Topological Equivalence Classification of Balanced Linearly Separable Boolean Functions on n-Dimensional Hypercube

2021 ◽  
Vol 31 (02) ◽  
pp. 2150031
Author(s):  
Qinbin He ◽  
Fangyue Chen ◽  
Wei Jin
Keyword(s):  
Spatial Structure ◽  
Boolean Functions ◽  
Conformal Transformation ◽  
Classification Algorithm ◽  
Equivalence Classes ◽  
Topological Equivalence ◽  
Novel Algorithm

The concept of conformal transformation is proposed through the study of the spatial structure of [Formula: see text]-dimensional hypercubes. Based on conformal transformation, a novel algorithm, called topological equivalence classification algorithm, is proposed for classifying balanced linearly separable Boolean functions. By the proposed algorithm, the topological equivalence classes of all balanced linearly separable Boolean functions and the number of Boolean functions in each of the topological equivalence classes are obtained. In addition, the properties of conformal transformation also show an application prospect for decomposing nonlinearly separable Boolean functions.

Classification of correlation-immune and minimal correlation-immune Boolean functions of 4 and 5 variables

2015 ◽  
Vol 25 (4) ◽  
Author(s):  
Evgeniy. K. Alekseev ◽  
Ekaterina K. Karelina
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
Equivalence Classes ◽  
Constant Function ◽  
Immune Functions

AbstractA classification of correlation-immune and minimal corelation-immune Boolean function of 4 and 5 variables with respect to the Jevons group is given. Representatives of the equivalence classes of correlationimmune functions of 4 and 5 variables are decomposed into minimal correlation-immune functions. Characteristics of various decompositions of the constant function 1 into minimal correlation-immune functions are presented.

A Novel Algorithm for MFSK Signal Classification

2013 ◽  
Vol 446-447 ◽  
pp. 1022-1027
Author(s):  
Juan Fei Xu ◽  
Fu Ping Wang ◽  
Zan Ji Wang
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Intermediate Frequency ◽  
Classification Algorithm ◽  
Signal Classification ◽  
New Classification ◽  
Low Input ◽  
Basic Features ◽  
Novel Algorithm

A new classification algorithm of M-ary FSK signals based on the extraction of signals features is presented in this paper. The implementation of the methodology does not require any apriori information. By extracting some basic features of intermediate frequency signals both in time domain and frequency domain, the classification of M-ary FSK signals is achieved. Simulation result shows that the proposed algorithm can classify 2FSK, 4FSK and 8FSK signals effectively under AWGN and and still keeps a good performance even at low input SNR.

The Research of Extracting Minimal Decision Rules from the Decision Table in Rough Sets

2010 ◽  
Vol 44-47 ◽  
pp. 3948-3953
Author(s):  
Wei Pan ◽  
Yi Jia Huang ◽  
Yang Sheng Wang ◽  
Hong Ji Yang
Keyword(s):  
Information Systems ◽  
Computational Complexity ◽  
Incomplete Information ◽  
Rough Sets ◽  
Decision Rules ◽  
Equivalence Classes ◽  
Decision Table ◽  
Incomplete Information Systems ◽  
Novel Algorithm

Analyzes the traditional methods of extracting decision rules in Rough Sets, defines the concept of the decision dependability and proposes a novel algorithm of extracting short decision rules. Only the length of decision rules is extended when the current decision rules can’t classify all the samples in the decision table. At the same time, three methods are proposed to reduce the computational complexity: 1) defines the concept of bound coefficient, 2) only classify the samples with the same decision values at a time thus averting the time-consuming classification of the equivalence classes with different decision values, 3) defines the Remain set and only classify the samples in the Remain set, so the computational complexity will decrease proportional with the reduction of the samples in the Remain set. Above-mentioned methods can be used directly for incomplete information systems and have great practicability.

scholarly journals A Note on 5-bit Quadratic Permutations’ Classification

2017 ◽  
pp. 398-404 ◽  
Author(s):  
Dušan Božilov ◽  
Begül Bilgin ◽  
Hacı Ali Sahin
Keyword(s):  
Boolean Functions ◽  
Equivalence Classes ◽  
Multiplicative Complexity ◽  
Affine Equivalence ◽  
Vectorial Boolean Functions ◽  
Symmetric Key ◽  
Differential Properties

Classification of vectorial Boolean functions up to affine equivalence is used widely to analyze various cryptographic and implementation properties of symmetric-key algorithms. We show that there exist 75 affine equivalence classes of 5-bit quadratic permutations. Furthermore, we explore important cryptographic properties of these classes, such as linear and differential properties and degrees of their inverses, together with multiplicative complexity and existence of uniform threshold realizations.

