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Bounded Depth Arithmetic Circuits: Counting and Closure

  • Eric Allender
  • Samir Datta
  • Andris Ambainis
  • David A. Mix Barrington
  • Huong LêThanh
Conference paper
Part of the Lecture Notes in Computer Science book series (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.

Keywords

Closure Property Grid Graph Arithmetic Circuit Boolean Circuit Reachability Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Eric Allender
    • 1
  • Samir Datta
    • 1
  • Andris Ambainis
    • 2
  • David A. Mix Barrington
    • 3
  • Huong LêThanh
    • 4
  1. 1.Department of Computer ScienceRutgers UniversityPiscataway
  2. 2.Computer Science DivisionUniversity of CaliforniaBerkeley
  3. 3.Department of Computer ScienceUniversity of MassachusettsAmherst
  4. 4.Laboratoire de Recherche en InformatiqueUniversité de Paris-SudParis

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