Learnability of exclusive-or expansion based on monotone DNF formulas

Eiji Takimoto, Yoshifumi Sakai, Akira Maraoka

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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 (Formula presented), where (Formula presented) 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.

Original languageEnglish
Title of host publicationAlgorithmic Learning Theory - 7th International Workshop, ALT 1996, Proceedings
EditorsSetsuo Arikawa, Arun K. Sharma
PublisherSpringer Verlag
Pages12-25
Number of pages14
ISBN (Print)3540618635, 9783540618638
Publication statusPublished - Jan 1 1996
Externally publishedYes
Event7th International Workshop on Algorithmic Learning Theory, ALT 1996 - Sydney, Australia
Duration: Oct 23 1996Oct 25 1996

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1160
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other7th International Workshop on Algorithmic Learning Theory, ALT 1996
CountryAustralia
CitySydney
Period10/23/9610/25/96

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Takimoto, E., Sakai, Y., & Maraoka, A. (1996). Learnability of exclusive-or expansion based on monotone DNF formulas. In S. Arikawa, & A. K. Sharma (Eds.), Algorithmic Learning Theory - 7th International Workshop, ALT 1996, Proceedings (pp. 12-25). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1160). Springer Verlag.