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Numbers Defined by Turing Machines

  • Rudolf Freund
  • Ludwig Staiger
Conference paper
Part of the Collegium Logicum book series (COLLLOGICUM, volume 2)

Abstract

We consider three types of Turing machines defining functions on infinite words and investigate some characteristic properties of these types of Turing machine mappings. Using the interpretation of infinite words as the expansions of numbers we obtain three classes of real respectively complex numbers. We prove that the three classes of complex numbers form algebraically closed subfields of the field of complex numbers.

Keywords

Recursive Relation Turing Machine Recursive Function Real Polynomial Input Tape 
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Copyright information

© Springer-Verlag/Wien 1996

Authors and Affiliations

  • Rudolf Freund
    • 1
  • Ludwig Staiger
    • 2
  1. 1.Institut für ComputersprachenTechnische Universität WienWienAustria
  2. 2.Institut für InformatikMartin-Luther-Universität Halle-WittenbergHalle (Saale)Germany

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