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On Negations in Boolean Networks

  • Chapter
Efficient Algorithms

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5760))

Abstract

Although it is well known by a counting argument that relative to the full basis most Boolean functions need exponentially many operations, for explicit Boolean functions only linear lower bounds with small constant factors are known. For monotone networks (i.e., networks without negations) exponential lower bounds for explicit monotone Boolean functions have been proved. We describe the state of the art and give some arguments why techniques developed for the proof of lower bounds for monotone networks cannot easily be extended to Boolean networks with negations.

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Author information

Authors and Affiliations

  1. Informatik V, Universität Bonn, Römerstr. 164, D-53117, Bonn, Germany

    Norbert Blum

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  1. Norbert Blum
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Editors and Affiliations

  1. Institut für Informatik, Universität Freiburg, Georges-Köhler-Allee 79, 79110, Freiburg, Germany

    Susanne Albers

  2. Institut für Informatik, Freie Universität Berlin, Takustr. 9, 14195, Berlin, Germany

    Helmut Alt

  3. Fachbereich IV - Informatik, Universität Trier, 54286, Trier, Germany

    Stefan Näher

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Blum, N. (2009). On Negations in Boolean Networks. In: Albers, S., Alt, H., Näher, S. (eds) Efficient Algorithms. Lecture Notes in Computer Science, vol 5760. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03456-5_2

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  • DOI: https://doi.org/10.1007/978-3-642-03456-5_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03455-8

  • Online ISBN: 978-3-642-03456-5

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