Skip to main content

On TAE Machines and Their Computational Power

Abstract

Trail-And-Error machines have been proposed by Hintikka and Mutanen as an alternative formulation of the notion of (mechanical) computation. These machines extend the capabilities of the Turing machine and widen the theory of computation.

This is a preview of subscription content, access via your institution.

References

  1. Gold, E.M.: Limiting recursion. J. Symb. Log. 30, 28–48 (1965)

    MathSciNet  Article  MATH  Google Scholar 

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

    MathSciNet  Article  MATH  Google Scholar 

  3. Hintikka, J.: Language, Truth and Logic in Mathematics. Kluwer Academic Publishers, Dordrecht (1998)

    Book  MATH  Google Scholar 

  4. Ord, T., Kieu, T.D.: The diagonal method and hypercomputation. Br. J. Philos. Sci. 56, 147–156 (2005)

    MathSciNet  Article  MATH  Google Scholar 

  5. Putnam, H.: Trial and error predicates and the solution to a problem of Mostowski. J. Symb. Log. 30, 49–57 (1965)

    MathSciNet  Article  MATH  Google Scholar 

  6. Syropoulos, A.: Hypercomputation: Computing Beyond the Church-Turing Barrier. Springer, New York (2008)

    Book  MATH  Google Scholar 

  7. Syropoulos, A.: Hypercomputation: fantasy or reality? A position paper. Parallel Proc. Lett. 23, 1350005 (2013)

    MathSciNet  Article  MATH  Google Scholar 

  8. Syropoulos, A.: Demystifying Computation: A Hands-On Introduction. World Scientific, London (2017)

    Book  Google Scholar 

  9. Weihrauch, K.: Computable Analysis: An Introduction. Springer, Berlin (2000)

    Book  MATH  Google Scholar 

Download references

Acknowledgements

I would like to thank Christos K.K. Loverdos for his help and suggestions. Also, I would like to thank the anonymous reviewer for his comments.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Apostolos Syropoulos.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Syropoulos, A. On TAE Machines and Their Computational Power. Log. Univers. 13, 165–170 (2019). https://doi.org/10.1007/s11787-018-0196-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11787-018-0196-5

Mathematics Subject Classification

  • Primary 99Z99
  • Secondary 00A00

Keywords

  • TAE-machines
  • Theory of computation
  • Hypercomputation