scholarly journals Separation results for boolean function classes

2021 ◽  
Author(s):  
Aniruddha Biswas ◽  
Palash Sarkar
Keyword(s):  
Boolean Function ◽  
Function Classes ◽  
Separation Results

scholarly journals On PAC learning algorithms for rich Boolean function classes

2007 ◽  
Vol 384 (1) ◽  
pp. 66-76 ◽  
Author(s):  
Lisa Hellerstein ◽  
Rocco A. Servedio
Keyword(s):  
Boolean Function ◽  
Learning Algorithms ◽  
Pac Learning ◽  
Function Classes

scholarly journals Definability of Boolean function classes by linear equations over GF(2)

2004 ◽  
Vol 142 (1-3) ◽  
pp. 29-34 ◽  
Author(s):  
Miguel Couceiro ◽  
Stephan Foldes
Keyword(s):  
Boolean Function ◽  
Linear Equations ◽  
Function Classes

scholarly journals Equational characterizations of Boolean function classes

2000 ◽  
Vol 211 (1-3) ◽  
pp. 27-51 ◽  
Author(s):  
Oya Ekin ◽  
Stephan Foldes ◽  
Peter L. Hammer ◽  
Lisa Hellerstein
Keyword(s):  
Boolean Function ◽  
Function Classes

scholarly journals Comparison of Quantitative Morphology of Layered and Arbitrary Patterns: Contrary to Visual Perception, Binary Arbitrary Patterns Are Layered from a Structural Point of View

2021 ◽  
Vol 11 (14) ◽  
pp. 6300
Author(s):  
Igor Smolyar ◽  
Daniel Smolyar
Keyword(s):  
Boolean Function ◽  
Layer Structure ◽  
Central Element ◽  
Morphological Characteristics ◽  
Building Blocks ◽  
Point Of View ◽  
Living Systems ◽  
Seismic Profiles ◽  
Contour Maps ◽  
Anisotropic Layers

Patterns found among both living systems, such as fish scales, bones, and tree rings, and non-living systems, such as terrestrial and extraterrestrial dunes, microstructures of alloys, and geological seismic profiles, are comprised of anisotropic layers of different thicknesses and lengths. These layered patterns form a record of internal and external factors that regulate pattern formation in their various systems, making it potentially possible to recognize events in the formation history of these systems. In our previous work, we developed an empirical model (EM) of anisotropic layered patterns using an N-partite graph, denoted as G(N), and a Boolean function to formalize the layer structure. The concept of isotropic and anisotropic layers was presented and described in terms of the G(N) and Boolean function. The central element of the present work is the justification that arbitrary binary patterns are made up of such layers. It has been shown that within the frame of the proposed model, it is the isotropic and anisotropic layers themselves that are the building blocks of binary layered and arbitrary patterns; pixels play no role. This is why the EM can be used to describe the morphological characteristics of such patterns. We present the parameters disorder of layer structure, disorder of layer size, and pattern complexity to describe the degree of deviation of the structure and size of an arbitrary anisotropic pattern being studied from the structure and size of a layered isotropic analog. Experiments with arbitrary patterns, such as regular geometric figures, convex and concave polygons, contour maps, the shape of island coastlines, river meanders, historic texts, and artistic drawings are presented to illustrate the spectrum of problems that it may be possible to solve by applying the EM. The differences and similarities between the proposed and existing morphological characteristics of patterns has been discussed, as well as the pros and cons of the suggested method.

On 1-stable perfectly balanced Boolean functions

2017 ◽  
Vol 27 (2) ◽  
Author(s):  
Stanislav V. Smyshlyaev
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
The Other ◽  
Correlation Immunity ◽  
Other Hand

AbstractThe paper is concerned with relations between the correlation-immunity (stability) and the perfectly balancedness of Boolean functions. It is shown that an arbitrary perfectly balanced Boolean function fails to satisfy a certain property that is weaker than the 1-stability. This result refutes some assertions by Markus Dichtl. On the other hand, we present new results on barriers of perfectly balanced Boolean functions which show that any perfectly balanced function such that the sum of the lengths of barriers is smaller than the length of variables, is 1-stable.

Statistical Complexity of Algorithms for Boolean Function Minimization

1965 ◽  
Vol 12 (3) ◽  
pp. 364-375 ◽  
Author(s):  
Franco Mileto ◽  
Gianfranco Putzolu
Keyword(s):  
Boolean Function ◽  
Function Minimization ◽  
Complexity Of Algorithms ◽  
Statistical Complexity

scholarly journals Robust Template Decomposition without Weight Restriction for Cellular Neural Networks Implementing Arbitrary Boolean Functions Using Support Vector Classifiers

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Yih-Lon Lin ◽  
Jer-Guang Hsieh ◽  
Jyh-Horng Jeng
Keyword(s):  
Neural Networks ◽  
Boolean Function ◽  
Past Research ◽  
Cellular Neural Network ◽  
Decomposition Methods ◽  
Cellular Neural Networks ◽  
Support Vector ◽  
Decomposition Algorithms ◽  
Weight Restriction ◽  
The Given

If the given Boolean function is linearly separable, a robust uncoupled cellular neural network can be designed as a maximal margin classifier. On the other hand, if the given Boolean function is linearly separable but has a small geometric margin or it is not linearly separable, a popular approach is to find a sequence of robust uncoupled cellular neural networks implementing the given Boolean function. In the past research works using this approach, the control template parameters and thresholds are restricted to assume only a given finite set of integers, and this is certainly unnecessary for the template design. In this study, we try to remove this restriction. Minterm- and maxterm-based decomposition algorithms utilizing the soft margin and maximal margin support vector classifiers are proposed to design a sequence of robust templates implementing an arbitrary Boolean function. Several illustrative examples are simulated to demonstrate the efficiency of the proposed method by comparing our results with those produced by other decomposition methods with restricted weights.

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