Physical computation: How general are Gandy's principles for mechanisms? [Book Review]

Minds and Machines 17 (2):217-231 (2007)
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   Thesis M
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