Learning read-once formulas with queries

Dana Angluin, Lisa Hellerstein, Marek Karpinski

    Research output: Contribution to journalArticle

    Abstract

    A read-once formula is a Boolean formula in which each variable occurs, at most, once. Such formulas are also called μ-formulas or Boolean trees. This paper treats the problem of exactly identifying an unknown read-once formula using specific kinds of queries. The main results are a polynomial-time algorithm for exact identification of monotone read-once formulas using only membership queries, and a polynomial-time algorithm for exact identification of general read-once formulas using equivalence and membership queries (a protocol based on the notion of a minimally adequate teacher). The results of the authors improve on Valiant's previous results for read-once formulas. It is also shown, that no polynomial-time algorithm using only membership queries or only equivalence queries can exactly identify all read-once formulas.

    Original languageEnglish (US)
    Pages (from-to)185-210
    Number of pages26
    JournalJournal of the ACM
    Volume40
    Issue number1
    DOIs
    StatePublished - Jan 1993

    Fingerprint

    Polynomials
    Query
    Polynomial-time Algorithm
    Equivalence
    Learning
    Monotone
    Unknown

    ASJC Scopus subject areas

    • Computational Theory and Mathematics
    • Computer Graphics and Computer-Aided Design
    • Hardware and Architecture
    • Information Systems
    • Software
    • Theoretical Computer Science

    Cite this

    Angluin, D., Hellerstein, L., & Karpinski, M. (1993). Learning read-once formulas with queries. Journal of the ACM, 40(1), 185-210. https://doi.org/10.1145/138027.138061

    Learning read-once formulas with queries. / Angluin, Dana; Hellerstein, Lisa; Karpinski, Marek.

    In: Journal of the ACM, Vol. 40, No. 1, 01.1993, p. 185-210.

    Research output: Contribution to journalArticle

    Angluin, D, Hellerstein, L & Karpinski, M 1993, 'Learning read-once formulas with queries', Journal of the ACM, vol. 40, no. 1, pp. 185-210. https://doi.org/10.1145/138027.138061
    Angluin D, Hellerstein L, Karpinski M. Learning read-once formulas with queries. Journal of the ACM. 1993 Jan;40(1):185-210. https://doi.org/10.1145/138027.138061
    Angluin, Dana ; Hellerstein, Lisa ; Karpinski, Marek. / Learning read-once formulas with queries. In: Journal of the ACM. 1993 ; Vol. 40, No. 1. pp. 185-210.
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