Identifying μ-formula decision trees with queries
COLT '90 Proceedings of the third annual workshop on Computational learning theory
Learning switch configurations
COLT '90 Proceedings of the third annual workshop on Computational learning theory
When won't membership queries help?
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Learning read-once formulas over fields and extended bases
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
Learning arithmetic read-once formulas
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Learning read-once formulas with queries
Journal of the ACM (JACM)
Learning &mgr;-branching programs with queries
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Asking questions to minimize errors
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
On learning embedded symmetric concepts
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
On learning counting functions with queries
COLT '94 Proceedings of the seventh annual conference on Computational learning theory
Learning from a consistently ignorant teacher
COLT '94 Proceedings of the seventh annual conference on Computational learning theory
On the learnability of Zn-DNF formulas (extended abstract)
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
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A formula is read-once if each variable appears on at most a single input. Angluin, Hellerstein, and Karpinski have shown that boolean formulas with AND, OR, and NOT gates are exactly identifiable in polynomial time using membership and equivalence queries [AHK89]. Hancock and Hellerstein have generalized this to allow a wider subclass of symmetric basis functions [HH91]. We show a polynomial time algorithm in this model for identifying read-once formulas whose gates compute arbitrary functions of fan-in k or less for some constant k (i.e. any f :{0,1}1≤c≤k → {0,1}). We further show that if there is a polynomial time membership and equivalence query algorithm to identify read-once formulas over some set of functions B that meets certain technical conditions, then there is also such an algorithm to identify read-once formulas over B&ugr;{f:{0,1}1≤c≤k → {0,1}}. Finally, we extend the previous results to show that there is a polynomial time identification algorithm for read-once formulas over the basis of all symmetric functions (and hence also over the union of arbitrary symmetric and arbitrary constant fan-in gates). Given standard cryptographic assumptions, none of these results are possible for read-twice formulas.