Efficient implementation of neighborhood logic for cellular automata via the Cellular Neural Network Universal Machine

2010 12th International Workshop on Cellular Nanoscale Networks and Their Applications (CNNA 2010)

et al. 2010

Perceptron is one of the most important aspects of artificial neural networks (ANN), while cellular neural networks (CNN) are biologically inspired systems in which computation emerges from the collective behavior of some locally coupled simple cells. However, whether the minimal number of the neurons in the hidden layer of a perceptron needed or a CNN template design for performing a prescribed task has not been completely characterized today. This article summarizes several algorithms for decomposing linearly non-separable Boolean function, specially a DNA-like decomposing algorithm and a shortest distance decomposing algorithm, with emphasis on the relationship between universal perceptron (UP) and CNN, and provides some examples to show the powerful ability of these algorithms in decomposing non-LSBF. Moreover, a new concept named CNN-UP is developed, which may lead to a useful new PC software in designing CNN and perceptron in the near future.

“…An efficient algorithm decomposing non-LSBF was introduced in [24]. The main steps of this CFC algorithm are:…”

Section: A Cfc and Compact Algorithmsmentioning

confidence: 99%

“…Therefore, it is imperative to implement a non-LSBF as the logic operations of a sequence of LSBF [24]- [26].…”

Section: Introductionmentioning

confidence: 99%

On CNN universal perceptron

2010 12th International Workshop on Cellular Nanoscale Networks and Their Applications (CNNA 2010)

et al. 2010

“…This resembles the rules for game of life, and therefore similar templates have been adopted [11]. In particular, the bias value has to be changed to account for the condition on the threshold.…”

Section: Innovation Models Based On Cnnsmentioning

confidence: 99%

Innovation Systems by Nonlinear Networks

Andriani¹,

Conti

Fortuna

et al. 2006

Nonlinear Dyn

Cellular Neural Networks (CNNs) constitute a powerful paradigm for modeling complex systems. Innovation systems are complex systems in which small and medium enterprises play the role of simple units interacting with each other. In this paper, innovation systems based on CNN are investigated. It is shown how a model based on CNN can reproduce the main features of innovation systems and how this model can be generalized to include different aspects of the actors of the financial market.

“…Several methods have been developed for decomposing a given non-LSBF [4,5]. It was found that an average of 20 linearly separable templates are required to implement randomly selected Boolean functions with nine inputs [9].…”

Section: Introductionmentioning

confidence: 99%

“…It is known that only the single-layer perceptron (SLP) networks or uncoupled standard CNN cells with binary inputs and outputs can be used to implement linearly separable Boolean functions (LSBF), and a majority of Boolean functions are not linearly separable [1][2][3][4][5][6]. The percentage of LSBF in the entire set of Boolean functions is getting smaller in spite of the fact that the number 434 F. CHEN, W. TANG AND G. CHEN of LSBF quickly increases as the number of input variables increases.…”

Section: Introductionmentioning

confidence: 99%

Single‐layer perceptron and dynamic neuron implementing linearly non‐separable Boolean functions

Wenhui

2008

Circuit Theory & Apps

SUMMARYThis paper presents a single-layer perceptron (SLP) scheme with an impulse activation function (IAF) and a dynamic neuron (DN) with a trapezoidal activation function (TAF). Combining with some interesting properties of the offset levels, it is shown that many linearly non-separable Boolean functions can be realized by using only one SLPwIAF or one DNwTAF. In the present work, a few appropriate IAF and TAF are adopted, and the inverse offset level method is used for the design of the SLPwIAF synaptic weights and the DNwTAF templates. The XOR and NXOR Boolean operations with two inputs and all 152 non-separable Boolean functions with three inputs can be easily implemented by one SLPwIAF or one DNwTAF. Finally, the entire set of 152 DNwTAF templates associated with 152 non-separable Boolean functions of three inputs is completely listed.