Exact learning of DNF formulas using DNF hypotheses

Lisa Hellerstein, Vijay Raghavan

    Research output: Contribution to journalArticle

    Abstract

    We show the following: (a) For any ε>0, log(3+ε)n-term DNF cannot be polynomial-query learned with membership and strongly proper equivalence queries. (b) For sufficiently large t, t-term DNF formulas cannot be polynomial-query learned with membership and equivalence queries that use t1+ε-term DNF formulas as hypotheses, for some ε<1 (c) Read-thrice DNF formulas are not polynomial-query learnable with membership and proper equivalence queries. (d) logn-term DNF formulas can be polynomial-query learned with membership and proper equivalence queries. (This complements a result of Bshouty, Goldman, Hancock, and Matar that logn-term DNF can be so learned in polynomial time.) Versions of (a)-(c) were known previously, but the previous versions applied to polynomial-time learning and used complexity theoretic assumptions. In contrast, (a)-(c) apply to polynomial-query learning, imply the results for polynomial-time learning, and do not use any complexity-theoretic assumptions.

    Original languageEnglish (US)
    Pages (from-to)435-470
    Number of pages36
    JournalJournal of Computer and System Sciences
    Volume70
    Issue number4
    DOIs
    StatePublished - Jun 2005

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    Polynomials
    Query
    Polynomial
    Equivalence
    Term
    Polynomial time
    Learning
    Complement
    Imply

    Keywords

    • Algorithms
    • Boolean functions
    • Certificates
    • Complexity theory
    • Computational learning theory
    • Disjunctive normal form
    • DNF

    ASJC Scopus subject areas

    • Computational Theory and Mathematics

    Cite this

    Exact learning of DNF formulas using DNF hypotheses. / Hellerstein, Lisa; Raghavan, Vijay.

    In: Journal of Computer and System Sciences, Vol. 70, No. 4, 06.2005, p. 435-470.

    Research output: Contribution to journalArticle

    Hellerstein, Lisa ; Raghavan, Vijay. / Exact learning of DNF formulas using DNF hypotheses. In: Journal of Computer and System Sciences. 2005 ; Vol. 70, No. 4. pp. 435-470.
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