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Learning of Bounded-Weight Boolean Functions

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Abstract

The complexity of exact learning of bounded-weight Boolean functions is considered in the paper separately using four types of queries: membership queries, equivalence queries, extended equivalence queries, and comparation queries. The values of the complexity for the first three types are obtained for all classes of functions at consideration. Upper and lower bounds of the complexity for comparation queries being of the same order are presented. Moreover, the exact value of the complexity of learning upper bounded-weight Boolean functions with the help of comparation queries is obtained.

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ACKNOWLEDGMENTS

The author thanks her scientific advisor Professor E.E. Gasanov for the problem formulation and assistance in her work.

Funding

The study is supported by the Interdisciplinary Scientific and Educational School on Brain, Cognitive Systems, and Artificial Intelligence of the Lomonosov Moscow State University.

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Authors and Affiliations

  1. Chair of Mathematical Theory of Intellectual Systems, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    A. V. Bystrygova

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  1. A. V. Bystrygova
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Correspondence to A. V. Bystrygova.

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The author declares that she has no conflicts of interest.

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Translated by E. Oborin

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Cite this article

Bystrygova, A.V. Learning of Bounded-Weight Boolean Functions. Moscow Univ. Math. Bull. 76, 251–258 (2021). https://doi.org/10.3103/S0027132221060036

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  • DOI: https://doi.org/10.3103/S0027132221060036

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