Learning read-once formulas with queries

  • Authors:
  • Dana Angluin;Lisa Hellerstein;Marek Karpinski

  • Affiliations:
  • -;-;-

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1993

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Abstract

A read-once formula is a Boolean formula in which each variable occurs, at most, once. Such formulas are also called &mgr;-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 [1]). The results of the authors improve on Valiant's previous results for read-once formulas [26]. It is also shown, that no polynomial-time algorithm using only membership queries or only equivalence queries can exactly identify all read-once formulas.