Graduate studies at Western
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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