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
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.
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