Abstract
We describe a possible physical device that computes a function that cannot be computed by a Turing machine. The device is physical in the sense that it is compatible with General Relativity. We discuss some objections, focusing on those which deny that the device is either a computer or computes a function that is not Turing computable. Finally, we argue that the existence of the device does not refute the Church–Turing thesis, but nevertheless may be a counterexample to Gandy's thesis.
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Shagrir, O., Pitowsky, I. Physical Hypercomputation and the Church–Turing Thesis. Minds and Machines 13, 87–101 (2003). https://doi.org/10.1023/A:1021365222692
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DOI: https://doi.org/10.1023/A:1021365222692