Consider the following paper, written by A. Steven Younger, Emmett Redd, Hava Siegelmann, and Conrad Bell:

>"A Physical Machine Based on a Super-Turing Computational Model" [found under title on the Web].

I quote the Abstract verbatim:

>We present evidence that the Turing Machine is too restrictive a model to sufficiently describe the computation of our analog computer and, therefore a more conprehensive model is needed.  We report on the construction of a prototype, the Optical Analog Recurrent Neural Network (OpticARRN), and experimental results showing that it performs computations which are beyond those of computers based on the Turing machine.  we conclude that the behavior of OpticARRN is better described by the super-Turing computational model proposed by Siegelmann.  To the best of our knowledge, this is the first application of analog recurrent neural networks realized in a physical computer based on this model.

(Suffice it to say, I leave the judgement as to the truth or falsity of the claim(s) made in the Abstract and the paper to the Reader.)


What I find personally (for what that's worth) interesting in this paper is this particular claim (found in Section 3, "Testing for Computation Beyond the Turing Limit"):

>In order to test super-Turing computation, a suitable problem must be found.  In this case, the answer came from the area of chaotic systems.  The dynamics of chaos are both aperiodic and defined on a continuous phase space.  As such, they cannot be mimicked by a Turing machine [Siegelmann, H. (1998). _Neural Networks and Analog Computation Beyond the Turing Limit_.  Boston: Birkhauser(p. 155)].

It is the validity of this claim that (seemingly) makes or breaks the experiment. Also, the reader should pay particular attention to their methodology for the interpretation of the experimental data.

Note that the experimental setup is shown in figure 1 on pg. 4 of the paper (at least on the copy of the paper I found on the Web).