Even Turing Machines Can Compute Uncomputable Functions (1998)
| Venue: | Unconventional Models of Computation |
| Citations: | 11 - 2 self |
BibTeX
@INPROCEEDINGS{Copeland98eventuring,
author = {B. Jack Copeland},
title = {Even Turing Machines Can Compute Uncomputable Functions},
booktitle = {Unconventional Models of Computation},
year = {1998},
pages = {150--164},
publisher = {Springer-Verlag}
}
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Abstract
Accelerated Turing machines are Turing machines that perform tasks commonly regarded as impossible, such as computing the halting function. The existence of these notional machines has obvious implications concerning the theoretical limits of computability. 2 1. Introduction Neither Turing nor Post, in their descriptions of the devices we now call Turing machines, made much mention of time (Turing 1936, Post 1936). 1 They listed the primitive operations that their devices perform - read a square of the tape, write a single symbol on a square of the tape (first deleting any symbol already present), move one square to the right, and so forth - but they made no mention of the duration of each primitive operation. The crucial concept is that of whether or not the machine halts after a finite number of operations. Temporal considerations are not relevant to the functioning of the devices as described, nor - so we are clearly supposed to believe - to the soundness of the proofs that Turi...
