Physical constraints on hypercomputation

Paul Cockshott, Lewis Mackenzie, Greg Michaelson

Research output: Contribution to journalArticle

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. © 2007 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)159-174
Number of pages16
JournalTheoretical Computer Science
Volume394
Issue number3
DOIs
Publication statusPublished - 8 Apr 2008

Keywords

  • Computability
  • Hyper-computing
  • Quantum-computing
  • Quantum-measurement

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