Super-tasks, accelerating Turing machines and uncomputability

Oron Shagrir

doi:10.1016/j.tcs.2003.12.007

Super-tasks, accelerating Turing machines and uncomputability

Oron Shagrir^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

Accelerating Turing machines are devices with the same computational structure as Turing machines (TM), but able to perform super-tasks. We ask whether performing super-tasks alone produces more computational power; for example, whether accelerating TM can solve the halting problem. We conclude that this is not the case. No accelerating TM solves the halting problem. The argument rests on an analysis of the reasoning that leads to Thomson's paradox. The key point is that the paradox rests on a conflation of different perspectives of accelerating processes. This leads to concluding that the same conflation underlies the claim that accelerating TM can solve the halting problem.

Original language	English
Pages (from-to)	105-114
Number of pages	10
Journal	Theoretical Computer Science
Volume	317
Issue number	1-3
DOIs	https://doi.org/10.1016/j.tcs.2003.12.007
State	Published - 4 Jun 2004

Bibliographical note

Funding Information:
I am thankful to Mark Burgin, Jack Copeland, Yuval Dolev, Itamar Pitowsky, Carl Posy and Michael Roubach for discussion and comments. This research was supported by The Israel Science Foundation (Grant No. 857/03–07).

Keywords

Accelerating Turing machines
Halting problem
Super-task
Thomson's paradox

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10.1016/j.tcs.2003.12.007

Cite this

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Super-tasks, accelerating Turing machines and uncomputability

Abstract

Bibliographical note

Keywords

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