. Association for Computing Machinery, 1991.Google Scholar
  3. [Ang88]
    Dana Angluin. Queries and concept learning. Machine Learning, 2:319–342, 1988.Google Scholar
  4. [BR92]
    Avrim Blum and Steven Rudich. Fast learning of k-term DNF formulas with queries. In Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pages 382–389. Association for Computing Machinery, 1992.Google Scholar
  5. [Bsh93]
    Nader H. Bshouty. Exact learning via the monotone theory. In Proceedings of the 34th Annual IEEE Symposium on Foundations of Computer Science, pages 302–311. IEEE, 1993.Google Scholar
  6. [Jac94]
    Jeffrey Jackson. An efficient membership-query algorithm for learning DNF with respect to the uniform distribution. In Proceedings of the 35th Annual IEEE Symposium on Foundations of Computer Science, pages 42–53, 1994.Google Scholar
  7. [Kha93]
    Michael Kharitonov. Cryptographic hardness of distribution-specific learning. In Proceedings of the 25th Annual ACM Symposium on Theory of Computing, pages 372–381, 1993.Google Scholar
  8. [KLPV87]
    Michael Kearns, Ming Li, Leonard Pitt, and Leslie G. Valiant. On the learnability of Boolean formulae. In Proceedings of the 19th Annual ACM Symposium on Theory of Computing, pages 185–294. Association for Computing Machinery, 1987.Google Scholar
  9. [PW90]
    Leonard Pitt and Manfred K. Warmuth. Prediction-preserving reducibility. Journal of Computer and System Sciences, 41:430–467, 1990.CrossRefGoogle Scholar
  10. [Val84]
    Leslie G. Valiant. A theory of the learnable. Communications of the ACM, 27(11):1134–1142, 1984.CrossRefGoogle Scholar
  11. [Val85]
    Leslie G. Valiant. Learning disjunctions of conjunctions. In Proceedings of the 9th International Joint Conference on Artificial Intelligence, volume 1, pages 1134–1142, Los Angeles, Aug. 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Akira Miyashiro
    • 1
  • Eiji Takimoto
    • 2
  • Yoshifumi Sakai
    • 3
  • Akira Maruoka
    • 2
  1. 1.Second Department of Energy Research, Hitachi Research LaboratoryHitachi, Ltd.IbarakiJapan
  2. 2.Graduate School of Information SciencesTohoku UniversitySendaiJapan
  3. 3.Department of Information and Computer Sciences, Faculty of EngineeringToyo UniversityKawagoeJapan

Personalised recommendations