Some typical properties of large AND/OR Boolean formulas

  • Hanno Lefmann
  • Petr Savický
Contributed Papers Complexity Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 969)


In this paper typical properties of large random Boolean AND/OR formulas are investigated. Such formulas with n variables are viewed as rooted binary trees chosen from the uniform distribution of all rooted binary trees with m leaves, where n is fixed and m tends to infinity. The leaves are labeled by literals and the inner nodes by the connectives AND/OR, both uniformly at random. In extending the investigation to infinite trees, we obtain a close relation between the formula size complexity of an arbitrary Boolean function f and the probability of its occurrence under this distribution, i.e., the negative logarithm of this probability differs from the formula size complexity of f only by a polynomial factor.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Hanno Lefmann
    • 1
    • 2
  • Petr Savický
    • 1
    • 2
  1. 1.Lehrstuhl Informatik IIUniversität DortmundDortmundGermany
  2. 2.Institute of Computer ScienceAcademy of Sciences of Czech RepublicPragueCzech Republic

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