Learning boolean functions in an infinite attribute space
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
When won't membership queries help?
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Computational learning theory: survey and selected bibliography
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Learning k-term DNF formulas with an incomplete membership oracle
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
A computational model of teaching
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Asking questions to minimize errors
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
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A read-once formula is a boolean formula in which each variable occurs at most once. Such formulas are also called u-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]). Our results improve on Valiant''s previous results for read-once formulas [18]. We also show that no polynomial time algorithm using only membership queries or only equivalence queries can exactly identify all read-once formulas.