Skip to main content
SpringerLink
Log in
Book cover

Conference on Computability in Europe

CiE 2006: Logical Approaches to Computational Barriers pp 378–387Cite as

Constraints on Hypercomputation

  • Conference paper

  • 956 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Turing, A.M.: On Computable Numbers with an Application to the Entschiedungsproblem. Proc. London Mathematical Soc. 42, 230–265 (1936)

    MATH  Google Scholar 

  2. Turing, A.M.: Systems of Logic Based on Ordinals. Proc. London Mathematical Soc. 45 (1939)

    Google Scholar 

  3. Turing, A.M.: Computing Machinery and Intelligence. Mind 39, 433–460 (1950)

    Article  MathSciNet  Google Scholar 

  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. Church, A.: An Unsolvable Problem of Elementary Number Theory. American Journal of Mathematics 58, 345–363 (1936)

    Article  MathSciNet  MATH  Google Scholar 

  6. Copeland, B.J.: Hypercomputation. Minds and Machines 12, 461–502 (2002)

    Article  MATH  Google Scholar 

  7. Copeland, B.J., Sylvan, R.: Beyond the universal turing machine. Australasian Journal of Philosophy 77(1), 46–66 (1999)

    Article  Google Scholar 

  8. Cotogno, P.: Hypercomputation and the Physical Church-Turing Thesis. Brit. J. Phil. Sci. 54, 181–223 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. Goldin, D., Smolka, S., Wegner, P.: Turing Machines, Transition Systems, and Interaction. Information and Computation 194(2), 101–128 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Davis, M.: Engines of Logic: Mathematicians and the Origins of the Computer. Norton (2001)

    Google Scholar 

  11. Einstein, A.: Relativity. Methuen and Company, London (1920)

    Google Scholar 

  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. Garzon, M.: Models of Massive Parallelism: Analysis of Cellular Automata and Neural Networks. In: EATCS. Springer, Heidelberg (1995)

    Google Scholar 

  14. Hamkins, J., Lewis, A.: Infinite Time Turing Machines. Journal of Symbolic Logic 65(2), 567–604 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  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. Wegner, P., Eberbach, E.: New models of computation. Computer Journal 47, 4–9 (2004)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Heriot Watt University, Scotland

    Greg Michaelson

  2. University of Glasgow, Scotland

    Paul Cockshott

Authors
  1. Greg Michaelson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paul Cockshott
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Swansea University, Singleton Park, SA2 8PP, Swansea, United Kingdom

    Arnold Beckmann

  2. Department of Computer Science, University of Wales Swansea, Singleton Park, SA2 8PP, Swansea, UK

    Ulrich Berger

  3. Universiteit van Amsterdam, Plantage Muidergracht 24, 1018, Amsterdam, TV, The Netherlands

    Benedikt Löwe

  4. School of Physical Sciences, Swansea University, Singleton Park, SA2 8PP, Swansea, Wales, United Kingdom

    John V. Tucker

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Michaelson, G., Cockshott, P. (2006). Constraints on Hypercomputation. In: Beckmann, A., Berger, U., Löwe, B., Tucker, J.V. (eds) Logical Approaches to Computational Barriers. CiE 2006. Lecture Notes in Computer Science, vol 3988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780342_40

Download citation

  • DOI: https://doi.org/10.1007/11780342_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35466-6

  • Online ISBN: 978-3-540-35468-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation