The complexity of symmetric boolean functions

  • Ingo Wegener
Part of the Lecture Notes in Computer Science book series (LNCS, volume 270)


The class of symmetric Boolean functions contains many fundamental functions, among them all types of counting functions. Hence the efficient computation of symmetric functions is a fundamental problem in computer science. Known results on the complexity of symmetric functions in several models of computation are described and new results on the complexity of symmetric functions with respect to bounded depth circuits and parallel random access machines are presented.


Boolean Function Symmetric Function Counting Function Polynomial Size Prime Implicant 
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  1. Ajtai M, Ben-Or M (1984) A theorem on probabilistic constant depth computations. 16.STOC: 471–474Google Scholar
  2. Ajtai M, Komlós J, Szemerédi E (1983) An 0(n log n) sorting network, 15.STOC: 1–9Google Scholar
  3. Barrington DA (1986) Bounded-width polynomial-size branching programs recognize exactly those languages in NC1. 18.STOC: 1–5Google Scholar
  4. Beame P (1986) Lower bounds in parallel machine computation. Ph.D.Thesis.Univ.TorontoGoogle Scholar
  5. Brustmann B, Wegener I (1986) The complexity of symmetric functions in bounded-depth circuits. To appear: Information Processing LettersGoogle Scholar
  6. Bublitz S, Schürfeld U, Voigt B, Wegener I (1986) Properties of complexity measures for PRAMs and WRAMs. To appear: Theoretical Computer ScienceGoogle Scholar
  7. Denenberg L, Gurevich Y, Shelah S (1983) Cardinalities definable by constant-depth, polynomial-size circuits. TR Harvard Univ.Google Scholar
  8. Fagin R, Klawe MM, Pippenger NJ, Stockmeyer L (1985) Bounded-depth, polynomial-size circuits for symmetric functions. Theoretical Computer Science 36: 239–250Google Scholar
  9. Hastad J (1986) Almost optimal lower bounds for small depth circuits. 18.STOC: 6–20Google Scholar
  10. Muller DE, Preparata FP (1975) Bounds to complexities of networks for sorting and switching. Journal of the ACM 22: 195–201Google Scholar
  11. Stockmeyer L, Vishkin U (1984) Simulation of parallel random access machines by circuits. SIAM J.on Computing 13:409–422Google Scholar
  12. Vishkin U, Wigderson A (1985) Trade-offs between depth and width in parallel computation. SIAM J.on Computing 14: 303–314Google Scholar
  13. Wegener I (1984) Optimal decision trees and one-time-only branching programs for symmetric Boolean functions. Information and Control 62: 129–143Google Scholar
  14. Wegener I (1986) The range of new lower bound techniques for WRAMs and bounded depth circuits. To appear: EIK.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Ingo Wegener
    • 1
  1. 1.FB 20 -InformatikJohann Wolfgang Goethe-UniversitätFrankfurt a.M.Fed.Rep.of Germany

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