Learning k-term monotone boolean formulae

Yoshifumi Sakai, Akira Maruoka

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

5 Citations (Scopus)

Abstract

Valiant introduced a computational model of learning by examples, and gave a precise definition of learnability based on the model. Since then, much effort has been devoted to characterize learnable classes of concepts on this model. Among such learnable classes is the one, denoted k-term MDNF, consisting of monotone disjunctive normal form formulae with at most k terms. In literature, k-term MDNF is shown to be learnable under the assumption that examples are drawn according to the uniform distribution. In this paper we generalize the result to obtain the statement that k-term MDNF is learnable even if positive examples are drawn according to such distribution that the maximum of the ratio of the probabilities of two positive examples is bounded from above by some polynomial.

Original languageEnglish
Title of host publicationAlgorithmic Learning Theory - 3rd Workshop, ALT 1992, Proceedings
EditorsShuji Doshita, Koichi Furukawa, Klaus P. Jantke, Toyaki Nishida
PublisherSpringer Verlag
Pages197-207
Number of pages11
ISBN (Print)9783540573692
DOIs
Publication statusPublished - 1993
Event3rd Workshop on Algorithmic Learning Theory, ALT 1992 - Tokyo, Japan
Duration: 1992 Oct 201992 Oct 22

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume743 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other3rd Workshop on Algorithmic Learning Theory, ALT 1992
CountryJapan
CityTokyo
Period92/10/2092/10/22

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Sakai, Y., & Maruoka, A. (1993). Learning k-term monotone boolean formulae. In S. Doshita, K. Furukawa, K. P. Jantke, & T. Nishida (Eds.), Algorithmic Learning Theory - 3rd Workshop, ALT 1992, Proceedings (pp. 197-207). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 743 LNAI). Springer Verlag. https://doi.org/10.1007/3-540-57369-0_39