CONCLUSION

In this paper the properties of the human auditory system have been discussed with particular consideration to the frequency resolution characteristic which is represented by the phenomenon of localization. The localization and processing by which the ear resolves weak signals from noise backgrounds may be explained, at least in part, by nature's use of a correlation process.

While the localization and noise discrimination processes could be equally well accomplished by the use of sharp frequency selective filters, filtering in the time domain is a preferred method employed by nature.

This may be due to the difficulty nature has encountered within the constraints of autocatalytic processes, of manufacturing and maintaining sharply tuned filters within the short and long time stabilities required and to the tolerances necessary.

An analog system for the realization of a similar behavior has been proposed and it has been shown that it permits the realization of a considerable noise improvement factor in the case of random noise.

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REFERENCES

deRosa, L. A. - "Considerations in the Design of a Molecular Electronic Analog of the Periphery Auditory Apparatus" Paper presented at NAECON Symposium, Dayton, Ohio, May 3, 1960

SYNTHESIS OF RELIABLE AUTOMATA AND STABLE NEURAL NETS

K. K. Maitra

RCA Research Laboratories

INTRODUCTION

The advent of microminiaturization, molecular electronics and integrated functional modules makes possible the assembly of very large numbers of functional elements in a small space. For the automata and computing machines of the future the number of functional modules used will be an almost nonexistent restriction. This certainly offers a great advantage, especially to future adaptive and special purpose machines which will require much larger numbers of functional elements than present day machines. On the other hand these modern electronic components have created a serious problem, namely that of reliability. Each basic functional module is most likely fabricated in one continuous operation, and hence has a fixed and mostly inaccessible internal structure, and is often unreliable. In view of the physical structure of the modules, it is often not possible to add redundancy at the individual component level which is one of the common ways of improving the reliability. Furthermore, in extremely complex and large assemblies it may be economically impracticable to depend entirely on preventive maintenance in order to improve the system reliability. The possibility of a failure in a single element causing a total system failure is unacceptable in such complex systems. The designer is therefore confronted with the problem of having to synthesize logical networks that are required to perform logical operations with a high degree of reliability, in which the building blocks are the relatively unreliable functional modules. This paper proposes a solution to this problem which departs from those of Von Neumannl on the one hand, and Moore and Shannon4 on the other: it does not depend on the availability of perfectly reliable "output elements, nor does it make use of redundancy at levels lower than the functional modules. scheme is derived to a great extent from the concept of "logical stability" of neural nets initially posed by Von Neumann2 and subsequently investigated by McCulloch3.

Our

The pioneering work of J. Von Neumann in probabilistic logicl and his studies of the possible components and connections in a search for an understanding of some of the observed behavioral phenomena in biological systems brought many interesting problems to the attention of neuropsychologists. An important problem posed by Von Neumann2 was that of accounting for the observed stability of human behavior, i.e., the ability of the human decision-making

I

Superior numerals wherever they appear refer to the literature in the list of references.

mechanism to maintain an overall stable behavior pattern even under abnormal conditions. McCulloch and his collaborators. investigated this problem, and demonstrated that certain networks composed of neuron-like elements exhibit the property of "logical stability" under a common shift of neural thresholds. That is, the terminal (input-output) behavior of the nets remains unaltered, even though the individual neurons may undergo transformation of their functional states due to environmental conditions causing a common shift in neural thresholds. It is speculated that the stability of neural nets contributes to the improved behaviorial reliability of human beings.

The chief factor contributing to the "logical stability" of complex neural networks with redundant elements is the fact that a formal neuron-like element, postulated by McCulloch, can assume different functional states out of a limited set of states. The functional state in which a neuron at any particular time may be found is determined by the level of its threshold signal. This paper extends the concept of fallible neurons, postulated by Von Neumann and McCulloch, to unreliable conventional logical elements, e.g., AND gates, OR gates, etc., as found in engineering applications. Our chief concern is with networks composed of these conventional logic modules. In a neuron, a change in the value of the threshold causes a change in the logical function performed by the neuron. Conventional logic modules behave in an analogous manner, where the functions performed by a single device are determined by the various healthy and unhealthy conditions of the internal components, and/or the drifts in the signals and control inputs. The behavior of a conventional functional module may therefore be described by a probability vector (P. P) associated with a logical function vector (f. fk). If the module is designed to perform the function f, then the corresponding probability P must be the largest element of the probability vector. This notion of the existence of a function vector in a single logical module lends itself to the possibility of constructing logically stable networks from relatively unreliable conventional elements. These stable networks may, in turn, used to replace the individual logic cells to obtain greater functional reliability.

1'

be

We start with the development of methods for the analysis of reliability of a class of networks constructed of redundant logical modules, namely, simple triplets" and higher

*

This description is adopted from McCulloch3.

order triplets (triplets constructed recursively from simple triplets). The basic tools used in this analysis are probabilistic logic and a so-called "stability map tailored to the present problem. The methods are applicable to triplet networks of any complexity and built of logical modules, which in turn are composed of any physical devices, e.g., the artificial neurons or switching elements found in practical systems. For the purpose of illustration, we have chosen specific resistor-rectifier logic realizations. We have shown how to synthesize more reliable two-input AND and OR gates by using appropriate triplet configurations of basic AND and OR gate modules of lesser reliability. The behavior of more complex networks composed recursively from simple triplet structures is studied. In particular, an interesting property of the recursive structures is observed, namely, that the reliability attains a unique maximum after the first few stages of recursion, subsequent to which the reliability approaches zero asymptotically. Another interesting result that we have established is that it is possible to synthesize the two logical connectives, namely, tautology and falsehood, with perfect reliability.