Boolean functions with a large number of subfunctions and small complexity and depth

  • Dietmar Uhlig
Part of the Lecture Notes in Computer Science book series (LNCS, volume 529)


If f(x1,...,xn) is a Boolean function on the variables x1,...,xn then f(*1,...,*n) where *i ∈ {0, 1, xi}, i = 1,...,n, is called subfunction of f. The number of subfunctions of f is at most 3n. Intuition suggests that a Boolean function with a large number of subfunctions has a large (combinatorial) complexity and a large depth. We show that this intuition is wrong. There exist Boolean functions with about 3n subfunctions (i. e. about the maximal number of subfunctions) and with a very small complexity and depth (about 2n and log2n, respectively).


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Dietmar Uhlig
    • 1
  1. 1.Ingenieurhochschule MittweidaMittweidaGermany

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