Learning hierarchical rule sets
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Learning in the presence of finitely or infinitely many irrelevant attributes
Journal of Computer and System Sciences
Optimal pooling designs with error detection
Journal of Combinatorial Theory Series A
Attribute-efficient learning in query and mistake-bound models
COLT '96 Proceedings of the ninth annual conference on Computational learning theory
Group testing with unreliable tests
Information Sciences: an International Journal
Adaptive versus nonadaptive attribute-efficient learning
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
COLT' 98 Proceedings of the eleventh annual conference on Computational learning theory
Randomized group testing for mutually obscuring defectives
Information Processing Letters
Improved algorithms for group testing with inhibitors
Information Processing Letters
Computational sample complexity and attribute-efficient learning
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the cut-off point for combinatorial group testing
Discrete Applied Mathematics
Lower bounds for identifying subset members with subset queries
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Classical versus quantum communication complexity
ACM SIGACT News
Optimal Attribute-Efficient Learning of Disjunction, Parity and Threshold Functions
EuroCOLT '97 Proceedings of the Third European Conference on Computational Learning Theory
Computational Aspects of Parallel Attribute-Efficient Learning
ALT '98 Proceedings of the 9th International Conference on Algorithmic Learning Theory
Group Testing Problems with Sequences in Experimental Molecular Biology
SEQUENCES '97 Proceedings of the Compression and Complexity of Sequences 1997
PAC learning with irrelevant attributes
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Approximate Location of Relevant Variables under the Crossover Distribution
SAGA '01 Proceedings of the International Symposium on Stochastic Algorithms: Foundations and Applications
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We consider exact learning of monotone Boolean functions by membership queries, in the case that only r of the n variables are relevant. The learner proceeds in a number of rounds. In each round he submits to the function oracle a set of queries which may be chosen depending on the results from previous rounds. In a STOC'98 paper we proved that O(2r + r log n) queries in O(r) rounds are sufficient. While the query bound is optimal for trivial information-theoretic reasons, it was open whether parallelism can be improved without increasing the amount of queries. In the present paper we prove a negative answer: Θ(r) rounds are necessary in the worst case, even for learning a very special type of monotone function. The proof is an adversary argument, based on a distance inequality in binary codes. On the other hand, a Las Vegas strategy based on another STOC'98 result can learn monotone functions in 2 log2 r + O(1) rounds, without using significantly more queries. We also study the constant factors in the deterministic case.