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

Minds and Machines 17 (2):217-231 (2007)
  Copy   BIBTEX

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.

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 101,628

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2009-01-28

Downloads
245 (#108,856)

6 months
32 (#116,132)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Oron Shagrir
Hebrew University of Jerusalem

Citations of this work

The Church-Turing Thesis.B. Jack Copeland - 2012 - In Ed Zalta (ed.), Stanford Encyclopedia of Philosophy. Stanford, CA: 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.
The philosophy of computer science.Raymond Turner - 2013 - Stanford Encyclopedia of Philosophy.

View all 10 citations / Add more citations

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.
On the Concept of a Random Sequence.Alonzo Church - 1940 - Bulletin of the American Mathematical Society 46 (2):130--135.

View all 31 references / Add more references