Learning conjunctions of two unate DNF formulas

Computational and informational results

Aaron Feigelson, Lisa Hellerstein

    Research output: Chapter in Book/Report/Conference proceedingChapter

    Abstract

    We consider the class R2, consisting of conjunctions of two unate DNF formulas. This class is a generalization of the class of 2-clause CNF formulas, and of the class of unate DNF formulas, both of which are properly learnable in polynomial time with membership and equivalence queries. We show that R2 can be properly learned with a polynomial number of polynomial-size membership and equivalence queries, but that it cannot be learned in polynomial time unless P = NP. Thus the barrier to learning R2 is computational rather than informational. In proving our results, we use recent techniques developed for the membership and equivalence query model, as well as Bshouty's work on the monotone dimension. We pose some related open questions on learning DNF formulas of small monotone dimension.

    Original languageEnglish (US)
    Title of host publicationProceedings of the Annual ACM Conference on Computational Learning Theory
    Editors Anon
    Pages255-265
    Number of pages11
    StatePublished - 1996
    EventProceedings of the 1996 9th Annual Conference on Computational Learning Theory - Desenzano del Garda, Italy
    Duration: Jun 28 1996Jul 1 1996

    Other

    OtherProceedings of the 1996 9th Annual Conference on Computational Learning Theory
    CityDesenzano del Garda, Italy
    Period6/28/967/1/96

    Fingerprint

    Polynomials
    Equivalence
    Query
    Monotone
    Polynomial time
    Polynomial
    Learning
    Class
    Model
    Generalization

    ASJC Scopus subject areas

    • Computational Mathematics

    Cite this

    Feigelson, A., & Hellerstein, L. (1996). Learning conjunctions of two unate DNF formulas: Computational and informational results. In Anon (Ed.), Proceedings of the Annual ACM Conference on Computational Learning Theory (pp. 255-265)

    Learning conjunctions of two unate DNF formulas : Computational and informational results. / Feigelson, Aaron; Hellerstein, Lisa.

    Proceedings of the Annual ACM Conference on Computational Learning Theory. ed. / Anon. 1996. p. 255-265.

    Research output: Chapter in Book/Report/Conference proceedingChapter

    Feigelson, A & Hellerstein, L 1996, Learning conjunctions of two unate DNF formulas: Computational and informational results. in Anon (ed.), Proceedings of the Annual ACM Conference on Computational Learning Theory. pp. 255-265, Proceedings of the 1996 9th Annual Conference on Computational Learning Theory, Desenzano del Garda, Italy, 6/28/96.
    Feigelson A, Hellerstein L. Learning conjunctions of two unate DNF formulas: Computational and informational results. In Anon, editor, Proceedings of the Annual ACM Conference on Computational Learning Theory. 1996. p. 255-265
    Feigelson, Aaron ; Hellerstein, Lisa. / Learning conjunctions of two unate DNF formulas : Computational and informational results. Proceedings of the Annual ACM Conference on Computational Learning Theory. editor / Anon. 1996. pp. 255-265
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