Results 131 to 140 of about 367 (158)

A note on the monotonicity of pseudo-Boolean functions

Zeitschrift für Operations Research, 1974
RecentlyWilde andSanchez-Anton [1971] have studied monotonically increasing pseudo-Boolean functions, and have given a very efficient method for their minimization. The role of this note is to give an equivalent formulation of this property and to show how the new formulation makes it possible to read the sought minimum directly from the expression of ...
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Analysis of Algorithms for the Evaluation of Monotonic Boolean Functions

IEEE Transactions on Computers, 1978
This correspondence considers the efficiency of some algorithms for the evaluation of monotonic Boolean functions. It is shown that algorithms based on the criterion of maximizing the local information gain about the Boolean function with n variables may sometimes require a number of computational steps which is n/log n times the computational steps of
Yuri Breitbart, Shmuel Gal
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On the Structure of Idempotent Monotone Boolean Functions

1998
Monotone Boolean functions have been extensively studied in the area of nonlinear digital filtering, specifically stack and morphological filtering. In fact, any Stack Filter of window-width n is uniquely specified by a monotone Boolean function of n variables.
Ilya Shmulevich, Edward J. Coyle
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On DNF Approximators for Monotone Boolean Functions

2014
We study the complexity of approximating monotone Boolean functions with disjunctive normal form (DNF) formulas, exploring two main directions. First, we construct DNF approximators for arbitrary monotone functions achieving one-sided error: we show that every monotone f can be e-approximated by a DNF g of size \(2^{n-\Omega_\epsilon(\sqrt{n ...
Eric Blais, Johan Håstad, Rocco A. Servedio, Li-Yang Tan   +3 more
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Learning Monotone Boolean Functions by Uniformly Distributed Examples

SIAM Journal on Computing, 1992
Summary: \textit{L. G. Valiant} [Commun. ACM 27, 1134-1142 (1984; Zbl 0587.68077); Philos. Trans. R. Soc. Lond., A 312, 441-446 (1984; Zbl 0544.68057)] introduced a new computational model of concept learning by example, gave the definition of learnability of classes of Boolean functions, and derived algorithms for learning specific classes of Boolean ...
Qian-Ping Gu, Akira Maruoka
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Fast sequential evaluation of monotonic Boolean functions

Information Sciences, 1980
Abstract A correspondence between the factored form representation of monotonic Boolean functions and the sequential evaluation procedures for them is shown to exist. Based on such a relationship, a criterion is developed for obtaining the cost of the sequential procedure directly from the factored form representation. Making use of this criterion, a
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Replaceability and computational equivalence for monotone boolean functions

Acta Informatica, 1985
Replacement rules have played an important role in the study of monotone boolean function complexity. In this paper, notions of replaceability and computational equivalence are formulated in an abstract algebraic setting, and examined in detail for finite distributive lattices - the appropriate algebraic context for monotone boolean functions.
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Monotonic Boolean functions and incompatible systems of inequalities

USSR Computational Mathematics and Mathematical Physics, 1986
Translation from Zh. Vychisl. Mat. Mat. Fiz. 26, No.10, 1592-1596 (Russian) (1986; Zbl 0611.94014).
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The realization of monotone Boolean functions (Preliminary Version)

Proceedings of the eighth annual ACM symposium on Theory of computing - STOC '76, 1976
In this paper we study the complexity of realizing a monotone but otherwise arbitrary Boolean function. We consider realizations by means of networks and formulae. In both cases the possibility exists that although a monotone function can always be realized in terms of monotone basis functions, a more economical realization may be possible if basis ...
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Clutter Decomposition and Monotonic Boolean Functions*

Annals of the New York Academy of Sciences, 1970
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