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A synaptic operator based on multiplication requires a large amount of hardware, particularly in digital implementations. In this brief, we introduce an extended class of synaptic operators which includes the standard multiplication as a particular case. The properties of the extended class of operators are established. Among these, it was found that the global stability theorem of cellular neural networks (CNN's) is applicable to the extended class of synaptic operator as well as for the multiplier-based synapse. This is an important property which allows for the replacement of the multiplication-based synaptic operator with another specific member of the extended class, here referred to as a comparative synapse, without changing the functionality of the overall CNN system. Instead of multiplication, which has an implementation complexity of O([n.sup.2]), the comparative synapse has a complexity of only O(n) in a digital implementation (where n is the resolution of the fixed-point implementation). The effectiveness of this new operator is demonstrated by a few examples of discrete-time CNN operating in all possible dynamic modes (equilibrium, periodic and chaotic).

The main difficulty in implementing cellular automata on the Cellular Neural Network Universal Machine (CNNUM) is the need to perform arbitrary logic functions of the input neighborhood. Since the architecture computes weighted sums of this neighborhood, by using a 'B-template,' it is limited to threshold logic, i.e., a logical operation to be computed by a single transient must be in the class of linearly separable Boolean functions. It was shown previously how a general logic function can be implemented on the CNNUM by cascading component functions from this class - namely by the direct implementation of the minterm or maxterm formulation of the desired function. However, for functions of a 3 x 3 input neighborhood this method may require up to 256 stages. We propose a more efficient method for implementing general logic functions on the CNNUM and other hardwares capable of performing a threshold logic function of an input neighborhood. The class of considered component functions is a superset of the minterms and maxterms but, for purposes of searchability, ease of implementation, and robustness, a subset of the general linearly separable Boolean functions. We have formulated an algorithm that will find a sequence of weight-restricted threshold logic functions (B-templates with weights from {-1, 0, +1} and a bias) that, when cascaded together using two-input logical operations, will result in the desired Boolean function. Two examples are given to exhibit the algorithm.

Many algorithms have been devised for halftoning digital images. These algorithms all suffer well-studied defects, which are especially apparent in the case where the resulting image is displayed at the marginally oversampled resolution and viewed at the critical pixel merge distance. Recently, it has been shown that a neural network approach may be useful for halftoning. Here, the feasibility of using neural networks in a practical application is considered. The cellular neural network (CNN) architecture is chosen for its proven implementability in VLSI and high speed operation. Since both the CNN and halftoning have a geometrically local character, the CNN provides a natural implementation. The CNN template weights are derived by analogy to the well-known error diffusion algorithm for halftoning. Some limitations of the neural network approach are analyzed providing an advance in designing template weights over previous methods. These limitations are shown to be especially critical in the case of the small interconnection neighborhoods needed for efficient implementation. Our design criteria are validated by direct simulation. The resulting halftones are shown to be more faithful reproductions of the original than those produced by the error diffusion algorithm. It is suggested that a CNN with optical inputs could provide a high-speed scanner/halftoner for applications such as FAX.

It is shown that the simplest integrated circuit implementations of the CNN Universal Machine can play the 'game of life,' and are therefore equivalent to a Turing Machine. In addition, a constructive proof is given for the direct implementation of general first-order cellular automata on such machines.

A significant increase in the information processing abilities of CNN's demands powerful information processing at the cell level. In this paper, the defining formula, the main properties, and several applications of a novel coupling cell are presented. Since it is able to implement any Boolean function, its functionality expands on those of digital RAM's by adding new capabilities such as learning and interpolation. While it is able to embed all previously accumulated knowledge regarding useful binary information processing tasks performed by standard CNN's, the pyramidal universal cell provides a broader context for defining other useful processing tasks, including extended gray scale or color image processing as well. Examples of applications in image processing are provided in this paper. Implementation issues are also considered. Assuming some compromise between area and speed, a VLSI implementation of CNN's based on pyramidal cells offers a speedup of up to one million times when compared to corresponding software implementations.