Skip to main content
SpringerLink
Log in

Outline of Partial Computability in Computable Topology

  • Conference paper
  • First Online:
Unveiling Dynamics and Complexity (CiE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10307))

Included in the following conference series:

Abstract

In the framework of computable topology we investigate properties of partial computable functions, in particular complexity of various problems in computable analysis in terms of index sets, the effective Borel and Lusin hierarchies.

The research has been partially supported by the DFG grants CAVER BE 1267/14-1 and WERA MU 1801/5-1.

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 EPUB and 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

References

  1. Ershov, Y.L.: Theory of numberings. In: Griffor, E.R. (ed.) Handbook of Computability Theory, pp. 473–503. Elsevier Science B.V., Amsterdam (1999)

    Chapter  Google Scholar 

  2. Edalat, A.: Domains for computation in mathematics, physics and exact real arithmetic. Bull. Symbolic Log. 3(4), 401–452 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  3. Gao, S.: Invariant Descriptive Set Theory. CRC Press, New York (2009)

    MATH  Google Scholar 

  4. Gregoriades, V., Kispeter, T., Pauly, A.: A comparison of concepts from computable analysis and effective descriptive set theory. Math. Struct. Comput. Sci. 1–23(2016). https://doi.org/10.1017/S0960129516000128. (Published online: 23 June 2016)

  5. Hemmerling, A.: Effective metric spaces and representations of the reals. Theor. Comput. Sci. 284(2), 347–372 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hemmerling, A.: On approximate and algebraic computability over the real numbers. Theor. Comput. Sci. 219(1–2), 185–223 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kechris, A.S.: Classical Descriptive Set Theory. Springer, New York (1995)

    Book  MATH  Google Scholar 

  8. Korovina, M., Kudinov, O.: Complexity for partial computable functions over computable Polish spaces. Math. Struct. Comput. Sci. (2016). doi:10.1017/S0960129516000438. (Published online: 19 December 2016)

  9. Korovina, M., Kudinov, O.: Computable elements and functions in effectively enumerable topological spaces. Mathematical structure in Computer Science (2016). doi:10.1017/S0960129516000141. (Published online: 23 June 2016)

  10. Korovina, M., Kudinov, O.: Index sets as a measure of continuous constraint complexity. In: Voronkov, A., Virbitskaite, I. (eds.) PSI 2014. LNCS, vol. 8974, pp. 201–215. Springer, Heidelberg (2015). doi:10.1007/978-3-662-46823-4_17

    Google Scholar 

  11. Korovina, M., Kudinov, O.: Towards computability over effectively enumerable topological spaces. Electr. Notes Theor. Comput. Sci. 221, 115–125 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Korovina, M., Kudinov, O.: Towards computability of higher type continuous data. In: Cooper, S.B., Löwe, B., Torenvliet, L. (eds.) CiE 2005. LNCS, vol. 3526, pp. 235–241. Springer, Heidelberg (2005). doi:10.1007/11494645_30

    Chapter  Google Scholar 

  13. Korovina, M., Kudinov, O.: Characteristic properties of majorant-computability over the reals. In: Gottlob, G., Grandjean, E., Seyr, K. (eds.) CSL 1998. LNCS, vol. 1584, pp. 188–203. Springer, Heidelberg (1999). doi:10.1007/10703163_14

    Chapter  Google Scholar 

  14. Moschovakis, Y.N.: Descriptive set theory. North-Holland, Amsterdam (2009)

    Book  MATH  Google Scholar 

  15. Moschovakis, Y.N.: Recursive metric spaces. Fund. Math. 55, 215–238 (1964)

    MathSciNet  MATH  Google Scholar 

  16. Rogers, H.: Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York (1967)

    MATH  Google Scholar 

  17. Soare, R.I.: Recursively Enumerable Sets and Degrees: A Study of Computable Functions and Computably Generated Sets. Springer Science and Business Media, Heidelberg (1987)

    Book  MATH  Google Scholar 

  18. Spreen, D.: On effective topological spaces. J. Symb. Log. 63(1), 185–221 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  19. Selivanov, V.: Towards the effective descriptive set theory. In: Beckmann, A., Mitrana, V., Soskova, M. (eds.) CiE 2015. LNCS, vol. 9136, pp. 324–333. Springer, Cham (2015). doi:10.1007/978-3-319-20028-6_33

    Chapter  Google Scholar 

  20. Weihrauch, K.: Computable Analysis. Springer, New York (2000)

    Book  MATH  Google Scholar 

  21. Weihrauch, K.: Computability on computable metric spaces. Theor. Comput. Sci. 113(1), 191–210 (1993)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. A.P. Ershov Institute of Informatics Systems, SbRAS, Novosibirsk, Russia

    Margarita Korovina

  2. Sobolev Institute of Mathematics, SbRAS, Novosibirsk, Russia

    Oleg Kudinov

Authors
  1. Margarita Korovina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Oleg Kudinov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Margarita Korovina .

Editor information

Editors and Affiliations

  1. University of Turku, Turku, Finland

    Jarkko Kari

  2. Christian-Albrechts-University of Kiel, Kiel, Germany

    Florin Manea

  3. Ã…bo Akademi University, Turku, Finland

    Ion Petre

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Korovina, M., Kudinov, O. (2017). Outline of Partial Computability in Computable Topology. In: Kari, J., Manea, F., Petre, I. (eds) Unveiling Dynamics and Complexity. CiE 2017. Lecture Notes in Computer Science(), vol 10307. Springer, Cham. https://doi.org/10.1007/978-3-319-58741-7_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-58741-7_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58740-0

  • Online ISBN: 978-3-319-58741-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation