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computational complexity

, Volume 5, Issue 2, pp 99–112 | Cite as

Top-down lower bounds for depth-three circuits

  • J. Håstad
  • S. Jukna
  • P. Pudlák
Article

Abstract

We present a top-down lower bound method for depth-three ⋎, ⋏, ¬-circuits which is simpler than the previous methods and in some cases gives better lower bounds. In particular, we prove that depth-three ⋎, ⋏, ¬-circuits that compute parity (or majority) require size at least\(2^{0.618...\sqrt n } (or 2^{0.849...\sqrt n } \), respectively). This is the first simple proof of a strong lower bound by a top-down argument for non-monotone circuits.

Key words

Computational complexity small-depth circuits 

subject classifications

68Q25 

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Copyright information

© Birkhäuser Verlag 1995

Authors and Affiliations

  • J. Håstad
    • 1
  • S. Jukna
    • 3
  • P. Pudlák
    • 2
  1. 1.Royal Institute of TechnologyStockholmSweden
  2. 2.Mathematical InstitutePragueCzech Republic
  3. 3.Institute of MathematicsVilniusLithuania

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