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Bounded Depth Arithmetic Circuits: Counting and Closure

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Book cover Automata, Languages and Programming

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1644))

Abstract

Constant-depth arithmetic circuits have been defined and studied in [AAD97,ABL98]; these circuits yield the function classes #AC0 and GapAC0. These function classes in turn provide new characterizations of the computational power of threshold circuits, and provide a link between the circuit classes AC0 (where many lower bounds are known) and TC0 (where essentially no lower bounds are known). In this paper, we resolve several questions regarding the closure properties of #AC0 and GapAC0 and characterize #AC0 in terms of counting paths in a family of bounded-width graphs.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Rutgers University, Piscataway, USA

    Eric Allender & Samir Datta

  2. Computer Science Division, University of California, Berkeley, USA

    Andris Ambainis

  3. Department of Computer Science, University of Massachusetts, Amherst, USA

    David A. Mix Barrington

  4. Laboratoire de Recherche en Informatique, Université de Paris-Sud, Paris, France

    Huong LêThanh

Authors
  1. Eric Allender
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  2. Samir Datta
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  3. Andris Ambainis
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  4. David A. Mix Barrington
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  5. Huong LêThanh
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Editor information

Editors and Affiliations

  1. Institute for Computer Science, Academy of Sciences of the Czech Republic, Pod vodarenskou vezi 2, 182 07, Prague 8 - Liben, Czech Republic

    Jirí Wiedermann

  2. ILLC-WINS-University of Amsterdam, Plantage Muidergracht 24, 1018, TV, Amsterdam, The Netherlands

    Peter van Emde Boas

  3. BRICS, Department of Computer Science, University of Aarhus, Ny Munkegade, Bldg. 540, DK, 8000, Aarhus C, Denmark

    Mogens Nielsen

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© 1999 Springer-Verlag Berlin Heidelberg

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Allender, E., Datta, S., Ambainis, A., Mix Barrington, D.A., LêThanh, H. (1999). Bounded Depth Arithmetic Circuits: Counting and Closure. In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds) Automata, Languages and Programming. Lecture Notes in Computer Science, vol 1644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48523-6_12

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  • DOI: https://doi.org/10.1007/3-540-48523-6_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66224-2

  • Online ISBN: 978-3-540-48523-0

  • eBook Packages: Springer Book Archive

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