Abstract
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.
This research was supported by GA CR, Grant No. 201/95/0976, and by Heinrich-Hertz-Stiftung while visiting Universität Dortmund, FB Informatik, LS II.
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© 1995 Springer-Verlag Berlin Heidelberg
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Lefmann, H., Savický, P. (1995). Some typical properties of large AND/OR Boolean formulas. In: Wiedermann, J., Hájek, P. (eds) Mathematical Foundations of Computer Science 1995. MFCS 1995. Lecture Notes in Computer Science, vol 969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60246-1_130
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DOI: https://doi.org/10.1007/3-540-60246-1_130
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