NonTuring Computations Via Malament–Hogarth SpaceTimes
 Gábor Etesi,
 István Németi
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We investigate the Church–Kalmár–Kreisel–Turing theses theoretical concerning (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–Turingtype 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 abovementioned 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 nonrecursive 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.
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 Title
 NonTuring Computations Via Malament–Hogarth SpaceTimes
 Journal

International Journal of Theoretical Physics
Volume 41, Issue 2 , pp 341370
 Cover Date
 20020201
 DOI
 10.1023/A:1014019225365
 Print ISSN
 00207748
 Online ISSN
 15729575
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Industry Sectors
 Authors

 Gábor Etesi ^{(1)}
 István Németi ^{(2)}
 Author Affiliations

 1. Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, Japan
 2. Alfréd Rényi Mathematical Institute of the Hungarian Academy of Science, Budapest, Hungary