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Family Complexity and VC-Dimension

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Information Theory, Combinatorics, and Search Theory

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7777))

Abstract

In 2003 Ahlswede, Khachatrian, Mauduit and Sárközy introduced the notion of family complexity of binary sequences, and in 2006 Ahlswede, Mauduit and Sárközy extended this definition to sequences of k symbols. Since that several further related papers have been published on this subject. In this paper our main goal is to present a survey of all these papers. We will also answer a question of Csiszár and Gách on the connection of family complexity and VC-dimension.

Research partially supported by Hungarian National Foundation for Scientific Research, grants K72731 and K100291, and the Agence Nationale de La Recherche, grant ANR-10-BLAN 0103 MUNUM.

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Author information

Authors and Affiliations

  1. Institut de Mathématiques de Luminy, CNRS, UMR 6206, 163 avenue de Luminy, Case 907, F-13288, Marseille Cedex 9, France

    Christian Mauduit

  2. Instituto de Matemática Pura e Aplicada, IMPA, CNRS,UMI 2924, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, RJ, Brasil

    Christian Mauduit

  3. Department of Algebra and Number Theory, Eötvös Loránd University, H-1117, Budapest, Pázmány Péter sétány 1/C, Hungary

    András Sárközy

Authors
  1. Christian Mauduit
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  2. András Sárközy
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Bielefeld, Universitätsstr. 25, 33615, Bielefeld, Germany

    Harout Aydinian  & Christian Deppe  & 

  2. Department of Computer Science, University of Salerno, via Ponte don Melillo, 84084, Fisciano, Italy

    Ferdinando Cicalese

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Mauduit, C., Sárközy, A. (2013). Family Complexity and VC-Dimension. In: Aydinian, H., Cicalese, F., Deppe, C. (eds) Information Theory, Combinatorics, and Search Theory. Lecture Notes in Computer Science, vol 7777. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36899-8_15

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  • DOI: https://doi.org/10.1007/978-3-642-36899-8_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36898-1

  • Online ISBN: 978-3-642-36899-8

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