We investigate Turing's notion of an A-type artificial neural network. We study a refinement of Turing's original idea, motivated by work of Teuscher, Bull, Preen and Copeland. Our A-types can process binary data by accepting and outputting sequences of binary vectors; hence we can associate a function to an A-type, and we say the A-type represents the function. There are two modes of data processing: clamped and sequential. We describe an evolutionary algorithm, involving graph-theoretic manipulations of A-types, which searches for A-types representing a given function. The algorithm uses both mutation and crossover operators. We implemented the algorithm and applied it to three benchmark tasks. We found that the algorithm performed much better than a random search. For two out of the three tasks, the algorithm with crossover performed better than a mutation-only version.

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In conventional filter design there are generally two underlying assumptions. First, it is assumed that the precise nature of the ooeration to be performed on a signal is known. Second, the signal conditioning is generally a linear operation.(There are certain notable exceptions such as waveform hard-limiting in d demndulat ion; but even in this example, it is the zero-crossing timing which is of interest --no information is being extracted from the signal in the limiting process.)If the nature of the transfer function is known and linear, there are many straight-forward approaches to designing appropriate filters.However, in certain interesting classes of signal processing applications, the description of the desired filter may not be known, or if it is known, it may be nonlinear and exhibit instability when implemented directly. If there are empirical data which represent the class of signals to be operated on in such cases, adaptive learning network (ALN) procedures may be used to synthesize filter forms which estimate or predict the desired parameter. The filters are transversal and are therefore always stable. Questions of stability associated with recursive filters are avoided. This paper presents a procedure for using PIN training techniques to synthesize a nonlinear filter directly from empirical data. The example used involves estimating the energy within a specified band of a broad-band signal. Though the design of a conventional energy estimator is straightforward, this knowledge was not used in the PIN training process --an important consideration. An afterthe-f act comparison is made between the ALN and a conventional system using an eight-pole Butterworth band pass filter. Data Base SynthesisThe data base used for designing and for subsequent testing of the AI.N was synthesized in the following manner.1,2,3 •The PILN was trained to mimic the characteristics of an eight-pole Butterworth filter whose 3db cutoff frequencies, 5] and were equal to 1 and 2, respectively. A rionnalized frequency range of 0 to 10 was used. (So, for example, a 30 kHz signal could be mapped into this range by interpreting it as divided by 3 kHz.)The frequency response of an ideal eight-pole Butterworth continuous filter is shown in Figure 1.To form the data base, three sets of 130 time signals, x(t), j 1 130, were generated.

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