On the Possibilities of Hypercomputing Supertasks

Minds and Machines 21 (1):83-96 (2011)
Authors
Vincent C. Müller
University of Leeds
Abstract
This paper investigates the view that digital hypercomputing is a good reason for rejection or re-interpretation of the Church-Turing thesis. After suggestion that such re-interpretation is historically problematic and often involves attack on a straw man (the ‘maximality thesis’), it discusses proposals for digital hypercomputing with Zeno-machines , i.e. computing machines that compute an infinite number of computing steps in finite time, thus performing supertasks. It argues that effective computing with Zeno-machines falls into a dilemma: either they are specified such that they do not have output states, or they are specified such that they do have output states, but involve contradiction. Repairs though non-effective methods or special rules for semi-decidable problems are sought, but not found. The paper concludes that hypercomputing supertasks are impossible in the actual world and thus no reason for rejection of the Church-Turing thesis in its traditional interpretation.
Keywords computing  computability  hypercomputing  effective computing  supertask  Church-Turing thesis  Copeland  Benacerraf  accelerated Turing machine  Zeno machine
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DOI 10.1007/s11023-011-9222-6
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The Emperor's New Mind.Roger Penrose - 1989 - Oxford University Press.
So How Does the Mind Work?Steven Pinker - 2005 - Mind and Language 20 (1):1-38.

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