Physical constraints on hypercomputation

Cockshott, W.P., Mackenzie, L.M. and Michaelson, G. (2008) Physical constraints on hypercomputation. Theoretical Computer Science, 394(3), pp. 159-174. (doi: 10.1016/j.tcs.2007.12.009)

Abstract

Many attempts to transcend the fundamental limitations to computability implied by the Halting Problem for Turing Machines depend on the use of forms of hypercomputation that draw on notions of infinite or continuous, as opposed to bounded or discrete, computation. Thus, such schemes may include the deployment of actualised rather than potential infinities of physical resources, or of physical representations of real numbers to arbitrary precision. Here, we argue that such bases for hypercomputation are not materially realisable and so cannot constitute new forms of effective calculability. A slightly amended version of this has now appeared in the journal Theoretical Computer Science A.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Mackenzie, Dr Lewis and Cockshott, Dr William
• Authors: Cockshott, W.P., Mackenzie, L.M., and Michaelson, G.
• Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: Theoretical Computer Science
• Publisher: Elsevier
• ISSN: 0304-3975
• Copyright Holders: Copyright © 2008 Elsevier
• First Published: First published in Theoretical Computer Science 394(3):159-174
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher

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