There are two issues of reliability in such a machine. First, if the machine is repeatedly started from the same initial state, there may be a probability less than unity of it producing a result which may be regarded as a calculation output. This is an issue of machine reliability. Second, there is the possibility that the results of the repeated calculations may differ from each other. This is an issue of calculation reliability. In an application such as weather forecasting, the fraction of results lying within a certain domain gives us some indication of the reliability of the forecast, and is useful information.
Some of the errors introduced by the arbiters may be errors in machine operation instructions, and therefore catastrophic. Clearly we should design the parallel nature of the machine to avoid such cases. Whilst not necessarily an easy task, this means not placing arbiters in the path of the development of 32 bit variables describing machine operation. Others may be errors in parameters, or data variables, in the problem being solved. Such errors may not be fatal, particularly if the machine is intended to do very fast analyses of systems which may have classically chaotic solutions.
We hypothesize that biological neural nets are particularly prone to arbitration errors; they are slow, and they are massively parallel. It may be that the organism exploits this in its decision-making activities by organising its net architecture somewhat along the lines suggested above, to make the arbitration errors introduced by processing coincide with noise in the sensory input driving the net. All such errors may then be lumped together and ignored, since chaotic attractors are robust in the presence of such added noise, and the organism takes its decisions from the global nature of the attractors. Clearly there will be the occasional gross error, but then we have come to expect this when we consider the processing abilities of biological systems.
Acknowledgements.
The authors have had helpful discussions with Jonathan Deane, Philip Aston, David Hamill, Roger Peel, G G Johnstone, A Shafarenko, and M Peter Kennedy, in the course of preparing this paper. The content is entirely the responsibility of the authors, however. Presentation of this work was in part supported by the British Science and Engineering Research Council (now EPSRC) under grant GRH41850.