Minds and Machines

, 19:391 | Cite as

A Brief Critique of Pure Hypercomputation

Article

Abstract

Hypercomputation—the hypothesis that Turing-incomputable objects can be computed through infinitary means—is ineffective, as the unsolvability of the halting problem for Turing machines depends just on the absence of a definite value for some paradoxical construction; nature and quantity of computing resources are immaterial. The assumption that the halting problem is solved by oracles of higher Turing degree amounts just to postulation; infinite-time oracles are not actually solving paradoxes, but simply assigning them conventional values. Special values for non-terminating processes are likewise irrelevant, since diagonalization can cover any amount of value assignments. This should not be construed as a restriction of computing power: Turing’s uncomputability is not a ‘barrier’ to be broken, but simply an effect of the expressive power of consistent programming systems.

Keywords

Diagonalization Halting problem Hypercomputation Super-task Zeno machine 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.BresciaItaly

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