Physical hypercomputation and the church–turing thesis

Minds and Machines 13 (1):87-101 (2003)
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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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Oron Shagrir
Hebrew University of Jerusalem

Citations of this work

Why we view the brain as a computer.Oron Shagrir - 2006 - Synthese 153 (3):393-416.
Computation in physical systems.Gualtiero Piccinini - 2010 - Stanford Encyclopedia of Philosophy.
The Physical Church–Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.
Quantum computing.Amit Hagar & Michael Cuffaro - 2019 - Stanford Encyclopedia of Philosophy.

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References found in this work

On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
Systems of logic based on ordinals..Alan Turing - 1939 - London,: Printed by C.F. Hodgson & son.

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