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On the Monotone Circuit Complexity of Quadratic Boolean Functions

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Algorithms and Computation (ISAAC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3341))

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Abstract

Several results on the monotone circuit complexity and the conjunctive complexity, i.e., the minimal number of AND gates in monotone circuits, of quadratic Boolean functions are proved. We focus on the comparison between single level circuits, which have only one level of AND gates, and arbitrary monotone circuits, and show that there is a huge gap between the conjunctive complexity of single level circuits and that of general monotone circuits for some explicit quadratic function. Almost tight upper bounds on the largest gap between the single level conjunctive complexity and the general conjunctive complexity over all quadratic functions are also proved. Moreover, we describe the way of lower bounding the single level circuit complexity, and give a set of quadratic functions whose monotone complexity is strictly smaller than its single level complexity.

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Author information

Authors and Affiliations

  1. Graduate School of Information Sciences, Tohoku University, Aoba 6-6-05, Aramaki, Sendai, 980-8579, Japan

    Kazuyuki Amano & Akira Maruoka

Authors
  1. Kazuyuki Amano
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  2. Akira Maruoka
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Fudan University, 200433, Shanghai, China

    Rudolf Fleischer

  2. Department of Computer Science, The Hong Kong University of Science and Technology, Hong Kong

    Gerhard Trippen

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© 2004 Springer-Verlag Berlin Heidelberg

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Amano, K., Maruoka, A. (2004). On the Monotone Circuit Complexity of Quadratic Boolean Functions. In: Fleischer, R., Trippen, G. (eds) Algorithms and Computation. ISAAC 2004. Lecture Notes in Computer Science, vol 3341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30551-4_5

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  • DOI: https://doi.org/10.1007/978-3-540-30551-4_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24131-7

  • Online ISBN: 978-3-540-30551-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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