Entropy and enumeration of Boolean functions

Shannon's notion of the entropy of a random variable is used to give simplified proofs of asymptotic formulas for the logarithms of the numbers of monotone Boolean functions and Horn (1951) functions, and for equivalent results concerning families of sets and closure operations.

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 45; no. 6; pp. 2096 - 2100
Main Author: Pippenger, H.
Format: Journal Article
Language:English
Published: New York IEEE 01.09.1999
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Boolean functions
Entropy
Functions
Mathematical models
Variables
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Description
Summary:Shannon's notion of the entropy of a random variable is used to give simplified proofs of asymptotic formulas for the logarithms of the numbers of monotone Boolean functions and Horn (1951) functions, and for equivalent results concerning families of sets and closure operations.
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ISSN:0018-9448
1557-9654
DOI:10.1109/18.782146