Towards a Theory of Infinite Time Blum-Shub-Smale Machines

  • Peter Koepke
  • Benjamin Seyfferth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7318)


We introduce a generalization of Blum-Shub-Smale machines on the standard real numbers ℝ that is allowed to run for a transfinite ordinal number of steps before terminating. At limit times, register contents are set to the ordinary limit of previous register contents in ℝ. It is shown that each such machine halts before time ω ω or diverges. We undertake first steps towards estimating the computational strength of these new machines.


Turing Machine Register Content Computation Node Binary Digit Branch Node 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Peter Koepke
    • 1
  • Benjamin Seyfferth
    • 1
  1. 1.Mathematisches InstitutRheinische Friedrich-Wilhelms-Universität BonnBonnGermany

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