Division Is In Uniform TC0

  • William Hesse
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2076)


Integer division has been known since 1986 [4 13 12] to be in slightly non-uniform TC0, i.e., computable by polynomial-size, constant depth threshold circuits. This has been perhaps the outstanding natural problem known to be in a standard circuit complexity class, but not known to be in its uniform version. We show that indeed division is in uniform TC0. A key step of our proof is the discovery of a first-order formula expressing exponentiation modulo any number of polynomial size.


Input Size Division Problem Iterate Multiplication Threshold Gate Turing Reduction 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • William Hesse
    • 1
  1. 1.Department of Computer ScienceUniversity of MassachusettsMA

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