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On the number of threshold functions
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A.A. Irmatov
Published/Copyright:
February 2, 2016
Abstract
A Boolean function is called a threshold function if its truth domain is a part of the n-cube cut off by some hyperplane. The number of threshold functions of n variables P(2, n) was estimated in [1, 2, 3]. Obtaining the lower bounds is a problem of special difficulty. Using a result of the paper [4], Zuev in [3] showed that for sufficiently large n
P(2, n) > 2n²(1-10/ln n).
In the present paper a new proof which gives a more precise lower bound of P(2, n) is proposed, namely, it is proved that for sufficiently large n
P(2, n) > 2n²(1-7/ln n)P(2, [(7(n-1)ln2)/ln(n- 1)]).
Published Online: 2016-2-2
Published in Print: 1993-1-1
© 2016 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Editorial
- The Steiner problem: a survey
- Exponents of classes of non-negative matrices
- Algebraic operations and identities generated by Grassmann's algebras
- Expansion of even permutations into two factors of the given cyclic structure
- Line hypergraphs
- On the number of threshold functions
- Large deviations of the height of a random tree
- Theorems on large deviations in the polynomial scheme of trials
- Forthcoming Papers
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Articles in the same Issue
- Editorial
- The Steiner problem: a survey
- Exponents of classes of non-negative matrices
- Algebraic operations and identities generated by Grassmann's algebras
- Expansion of even permutations into two factors of the given cyclic structure
- Line hypergraphs
- On the number of threshold functions
- Large deviations of the height of a random tree
- Theorems on large deviations in the polynomial scheme of trials
- Forthcoming Papers
- Contents
