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Exponential Lower Bounds for Depth 3 Arithmetic Circuits in Algebras of Functions over Finite Fields

  • D. Grigoriev
  • A. Razborov

Abstract.

A depth 3 arithmetic circuit can be viewed as a sum of products of linear functions. We prove an exponential complexity lower bound on depth 3 arithmetic circuits computing some natural symmetric functions over a finite field F. Also, we study the complexity of the functions f : D n F for subsets DF. In particular, we prove an exponential lower bound on the complexity of depth 3 arithmetic circuits computing some explicit functions f:(F*) n F (in particular, the determinant of a matrix).

Keywords: Exponential lower bounds, Depth 3 arithmetic circuits, Finite fields. 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • D. Grigoriev
    • 1
  • A. Razborov
    • 2
  1. 1.IMR Université Rennes-1, Beaulieu 35042, Rennes, France (e-mail: dima@maths.univ-rennes1.fr)FR
  2. 2.Steklov Mathematical Institute, Gubkina 8, 117966, GSP-1, Moscow, Russia (e-mail: razborov@genesis.mi.ras.ru)RU

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