Classification method of marine target motion pattern based on spatial-temporal trajectories

2021 ◽  
pp. 1-15
Author(s):  
Baichen Jiang ◽  
Wei Zhou ◽  
Jian Guan ◽  
Jialong Jin
Keyword(s):  
Pattern Classification ◽  
Training Sample ◽  
Classification Algorithm ◽  
Classification Model ◽  
Motion Pattern ◽  
Motion Patterns ◽  
Lp Norm ◽  
Sparse Representation Classification ◽  
Route Safety

Classifying the motion pattern of marine targets is of important significance to promote target surveillance and management efficiency of marine area and to guarantee sea route safety. This paper proposes a moving target classification algorithm model based on channel extraction-segmentation-LCSCA-lp norm minimization. The algorithm firstly analyzes the entire distribution of channels in specific region, and defines the categories of potential ship motion patterns; on this basis, through secondary segmentation processing method, it obtains several line segment trajectories as training sample sets, to improve the accuracy of classification algorithm; then, it further uses the Leastsquares Cubic Spline Curves Approximation (LCSCA) technology to represent the training sample sets, and builds a motion pattern classification sample dictionary; finally, it uses lp norm minimized sparse representation classification model to realize the classification of motion patterns. The verification experiment based on real spatial-temporal trajectory dataset indicates that, this method can effectively realize the motion pattern classification of marine targets, and shows better time performance and classification accuracy than other representative classification methods.

On a new classification of Boolean functions

2019 ◽  
Vol 10 (2) ◽  
pp. 159-168
Author(s):  
Sergei N Fedorov
Keyword(s):  
Boolean Functions ◽  
New Classification

Рассматривается недавно предложенный подход к исследованию булевых функций, в основе которого лежит понятие класса $\Delta$-эквивалентности: множества булевых функций с одной и той же функцией автокорреляции. Такая классификация представляется полезной, поскольку многие криптографические характеристики булевых функций, принадлежащих одному и тому же классу $\Delta$-эквивалентности, одинаковы.

scholarly journals Boolean differential equations: A common model for classes, lattices, and arbitrary sets of Boolean functions

2015 ◽  
Vol 28 (1) ◽  
pp. 51-76 ◽  
Author(s):  
Bernd Steinbach ◽  
Christian Posthoff
Keyword(s):  
Differential Equations ◽  
Boolean Functions ◽  
Differential Calculus ◽  
Short Introduction ◽  
The Core ◽  
Boolean Equation ◽  
General Difference ◽  
Derivatives Of

The Boolean Differential Calculus (BDC) significantly extends the Boolean Algebra because not only Boolean values 0 and 1, but also changes of Boolean values or Boolean functions can be described. A Boolean Differential Equation (BDe) is a Boolean equation that includes derivative operations of the Boolean Differential Calculus. This paper aims at the classification of BDEs, the characterization of the respective solutions, algorithms to calculate the solution of a BDe, and selected applications. We will show that not only classes and arbitrary sets of Boolean functions but also lattices of Boolean functions can be expressed by Boolean Differential equations. In order to reach this aim, we give a short introduction into the BDC, emphasize the general difference between the solutions of a Boolean equation and a BDE, explain the core algorithms to solve a BDe that is restricted to all vectorial derivatives of f (x) and optionally contains Boolean variables. We explain formulas for transforming other derivative operations to vectorial derivatives in order to solve more general BDEs. New fields of applications for BDEs are simple and generalized lattices of Boolean functions. We describe the construction, simplification and solution. The basic operations of XBOOLE are sufficient to solve BDEs. We demonstrate how a XBooLe-problem program (PRP) of the freely available XBooLe-Monitor quickly solves some BDes.

scholarly journals A High Performace of Local Binary Pattern on Classify Javanese Character Classification

2018 ◽  
Vol 5 (1) ◽  
pp. 8 ◽  
Author(s):  
Ajib Susanto ◽  
Daurat Sinaga ◽  
Christy Atika Sari ◽  
Eko Hari Rachmawanto ◽  
De Rosal Ignatius Moses Setiadi
Keyword(s):  
Feature Extraction ◽  
Image Classification ◽  
Local Binary Pattern ◽  
Nearest Neighbor ◽  
Classification Algorithm ◽  
K Nearest Neighbor ◽  
Characteristic Extraction ◽  
Research Objects ◽  
Character Classification

The classification of Javanese character images is done with the aim of recognizing each character. The selected classification algorithm is K-Nearest Neighbor (KNN) at K = 1, 3, 5, 7, and 9. To improve KNN performance in Javanese character written by the author, and to prove that feature extraction is needed in the process image classification of Javanese character. In this study selected Local Binary Patter (LBP) as a feature extraction because there are research objects with a certain level of slope. The LBP parameters are used between [16 16], [32 32], [64 64], [128 128], and [256 256]. Experiments were performed on 80 training drawings and 40 test images. KNN values after combination with LBP characteristic extraction were 82.5% at K = 3 and LBP parameters [64 64].

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