文章基本信息

标题：Learning Circuits with few Negations
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作者：Eric Blais ; Cl{\'e}ment L. Canonne ; Igor C. Oliveira 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2015
卷号：40
页码：512-527
DOI：10.4230/LIPIcs.APPROX-RANDOM.2015.512
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in any circuit computing them, a complexity measure that interpolates between monotone functions and the class of all functions. We study this generalization of monotonicity from the vantage point of learning theory, establishing nearly matching upper and lower bounds on the uniform-distribution learnability of circuits in terms of the number of negations they contain. Our upper bounds are based on a new structural characterization of negation-limited circuits that extends a classical result of A.A. Markov. Our lower bounds, which employ Fourier-analytic tools from hardness amplification, give new results even for circuits with no negations (i.e. monotone functions).
关键词：Boolean functions; monotonicity; negations; PAC learning