Mathematical systems theory

, Volume 17, Issue 1, pp 13–27 | Cite as

Parity, circuits, and the polynomial-time hierarchy

  • Merrick Furst
  • James B. Saxe
  • Michael Sipser


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.


Computational Mathematic Programmable Logic Parity Function Transitive Closure Closure Function 
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Copyright information

© Springer-Verlag New York Inc 1984

Authors and Affiliations

  • Merrick Furst
    • 1
  • James B. Saxe
    • 1
  • Michael Sipser
    • 2
  1. 1.Department of Computer ScienceCarnegie-Mellon UniversityPittsburghUSA
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyBostonUSA

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