Minds and Machines

, Volume 12, Issue 4, pp 521–539 | Cite as

Infinite Time Turing Machines

  • Joel David Hamkins


Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and limitations of supertask algorithms.

infinite time jump theorem Post's problem supertask Turing degrees Turing machine 


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  1. Buchi, J.R. (1962), Logic, Methodology and Philosophy and Science, in Proc.1960 Int.Congr., Vol. 1 of 1, Stanford, CA: Stanford University Press.Google Scholar
  2. Chihara, C.S. (1965), ‘On the Possibility of Completing an Infinite Process’, Philosophical Review 74, pp. 74–87.Google Scholar
  3. Copeland, J. (1998a), Super Turing-Machines, Complexity 4, pp. 30–32.Google Scholar
  4. Copeland, J. (1998b), Even TuringMachines Can Compute Uncomputable Functions, in C. Calude, J. Casti, M. Dinneen, eds, Unconventional Models of Computation, London: Springer, pp. 150–164.Google Scholar
  5. Copeland, J. (2002), Accelerating TuringMachines, Minds and Machines, in C. Cleland, ed., Special Issue on Effective Procedures, (in press).Google Scholar
  6. Earman, J. (1995), Bangs, Crunches, Whimpers and Shrieks: Singularities and Acausalities in Relativistic Spacetimes, Oxford University Press, New York: The Clarendon Press.Google Scholar
  7. Earman J. and Norton, J.D. (1993), ‘Forever is a Day: Supertasks in Pitowski and Malament-Hogarth Spacetimes’, Philos.Sci. 60(1), pp. 22–42.Google Scholar
  8. Feferman, S. and Spector, C. (1962), ‘Incompleteness Along Paths in Progressions of Theories’, The Journal of Symbolic Logic 27, pp. 383–390.Google Scholar
  9. Hamkins J.D. and Lewis A. (2000), ‘Infinite Time Turing Machines’, The Journal of Symbolic Logic 65(2), pp. 567–604.Google Scholar
  10. Hamkins J.D. and Seabold, D. (2001), ‘Infinite Time Turing Machines with Only One Tape’, Mathematical Logic Quarterly 47(2), pp. 271–287.Google Scholar
  11. Hamkins J.D. and Lewis, A. (2002) ‘Post's Problem for Supertasks Has Both Positive and Negative Solutions’, Archive for Mathematical Logic 41(6), pp. 507–523.Google Scholar
  12. Hogarth, (1992), ‘Does General Relativity Allow an Observer to View an Eternity in a Finite Time?’ Foundations of Physics Letters 5, pp. 173–181.Google Scholar
  13. Hogarth, (1994), ‘Non-Turing Computers and Non-Turing Computability,’ in D. Hull, M. Forbes and R.B. Burian, eds., Vol. 1 of East Lansing: Philosophy of Science Association, pp. 126–138.Google Scholar
  14. Löwe, B. (2001), ‘Revision Sequences and Computers with an Infinite Amount of Time’, Logic Comput. 11(1), pp. 25–40.Google Scholar
  15. Laraudogoitia, J.P. (1996), ‘A Beautiful Supertask’, Mind 105(417), pp. 81–84.Google Scholar
  16. Pitowsky, (1990), ‘The Physical Church Thesis and Physical Computational Complexity’, Iyyun 39, pp. 81–99.Google Scholar
  17. Sacks, G.E. (1990), Higher Recursion Theory, Berlin, Springer.Google Scholar
  18. Soare, R.I. (1987), Recursively Enumerable Sets and Degrees, New York, Springer.Google Scholar
  19. Thomson, (1954-55), ‘Tasks and Super-Tasks’, Analysis XV, pp. 1–13.Google Scholar
  20. Welch, P. (1999), ‘Friedman's Trick: Minimality Arguments in the Infinite Time Turing Degrees’, in Sets and Proofs, Proceedings ASL Logic Colloquium, 258, pp. 425–436.Google Scholar
  21. Welch, P. (2000a), ‘The Lengths of Infinite time Turing Machine Computations’, Bulletin of the London Mathematical Society 32(2), pp. 129–136.Google Scholar
  22. Welch, P. (200b), ‘Eventually Infinite Time Turing Machine Degrees: Infinite tTime Decidable Reals’, Journal of Symbolic Logic 65(3), p. 11.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Joel David Hamkins
    • 1
  1. 1.The City University of New YorkNew YorkUSA

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