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Constraints on Hypercomputation

  • Greg Michaelson
  • Paul Cockshott
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3988)

Abstract

Wegner and Eberbach [16] have argued that there are fundamental limitations to Turing Machines as a foundation of computability and that these can be overcome by so-called superTuring models. In this paper we contest their claims for interaction machines and the π-calculus.

Keywords

Cellular Automaton Turing Machine Digital Computer Interaction Machine Universal Computer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Turing, A.M.: On Computable Numbers with an Application to the Entschiedungsproblem. Proc. London Mathematical Soc. 42, 230–265 (1936)MATHGoogle Scholar
  2. 2.
    Turing, A.M.: Systems of Logic Based on Ordinals. Proc. London Mathematical Soc. 45 (1939)Google Scholar
  3. 3.
    Turing, A.M.: Computing Machinery and Intelligence. Mind 39, 433–460 (1950)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bracha, G., Toueg, S.: Asynchronous consensus and byzantine protocol in a faulty environment. Technical Report TR-83-559, CS Dept. Cornell University, Ithaca, NY 14853 (1983)Google Scholar
  5. 5.
    Church, A.: An Unsolvable Problem of Elementary Number Theory. American Journal of Mathematics 58, 345–363 (1936)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Copeland, B.J.: Hypercomputation. Minds and Machines 12, 461–502 (2002)CrossRefMATHGoogle Scholar
  7. 7.
    Copeland, B.J., Sylvan, R.: Beyond the universal turing machine. Australasian Journal of Philosophy 77(1), 46–66 (1999)CrossRefGoogle Scholar
  8. 8.
    Cotogno, P.: Hypercomputation and the Physical Church-Turing Thesis. Brit. J. Phil. Sci. 54, 181–223 (2003)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Goldin, D., Smolka, S., Wegner, P.: Turing Machines, Transition Systems, and Interaction. Information and Computation 194(2), 101–128 (2004)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Davis, M.: Engines of Logic: Mathematicians and the Origins of the Computer. Norton (2001)Google Scholar
  11. 11.
    Einstein, A.: Relativity. Methuen and Company, London (1920)Google Scholar
  12. 12.
    Ekdahl, B.: Interactive Computing does not supersede Church’s thesis. In: Proc. Computer Science, 17th Int. Conf. San Diego, Association of Management and the International Association of Management, pp. 261–265 (1999)Google Scholar
  13. 13.
    Garzon, M.: Models of Massive Parallelism: Analysis of Cellular Automata and Neural Networks. In: EATCS. Springer, Heidelberg (1995)Google Scholar
  14. 14.
    Hamkins, J., Lewis, A.: Infinite Time Turing Machines. Journal of Symbolic Logic 65(2), 567–604 (2000)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Turner, D., Pierce, B.: Pict: A programming language based on the picalculus. In: Plotkin, G., Stirling, C., Tofte, M. (eds.) Proof, Language and Interaction: Essays in Honour of Robin Milner, pp. 455–494. MIT Press, Cambridge (2000)Google Scholar
  16. 16.
    Wegner, P., Eberbach, E.: New models of computation. Computer Journal 47, 4–9 (2004)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Greg Michaelson
    • 1
  • Paul Cockshott
    • 2
  1. 1.Heriot Watt UniversityScotland
  2. 2.University of GlasgowScotland

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