Learning Read-Once Formulas with Queries

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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 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 1993. 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. © 1993, ACM. All rights reserved.

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Angluin, D., Hellerstein, L., & Karpinski, M. (1993). Learning Read-Once Formulas with Queries. Journal of the ACM (JACM), 40(1), 185–210. https://doi.org/10.1145/138027.138061

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