From: Christopher Barton (CJB153@mercury.anglia.ac.uk)
Date: Fri Apr 27 2001 - 13:26:26 MDT
Below is an abstract of a paper I thought some of you might find interesting. It's not light on mathematics, but it might be a new angle on the recent dicussions on the limits of computing.
I've got a postscript if anyone wants a look.
James
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Title: Non-Turing computations via Malament-Hogarth space-times
Authors: Gabor Etesi (Yukawa Institute, Japan), Istvan Nemeti (Renyi
Institute, Hungary)
Comments: 24 pages, LaTex with two eps-figures
We investigate the Church-Kalm\'ar-Kreisel-Turing Theses concerning
theoretical (necessary) limitations of future computers and of deductive
sciences, in view of recent results of classical general relativity
theory.
We argue that (i) there are several distinguished Church-Turing-type
Theses (not only one) and (ii) validity of some of these theses depend on
the background physical theory we choose to use. In particular, if we
choose classical general relativity theory as our background theory, then
the above mentioned limitations (predicted by these Theses) become no more
necessary, hence certain forms of the Church-Turing Thesis cease to be
valid (in general relativity). (For other choices of the background theory
the answer might be different.)
We also look at various ``obstacles'' to computing a non-recursive
function (by relying on relativistic phenomena) published in the
literature and show that they can be avoided (by improving the ``design''
of our future computer). We also ask ourselves, how all this reflects on
the arithmetical hierarchy and the analytical hierarchy of uncomputable
functions. (37kb)
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