Physical computation: How general are Gandy's principles for mechanisms?

Minds and Machines 17 (2):217-231 (2007)
Authors
Oron Shagrir
Hebrew University of Jerusalem
Abstract
What are the limits of physical computation? In his ‘Church’s Thesis and Principles for Mechanisms’, Turing’s student Robin Gandy proved that any machine satisfying four idealised physical ‘principles’ is equivalent to some Turing machine. Gandy’s four principles in effect define a class of computing machines (‘Gandy machines’). Our question is: What is the relationship of this class to the class of all (ideal) physical computing machines? Gandy himself suggests that the relationship is identity. We do not share this view. We will point to interesting examples of (ideal) physical machines that fall outside the class of Gandy machines and compute functions that are not Turing-machine computable.
Keywords Accelerating Turing machine   Asynchronous computation   Church's thesis   Davies   Determinism   Gandy   Hogarth   Hypercomputation   Physical computation   Pitowsky   Supertask
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DOI 10.1007/s11023-007-9058-2
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References found in this work BETA

Shadows of the Mind.Roger Penrose - 1994 - Oxford University Press.
On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.

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Citations of this work BETA

The Physical Church-Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.
Concrete Digital Computation: What Does It Take for a Physical System to Compute? [REVIEW]Nir Fresco - 2011 - Journal of Logic, Language and Information 20 (4):513-537.

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