Parity, circuits, and the polynomial-time hierarchy

@article{Furst1981ParityCA,
  title={Parity, circuits, and the polynomial-time hierarchy},
  author={Merrick L. Furst and James B. Saxe and Michael Sipser},
  journal={Mathematical systems theory},
  year={1981},
  volume={17},
  pages={13-27}
}
A super-polynomial lower bound is given for the size of circuits of fixed depth computing the parity function. Introducing the notion of polynomial-size, constant-depth reduction, similar results are shown for the majority, multiplication, and transitive closure functions. Connections are given to the theory of programmable logic arrays and to the relativization of the polynomial-time hierarchy. 

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