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Scandinavian Workshop on Algorithm Theory

SWAT 2000: Algorithm Theory - SWAT 2000 pp 504–512Cite as

Parallel Attribute-Efficient Learning of Monotone Boolean Functions

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1851))

Abstract

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(2 r + r logn) 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 2log2 r + O(1) rounds, without using significantly more queries. We also study the constant factors in the deterministic case.

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Authors and Affiliations

  1. Theoretische Informatik II, Fern Universität, 58084, Hagen, Germany

    Peter Damaschke

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  1. Peter Damaschke
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© 2000 Springer-Verlag Berlin Heidelberg

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Damaschke, P. (2000). Parallel Attribute-Efficient Learning of Monotone Boolean Functions. In: Algorithm Theory - SWAT 2000. SWAT 2000. Lecture Notes in Computer Science, vol 1851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44985-X_42

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  • DOI: https://doi.org/10.1007/3-540-44985-X_42

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67690-4

  • Online ISBN: 978-3-540-44985-0

  • eBook Packages: Springer Book Archive

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