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Supertasks do not increase computational power

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Abstract

It is generally assumed that supertasks increase computational power. It is argued, for example, that supertask machines can compute beyond the Turing limit, e.g., compute the halting function. We challenge this assumption. We do not deny that supertask machines can compute beyond the Turing limit. Our claim, rather, is that the (hyper) computational power of these machines is not related to supertasks, but to the “right kind” of computational structure.

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References

  • Andréka H, Németi I, Németi P (2009) General relativistic hypercomputing and foundation of mathematics. Nat Comput 8:499–516

    Article  MATH  MathSciNet  Google Scholar 

  • Beggs EJ, Tucker JV (2006) Embedding infinitely parallel computation in Newtonian kinematics. Appl Math Comput 178:25–43

    Article  MATH  MathSciNet  Google Scholar 

  • Benacerraf P (1962) Tasks, super-tasks, and the modern eleatics. J Philos 59:765–784

    Article  Google Scholar 

  • Blake RM (1926) The paradox of temporal process. J Philos 23:645–654

    Article  Google Scholar 

  • Boolos GS, Jeffrey RC (1980) Computability and logic, 2nd edn. Cambridge University Press, Cambridge

    Google Scholar 

  • Calude CS, Staiger L (2010) A note on accelerated Turing machines. Math Struct Comput Sci 20:1011–1017

    Google Scholar 

  • Cohen RS, Gold AY (1978) ω-computations on Turing machines. Theor Comput Sci 6:1–23

    Article  MATH  MathSciNet  Google Scholar 

  • Copeland JB (1998a) Even Turing machines can compute uncomputable functions. In: Calude CS, Casti J, Dinneen MJ (eds) Unconventional models of computation. Springer, Singapore, pp 150–164

    Google Scholar 

  • Copeland JB (1998b) Super Turing-machines. Complexity 4:30–32

    Article  MathSciNet  Google Scholar 

  • Copeland JB (2002) Accelerating Turing machines. Mind Mach 12:281–300

    Article  MATH  Google Scholar 

  • Copeland JB, Shagrir O (2011) Do accelerating Turing machines compute the uncomputable? Minds Mach 21:221–239

    Google Scholar 

  • Davies BE (2001) Building infinite machines. Br J Philos Sci 52:671–682

    Article  MATH  Google Scholar 

  • Earman J, Norton JD (1993) Forever is a day: Supertasks in Pitowsky and Malament-Hogarth spacetimes. Philos Sci 60:22–42

    Article  MathSciNet  Google Scholar 

  • Etesi G, Németi I (2002) Non-Turing computations via Malament-Hogarth space-times. Int J Theoret Phys 41:341–370

    Article  MATH  Google Scholar 

  • Fearnley LG (2009) On accelerated Turing machines. Honours thesis in Computer Science. University of Auckland

  • Fraser R, Akl SG (2008) Accelerating machines: a review. Int J Parallel Emergent Distrib Syst 23:81–104

    Article  MATH  MathSciNet  Google Scholar 

  • Gandy R (1980) Church’s thesis and principles of mechanisms. In: Barwise J, Keisler HJ, Kunen K (eds) The Kleene Symposium. North-Holland, Amsterdam, pp 123–148

  • Hamkins JD (2002) Infinite time Turing machines. Mind Mach 12:521–539

    Article  MATH  Google Scholar 

  • Hamkins JD, Lewis A (2000) Infinite time Turing machines. J Symb Log 65:567–604

    Article  MATH  MathSciNet  Google Scholar 

  • Hogarth M (1992) Does general relativity allow an observer to view an eternity in a finite time? Found Phys Lett 5:173–181

    Article  MathSciNet  Google Scholar 

  • Hogarth M (1994) Non-Turing computers and non-Turing computability. Proc Philos Sci Assoc 1:126–138

    Google Scholar 

  • Hogarth M (2004) Deciding arithmetic using SAD computers. Br J Philos Sci 55:681–691

    Article  MATH  MathSciNet  Google Scholar 

  • Laraudogoitia JP (2009) Supertasks. Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/spacetime-supertasks/

  • Lewis HR, Papadimitriou CH (1981) Elements of the theory of computation. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  • Löwe B (2001) Revision sequences and computers with an infinite amount of time. Log Comput 11:25–40

    Article  MATH  Google Scholar 

  • Pitowsky I (1990) The physical Church Thesis and physical computational complexity. Iyyun 39:81–99

  • Potgieter PH, Rosinger E (2010) Output concepts for accelerated Turing machines. Nat Comput 9:853–864

    Google Scholar 

  • Russell BAW (1915) Our knowledge of the external world as a field for scientific method in philosophy. Open Court, Chicago

  • Schaller M, Svozil K (2010) Zeno squeezing of cellular automata. Int J Unconv Comput 6:399–416

    Google Scholar 

  • Shagrir O (2004) Super-tasks, accelerating Turing machines and uncomputability. Theor Comput Sci 317:105–114

    Article  MATH  MathSciNet  Google Scholar 

  • Shagrir O, Pitowsky I (2003) Physical hypercomputation and the Church–Turing thesis. Minds Mach 13:87–101

    Google Scholar 

  • Steinhart E (2002) Logically possible machines. Mind Mach 12:259–280

    Article  MATH  Google Scholar 

  • Steinhart E (2003) The physics of information. In: Floridi L (ed.) The Blackwell Guide to the Philosophy of Computing and Information. Blackwell Publishing, Malden, pp 178–185

  • Stewart I (1991) Deciding the undecidable. Nature 352:664–665

    Article  Google Scholar 

  • Svozil K (1998) The Church-Turing thesis as a guiding principle for physics. In: Calude CS, Casti J, Dinneen MJ (eds) Unconventional models of computation. Springer, Singapore, pp 371–385

    Google Scholar 

  • Turing AM (1936) On computable numbers, with an application to the Entscheidungs problem. Proceedings of the London Mathematical Society (2) 42:230–265. Correction in 43 (1937) 544–546. Reprinted in Davis M (ed.) The undecidable: basic papers on undecidable propositions, unsolvable problems and computable functions. Raven, Hewlett (1965), 116–154. Page numbers refer to the 1965 edition

  • Welch PD (2008) The extent of computation in Malament-Hogarth spacetimes. Br J Philos Sci 59:659–674

    Article  MATH  MathSciNet  Google Scholar 

  • Weyl H (1949) Philosophy of mathematics and natural science. Princeton University Press, Princeton

    MATH  Google Scholar 

Download references

Acknowledgments

Thanks to the participants of the Workshop on Physics and Computation at Ponta Delgada (2009) and to three anonymous referees for corrections and suggestions. This research was supported by the Israel Science Foundation, grant 725/08.

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  1. Philosophy and Cognitive Science, The Hebrew University of Jerusalem, Jerusalem, Israel

    Oron Shagrir

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  1. Oron Shagrir
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Correspondence to Oron Shagrir.

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Shagrir, O. Supertasks do not increase computational power. Nat Comput 11, 51–58 (2012). https://doi.org/10.1007/s11047-011-9280-y

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