IDENTIFICATION AND REALIZATION OF LINEARLY SEPARABLE BOOLEAN FUNCTIONS VIA CELLULAR NEURAL NETWORKS

2008 ◽  
Vol 18 (11) ◽  
pp. 3299-3308 ◽  
Author(s):  
BO MI ◽  
XIAOFENG LIAO ◽  
CHUANDONG LI
Keyword(s):  
Neural Networks ◽  
Directed Graph ◽  
Boolean Functions ◽  
Cellular Neural Networks ◽  
Truth Table

In this paper, an effective method for identifying and realizing linearly separable Boolean functions (LSBF) of six variables via Cellular Neural Networks (CNN) is presented. We characterized the basic relations between CNN genes and the truth table of Boolean functions. In order to implement LSBF independently, a directed graph is employed to sort the offset levels according to the truth table. Because any linearly separable Boolean gene (LSBG) can be derived separately, our method will be more practical than former schemes [Chen & Chen, 2005a, 2005b; Chen & He, 2006].

REALIZATION OF BOOLEAN FUNCTIONS VIA CNN WITH VON NEUMANN NEIGHBORHOODS

2006 ◽  
Vol 16 (05) ◽  
pp. 1389-1403 ◽  
Author(s):  
FANGYUE CHEN ◽  
GUOLONG HE ◽  
GUANRONG CHEN
Keyword(s):  
Neural Networks ◽  
Boolean Functions ◽  
Cellular Neural Networks ◽  
Gene Bank ◽  
Truth Table ◽  
Bifurcation Method ◽  
Von Neumann ◽  
The Family ◽  
Binary Input ◽  
Input Variables

Recently, an effective method for realizing linearly separable Boolean functions via Cellular Neural Networks (CNN), called the threshold bifurcation method, was introduced, with a CNN gene bank of four variables established [Chen & Chen, 2005]. Based on this success, the present paper is to further explore the realization of all linearly separable Boolean functions of five variables via CNN with von Neumann neighborhoods. This paper provides: (i) important and essential relations among the genes (or templates) and the offsets of an uncoupled CNN as well as the basis of the binary input vectors set, (ii) a neat truth table of uncoupled CNN with five input variables, (iii) 94572 linearly separable Boolean functions (LSBF) in the family of 225 = 4.294967296 × 109 Boolean functions of five variables, realizable by a single CNN, and (iv) all 94572 CNN linearly separable Boolean genes (LSBG), which can be determined to form the CNN gene bank of five variables.

scholarly journals REALIZATION AND BIFURCATION OF BOOLEAN FUNCTIONS VIA CELLULAR NEURAL NETWORKS

2005 ◽  
Vol 15 (07) ◽  
pp. 2109-2129 ◽  
Author(s):  
FANGYUE CHEN ◽  
GUANRONG CHEN
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Boolean Function ◽  
Boolean Functions ◽  
Cellular Neural Network ◽  
Cellular Neural Networks ◽  
Gene Bank ◽  
Engineering Applications ◽  
Binary Input

In this work, we study the realization and bifurcation of Boolean functions of four variables via a Cellular Neural Network (CNN). We characterize the basic relations between the genes and the offsets of an uncoupled CNN as well as the basis of the binary input vectors set. Based on the analysis, we have rigorously proved that there are exactly 1882 linearly separable Boolean functions of four variables, and found an effective method for realizing all linearly separable Boolean functions via an uncoupled CNN. Consequently, any kind of linearly separable Boolean function can be implemented by an uncoupled CNN, and all CNN genes that are associated with these Boolean functions, called the CNN gene bank of four variables, can be easily determined. Through this work, we will show that the standard CNN invented by Chua and Yang in 1988 indeed is very essential not only in terms of engineering applications but also in the sense of fundamental mathematics.

New Criteria on Stability of Dynamic Memristor Delayed Cellular Neural Networks

2020 ◽  
pp. 1-13
Author(s):  
Kun Deng ◽  
Song Zhu ◽  
Wei Dai ◽  
Chunyu Yang ◽  
Shiping Wen
Keyword(s):  
Neural Networks ◽  
Cellular Neural Networks ◽  
New Criteria

scholarly journals Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

2011 ◽  
Vol 21 (4) ◽  
pp. 649-658 ◽  
Author(s):  
Qianhong Zhang ◽  
Lihui Yang ◽  
Daixi Liao
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
Inequality Technique

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.

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