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computational complexity

, Volume 1, Issue 2, pp 113–129 | Cite as

On the power of small-depth threshold circuits

  • Johan Håstad
  • Mikael Goldmann
Article

Abstract

We investigate the power of threshold circuits of small depth. In particular, we give functions that require exponential size unweighted threshold circuits of depth 3 when we restrict the bottom fanin. We also prove that there are monotone functionsf k that can be computed in depthk and linear size ⋎, ⋏-circuits but require exponential size to compute by a depthk−1 monotone weighted threshold circuit.

Key words

Circuit complexity monotone circuits threshold circuits lower bounds 

Subject classifications

68Q15 68Q99 

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Copyright information

© Birkhäuser Verlag 1991

Authors and Affiliations

  • Johan Håstad
    • 1
  • Mikael Goldmann
    • 1
  1. 1.Department of Numerical Analysis and Computing ScienceRoyal Institute of TechnologyStockholmSWEDEN

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