Results 121 to 130 of about 394 (158)
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Russian Mathematical Surveys, 2003
Summary: Monotone Boolean functions are an important object in discrete mathematics and mathematical cybernetics. Topics related to these functions have been actively studied for several decades. Many results have been obtained, and many papers published.
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Summary: Monotone Boolean functions are an important object in discrete mathematics and mathematical cybernetics. Topics related to these functions have been actively studied for several decades. Many results have been obtained, and many papers published.
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Interactive learning of monotone Boolean functions
Information Sciences, 1996This paper presents some optimal interactive algorithms for some problems related to learning of monotone Boolean functions. These algorithms are based on the fundamental Hansel theorem. The advantage of the algorithms is that they are not heuristics, as is often the case of many known algorithms for general Boolean functions, but they are optimal in ...
Boris Kovalerchuk +3 more
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The complexity of monotone boolean functions
Mathematical Systems Theory, 1977We study the realization of monotone Boolean functions by networks. Our main result is a precise version of the following statement: the complexity of realizing a monotone Boolean function ofn arguments is less by the factor (2/πn)1/2, whereπ is the circular ratio, than the complexity of realizing an arbitrary Boolean function ofn arguments.
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On the nonlinearity of monotone Boolean functions
Cryptography and Communications, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Approximation of a partial boolean function by a monotonic boolean function
USSR Computational Mathematics and Mathematical Physics, 1978Abstract THE PROBLEM of finding a monotonic Boolean function best approximation a specified partial (not defined everywhere) Boolean function, is solved by a flow algorithm. Among the monotonic functions giving the best approximation, the function possessing the simplest disjunctive normal form is chosen.
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The Monotone Circuit Complexity of Quadratic Boolean Functions
Algorithmica, 2004Several results on the monotone circuit complexity and the conjunctive complexity, i.e., the minimal number of AND gates in monotone circuits, of quadratic Boolean functions are proved We focus on the comparison between single level circuits, which have only one level of AND gates, and arbitrary monotone circuits, and show that there is a huge gap ...
Kazuyuki Amano, Akira Maruoka
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A note on the monotonicity of pseudo-Boolean functions
Zeitschrift für Operations Research, 1974RecentlyWilde 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, 1978This 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
1998Monotone 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
2014We 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 +3 more
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