Skip to main content
SpringerLink
Log in

Numbers Defined by Turing Machines

  • Conference paper
Book cover Collegium Logicum

Part of the book series: Collegium Logicum ((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.

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

Access this chapter

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Eilenberg: Automata, Languages and Machines, Vol. A ( Academic Press, New York, 1974 ).

    MATH  Google Scholar 

  2. R. Freund: Real Functions and Numbers Defined by Turing Machines, Theoret. Comp. Sci. 23 (1983) 287–304.

    Article  MathSciNet  MATH  Google Scholar 

  3. M. L. Minsky: Berechnung: Endliche und unendliche Maschinen (Verlag Berliner Union, Stuttgart, 1971 ).

    MATH  Google Scholar 

  4. H. Rogers: Theory of Recursive Functions and Effective Computability (McGraw Hill, 1967).

    Google Scholar 

  5. A. Salomaa: Formal Languages ( Academic Press, New York, 1973 ).

    MATH  Google Scholar 

  6. L. Staiger: Hierarchies of Recursive w-Languages, J. Inform. Process. Cybernet. EIK 22 (1986) 5 /6, 219–241.

    MathSciNet  Google Scholar 

  7. L. Staiger: Sequential Mappings of w-Languages, RAIRO Infor. Théor. Appl. 21 (1987) 2, 147–173.

    MathSciNet  Google Scholar 

  8. L. Staiger and K. Wagner, Rekursive Folgenmengen I, Z. Math Logik Grund-lag. Math. 24 (1978) 523–538.

    Article  MathSciNet  MATH  Google Scholar 

  9. K. Wagner: Arithmetische Operatoren, Z. Math Logik Grundlag. Math. 22 (1976) 553–570.

    Article  MATH  Google Scholar 

  10. K. Weihrauch: Computability ( Springer-Verlag, Berlin, 1987 ).

    MATH  Google Scholar 

  11. K. Weihrauch: A simple Introduction to Computable Analysis, Technical Report 171, Fernuniversität Hagen, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Computersprachen, Technische Universität Wien, Resselgasse 3, A-1040, Wien, Austria

    Rudolf Freund

  2. Institut für Informatik, Martin-Luther-Universität Halle-Wittenberg, Weinbergweg 17, D-06120, Halle (Saale), Germany

    Ludwig Staiger

Authors
  1. Rudolf Freund
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ludwig Staiger
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag/Wien

About this paper

Cite this paper

Freund, R., Staiger, L. (1996). Numbers Defined by Turing Machines. In: Collegium Logicum. Collegium Logicum, vol 2. Springer, Vienna. https://doi.org/10.1007/978-3-7091-9461-4_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-9461-4_8

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82796-3

  • Online ISBN: 978-3-7091-9461-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation