On the Distribution of the Number of Monotone Boolean Functions Relative to the Number of Lower Units

@article{Korshunov2002OnTD,
  title={On the Distribution of the Number of Monotone Boolean Functions Relative to the Number of Lower Units},
  author={Aleksey D. Korshunov and Ilya Shmulevich},
  journal={Mathematics eJournal},
  year={2002}
}
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21 Citations
Highly Influential Citations
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Background Citations
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21 Citations

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Random Uniform and Pure Random Simplicial Complexes
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Singleton and 2-periodic attractors of sign-definite Boolean networks
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The hypercube, Qd, is a natural and much studied combinatorial object, and we discuss various extremal problems related to it. A subgraph of the hypercube is said to be (Qd, F )-saturated if it…
Random Growth Models with Polygonal Shapes 1
We consider discrete-time random perturbations of monotone cellular automata (CA) in two dimensions. Under general conditions, we prove the existence of half-space velocities, and then establish the…
Random growth models with polygonal shapes
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Abstracts of Workshop on Computational Algebraic Statistics, Theories and Applications
s of Workshop on Computational Algebraic Statistics, Theories and Applications December 10-11, 2008 Kyoto, Japan CASTA2008 Supported by JSPS Grants-in-Aid for Scientific Research No.18200019, No.…
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References

SHOWING 1-10 OF 24 REFERENCES
On the Fourier spectrum of monotone functions
TLDR
It is shown that this is tight in the sense that for any subexponential time algorithm there is a monotone Boolean function for which this algorithm cannot approximate with error better than O(1/=n).
Properties of Complexity Measures for Prams and Wrams
On Dedekind’s problem: The number of monotone Boolean functions
with an = ce~nli, /3„ = e'(Iog w)/«1'2.The number \p(n) is equal to the number of ideals, or of antichains,or of monotone increasing functions into 0 and 1 definable on thelattice of subsets of an…
Interactive Learning of Monotone Boolean Functions
On Dedekind’s problem: the number of isotone Boolean functions. II
It is shown that 0(n), the size of the free distributive lattice on n generators (which is the number of isotone Boolean functions on subsets of an n element set), satisfies [n1 i (n) < 2(1 +0(1og…
A computation of the eighth Dedekind number
We compute the eighth Dedekind number, or the number of monotone collections of subsets of a set with eight elements. The number obtained is 56, 130, 437, 228, 687, 557, 907, 788.
OBDDs of a Monotone Function and of Its Prime Implicants
TLDR
It is shown that there exists a monotone function which has an O(n) size sum-of-products but cannot be represented by a polynomial size OBDD, and that the relationship between the two OBDDs of a monOTone function and of its prime implicant set is unclear.
Order and symmetry of simple games
The aim of the paper is to use some known results of the theory of boolean functions and of the theory of finite groups for the classification and construction of simple games.Simple games can be…
Stack filters
TLDR
This investigation of the properties of stack filters produces several new, useful, and easily implemented filters, including two which are named asymmetric median filters.
An Introduction To Probability Theory And Its Applications
TLDR
A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.
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