Super-tasks, accelerating Turing machines and uncomputability

Oron Shagrir*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


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 languageAmerican English
Pages (from-to)105-114
Number of pages10
JournalTheoretical Computer Science
Issue number1-3
StatePublished - 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).


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


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