Infinite Time Register Machines

  • Peter Koepke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3988)


Infinite time register machines (ITRMs) are register machines which act on natural numbers and which may run for arbitrarily many ordinal steps. Successor steps are determined by standard register machine commands, at limits the register contents are defined as lim inf’s of the previous register contents. We prove that a real number is computable by an ITRM iff it is hyperarithmetic.


Turing Machine Maximum Element Recursive Function Register Program Main Loop 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cutland, N.J.: Computability: An Introduction to Recursive Function Theory. In: Perspectives in Mathematical Logic. Cambridge University Press, Cambridge (1980)Google Scholar
  2. 2.
    Hamkins, J.D., Lewis, A.: Infinite Time Turing Machines. J. Symbolic Logic 65(2), 567–604 (2000)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Koepke, P.: Turing computations on ordinals. Bulletin of Symbolic Logic 11(3), 377–397 (2005)CrossRefMATHGoogle Scholar
  4. 4.
    Koepke, P.: Computing a Model of Set Theory. In: Cooper, S.B., Löwe, B., Torenvliet, L. (eds.) CiE 2005. LNCS, vol. 3526, pp. 223–232. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Koepke, P., Friedman, S.: An elementary approach to the fine structure of L. Bulletin of Symbolic Logic 3(4), 453–468 (1997)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Koepke, P., Koerwien, M.: Ordinal computations. In: Mathematics of Computation at CiE 2005; Special issue of the journal Mathematical Structures in Computer Science, 17 pages (to appear, 2005)Google Scholar
  7. 7.
    Koepke, P., Siders, R.: Computing the recursive truth predicate on ordinal register machines. In: Beckmann, A., Berger, U., Löwe, B., Tucker, J.V. (eds.) CiE 2006. LNCS, vol. 3988. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Sacks, G.E.: Higher Recursion Theory. In: Perspectives in Mathematical Logic. Springer, Berlin (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Peter Koepke
    • 1
  1. 1.Mathematisches InstitutUniversity of BonnBonnGermany

Personalised recommendations