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Learnability of exclusive-or expansion based on monotone DNF formulas

  • Eiji Takimoto
  • Yoshifumi Sakai
  • Akira Maruoka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1160)

Abstract

The learnability of the class of exclusive-or expansion based on monotone DNF formulas is investigated. The class consists of the formulas of the form f=f1 ⊕ ... ⊕ fd, where f1 > ... > fd are monotone DNF formulas. It is shown that any Boolean function can be represented as an formula in this class, and that the representation in the simplest form is unique. Learning algorithms that learn such formulas using various queries are presented: An algorithm with subset and superset queries and one with membership and equivalence queries are given. The former can learn any formula in the class, while the latter is proved to learn formulas of bounded depth, i.e., formulas represented as exclusive-or of a constant number of monotone DNF formulas. In spite of seemingly strong restriction of the depth being constant, the class of formulas of bounded depth includes functions with very high complexity in terms of DNF and CNF representations, so the latter algorithm could learn Boolean functions significantly complex otherwise represented.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Eiji Takimoto
    • 1
  • Yoshifumi Sakai
    • 2
  • Akira Maruoka
    • 1
  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan
  2. 2.Department of Information and Computer SciencesFaculty of Engineering, Toyo UniversityKawagoeJapan

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