On the complexity of balanced Boolean functions

  • A. Bernasconi
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Part of the Lecture Notes in Computer Science book series (LNCS, volume 1203)


This paper introduces the notions of balanced and strongly balanced Boolean functions and examines the complexity of these functions using harmonic analysis on the hypercube. The results are applied to derive a lower bound related to AC0 functions.


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  1. 1.
    A. Bernasconi, B. Codenotti. Sensitivity of Boolean Functions, Abstract Harmonic Analysis and Circuit Complexity. ICSI Technical Report TR-93-030 (1993).Google Scholar
  2. 2.
    A. Bernasconi, B. Codenotti, J. Simon. On the Fourier Analysis of Boolean Functions. Submitted for publication (1996).Google Scholar
  3. 3.
    M. Furst, J. Saxe, M. Sipser. Parity, circuits, and the polynomial-time hierarchy. Math. Syst. Theory, Vol. 17 (1984), pp. 13–27.Google Scholar
  4. 4.
    J. Håstad. Computational limitations for small depth circuits. Ph.D. Dissertation, MIT Press, Cambridge, Mass. (1986).Google Scholar
  5. 5.
    S.L. Hurst, D.M. Miller, J.C. Muzio. Spectral Method of Boolean Function Complexity. Electronics Letters, Vol. 18 (33) (1982), pp. 572–574.Google Scholar
  6. 6.
    R. J. Lechner. Harmonic Analysis of Switching Functions. In Recent Development in Switching Theory, Academic Press (1971), pp. 122–229.Google Scholar
  7. 7.
    N. Linial, Y. Mansour, N. Nisan. Constant Depth Circuits, Fourier Transform, and Learnability. Journal of the ACM, Vol. 40 (3) (1993), pp. 607–620.Google Scholar
  8. 8.
    H. U. Simon. A tight Ω(log log n) bound on the time for parallel RAM's to compute nondegenerate Boolean functions. FCT'83, Lecture Notes in Computer Science 158 (1983).Google Scholar
  9. 9.
    I. Wegener. The complexity of Boolean functions. Wiley-Teubner Series in Comp. Sci., New York — Stuttgart (1987).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • A. Bernasconi
    • 1
    • 2
  1. 1.Dipartimento di InformaticaUniversità di PisaItaly
  2. 2.Istituto di Matematica Computazionale del C.N.R.Pisa

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