Top-down lower bounds for depth-three circuits

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.

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Håstad, J., Jukna, S. & Pudlák, P. Top-down lower bounds for depth-three circuits. Comput Complexity 5, 99–112 (1995). https://doi.org/10.1007/BF01268140

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Key words

  • Computational complexity
  • small-depth circuits

subject classifications

  • 68Q25