Physical Computation: How General are Gandy's Principles for Mechanisms?

Authors:
B. Jack Copeland;Oron Shagrir
Affiliations:
School of Philosophy, University of Canterbury, Christchurch, New Zealand;Department of Philosophy, The Hebrew University of Jerusalem, Jerusalem, Israel 91905
Venue:
Minds and Machines
Year:
2007

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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.