Learnability of exclusive-or expansion based on monotone DNF formulas

Eiji Takimoto; Yoshifumi Sakai; Akira Maraoka

doi:10.1007/3-540-61863-5_30

Learnability of exclusive-or expansion based on monotone DNF formulas

Eiji Takimoto, Yoshifumi Sakai, Akira Maraoka

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	Algorithmic Learning Theory - 7th International Workshop, ALT 1996, Proceedings
Editors	Setsuo Arikawa, Arun K. Sharma
Publisher	Springer Verlag
Pages	12-25
Number of pages	14
ISBN (Print)	3540618635, 9783540618638
DOIs	https://doi.org/10.1007/3-540-61863-5_30
Publication status	Published - 1996
Externally published	Yes
Event	7th International Workshop on Algorithmic Learning Theory, ALT 1996 - Sydney, Australia Duration: Oct 23 1996 → Oct 25 1996

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1160
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	7th International Workshop on Algorithmic Learning Theory, ALT 1996
Country	Australia
City	Sydney
Period	10/23/96 → 10/25/96

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/3-540-61863-5_30

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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. https://doi.org/10.1007/3-540-61863-5_30

Learnability of exclusive-or expansion based on monotone DNF formulas. / Takimoto, Eiji; Sakai, Yoshifumi; Maraoka, Akira.

Algorithmic Learning Theory - 7th International Workshop, ALT 1996, Proceedings. ed. / Setsuo Arikawa; Arun K. Sharma. Springer Verlag, 1996. p. 12-25 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1160).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Takimoto, E, Sakai, Y & Maraoka, A 1996, Learnability of exclusive-or expansion based on monotone DNF formulas. in S Arikawa & AK Sharma (eds), Algorithmic Learning Theory - 7th International Workshop, ALT 1996, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1160, Springer Verlag, pp. 12-25, 7th International Workshop on Algorithmic Learning Theory, ALT 1996, Sydney, Australia, 10/23/96. https://doi.org/10.1007/3-540-61863-5_30

Takimoto E, Sakai Y, Maraoka A. Learnability of exclusive-or expansion based on monotone DNF formulas. In Arikawa S, Sharma AK, editors, Algorithmic Learning Theory - 7th International Workshop, ALT 1996, Proceedings. Springer Verlag. 1996. p. 12-25. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-61863-5_30

Takimoto, Eiji ; Sakai, Yoshifumi ; Maraoka, Akira. / Learnability of exclusive-or expansion based on monotone DNF formulas. Algorithmic Learning Theory - 7th International Workshop, ALT 1996, Proceedings. editor / Setsuo Arikawa ; Arun K. Sharma. Springer Verlag, 1996. pp. 12-25 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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