Skip to main content
SpringerLink
Log in

Generalized kolmogorov complexity in relativized separations

  • Communications
  • Conference paper
  • First Online:
Mathematical Foundations of Computer Science 1990 (MFCS 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 452))

Abstract

We describe several developments of a technique, due to Hartmanis, that uses Kolmogorov complexity to prove the existence of relativizations separating complexity classes. The main advantage of these proofs is that they clearly show the limitations of certain classes of oracle machines and the relevance of these limitations for the proof. Such limitations refer to the extent to which the machines defining the class are able to process Kolmogorov-complex structures.

(Extended abstract)

The work of R. Gavaldà and J.L. Balcázar was partially supported by the ESPRIT II Basic Research Actions Program of the EC under contract No. 3075 (project ALCOM).

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

8. References

  1. E. Allender, C. Wilson: “Downward translations of equality”. Rutgers University Technical Report DCS-TR-258, 1989.

    Google Scholar 

  2. J.L. Balcázar, J. Díaz, J. Gabarró: Structural Complexity I. EATCS Monographs on Theoretical Computer Science, vol. 11 (1988), Springer-Verlag.

    Google Scholar 

  3. J.L. Balcázar, J. Díaz, J. Gabarró: Structural Complexity II. EATCS Monographs on Theoretical Computer Science, vol. 22 (1990), Springer-Verlag (in press).

    Google Scholar 

  4. H. Buhrman, E. Spaan, L. Torenvliet: “On adaptive resource bounded computations” (submitted for publication).

    Google Scholar 

  5. R. Gavaldà: “Separations of exponential time and polynomial space”. Research report, LSI Department, Univ. Politècnica de Catalunya (in preparation).

    Google Scholar 

  6. J. Hartmanis: “Generalized Kolmogorov complexity and the structure of feasible computations”. In: Proc. 24th IEEE Symposium on Foundations of Computer Science (1983), 439–445.

    Google Scholar 

  7. R. Ladner, N. Lynch: “Relativization of questions about log space computability”. Mathematical Systems Theory 10 (1976), 19–32.

    Google Scholar 

  8. R. Ladner, N. Lynch, A. Selman: “A comparison of polynomial time reducibilities”. Theoretical Computer Science 1 (1975), 103–123.

    Google Scholar 

  9. M. Li, P.M.B. Vitányi: “Two decades of applied Kolmogorov complexity”. In: Proc. 3rd Structure in Complexity Theory Conference (1988), 80–101.

    Google Scholar 

  10. P. Orponen: “Complexity classes of alternating machines with oracles”. In: Proc. 10th Int. Coll. Automata, Languages, and Programming (1983), 573–584. Springer-Verlag Lecture Notes in Computer Science 154.

    Google Scholar 

  11. K. Wagner: “Bounded query computations”. In: Proc. 3rd Structure in Complexity Theory Conference (1988), 260–277.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departament de Llenguatges i Sistemes Informàtics, Univ. Politècnica de Catalunya, 08028, Barcelona, Spain

    Ricard Gavaldà & José L. Balcázar

  2. Faculteit Wiskunde en Informatica, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV, Amsterdam

    Leen Torenvliet

  3. Department of Computer Science, Tokyo Institute of Technology, Meguro-ku, 152, Ookayama, Tokyo, Japan

    Osamu Watanabe

Authors
  1. Ricard Gavaldà
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leen Torenvliet
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Osamu Watanabe
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. José L. Balcázar
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Branislav Rovan

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gavaldà, R., Torenvliet, L., Watanabe, O., Balcázar, J.L. (1990). Generalized kolmogorov complexity in relativized separations. In: Rovan, B. (eds) Mathematical Foundations of Computer Science 1990. MFCS 1990. Lecture Notes in Computer Science, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029618

Download citation

  • DOI: https://doi.org/10.1007/BFb0029618

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52953-8

  • Online ISBN: 978-3-540-47185-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation