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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| Veröffentlicht in: | IEEE transactions on information theory Jg. 45; H. 6; S. 2096 - 2100 |
|---|---|
| 1. Verfasser: | |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
IEEE
01.09.1999
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Schlagworte: | |
| ISSN: | 0018-9448, 1557-9654 |
| Online-Zugang: | Volltext |
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| Abstract | 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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| AbstractList | 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. 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 This study demonstrates how Shannon's notion of the entropy of a discrete random variable can be used to solve some problems of combinatorial enumeration. In particular, simplified proofs are derived for asymptotic formulas for the logarithms of the numbers of monotone Boolean functions and Horn functions, and for equivalent results concerning families of sets and closure operations. 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 functions, and for equivalent results concerning families of sets and closure operations. |
| Author | Pippenger, H. |
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| Cites_doi | 10.1016/0097-3165(77)90083-8 10.1002/j.1538-7305.1948.tb00917.x 10.2307/2036446 10.1016/0304-3975(91)90359-A 10.1016/0097-3165(76)90079-0 10.1137/0605009 10.1137/S0895480190283595 10.37236/1377 10.2307/2268661 10.1109/TIT.1974.1055150 10.1016/0097-3165(86)90019-1 |
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| References | ref12 coppersmith (ref6) 1998; 5 ref10 jelinek (ref11) 1968 korshunov (ref13) 1980; 38 de bruijn (ref3) 1951; 23 dedekind (ref7) 1897; 2 ref17 massey (ref15) 1974; it 20 ref16 ref18 ref8 ref9 ref4 andreyev (ref2) 1985 ref5 alekseyev (ref1) 1989; 1 lindstro¨m (ref14) 1964; 9 |
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| SubjectTerms | Boolean functions Entropy Functions Mathematical models Variables |
| Title | Entropy and enumeration of Boolean functions |
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