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Density and Universality

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Extremal Combinatorics

Part of the book series: Texts in Theoretical Computer Science. An EATCS Series ((TTCS))

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Abstract

In many applications (testing logical circuits, construction of k-wise independent random variables, etc.), vector sets A⊆{0,1}n with the following property play an important role:

For any subset of k coordinates S={i 1,…,i k } the projection of A onto the indices in S contains all possible 2k configurations.

Such sets are called (n,k)-universal. If the same holds not for all but only for at least one subset S of k indices, then A is called (n,k)-dense. The maximal number k, for which A is (n,k)-dense, is also known as the Vapnik–Chervonenkis dimension of A.

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Correspondence to Stasys Jukna .

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© 2011 Springer-Verlag Berlin Heidelberg

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Jukna, S. (2011). Density and Universality. In: Extremal Combinatorics. Texts in Theoretical Computer Science. An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17364-6_10

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  • DOI: https://doi.org/10.1007/978-3-642-17364-6_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17363-9

  • Online ISBN: 978-3-642-17364-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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