Skip to main content
SpringerLink
Log in

A topological view of some problems in complexity theory

  • Invited Lectures
  • Conference paper
  • First Online:
Book cover Mathematical Foundations of Computer Science 1984 (MFCS 1984)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 176))

Abstract

We present a new, combinatorial proof of the classical theorem that the analytic sets are not closed under complement. Possible connections with questions in complexity theory are discussed.

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.

References

  1. M. Ajtai, "Σ 11 -formulae on finite structures", Annals of Pure and Applied Logic 24, 1983, 1–48.

    Google Scholar 

  2. M. Furst, J.B. Saxe, M. Sipser, "Parity, circuits, and the polynomial time hierarchy", Proceedings of the 22nd Annual Symposium on Foundations of Computer Science, 1981, 260–270.

    Google Scholar 

  3. K. Kuratowski, Topology, Academic Press, 1966.

    Google Scholar 

  4. Y. Moschavakis, Descriptive Set Theory, North-Holland, 1980.

    Google Scholar 

  5. M. Sipser, "On polynomial versus exponential growth", unpublished report, 1981.

    Google Scholar 

  6. M. Sipser, "Borel sets and circuit complexity", Proceedings of the 15th Annual Symposium on Theory of Computing, 1983, 61–69.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, Massachusetts Institute of Technology, 02139, Cambridge, Massachusetts

    Michael Sipser

Authors
  1. Michael Sipser
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

M. P. Chytil V. Koubek

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sipser, M. (1984). A topological view of some problems in complexity theory. In: Chytil, M.P., Koubek, V. (eds) Mathematical Foundations of Computer Science 1984. MFCS 1984. Lecture Notes in Computer Science, vol 176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030341

Download citation

  • DOI: https://doi.org/10.1007/BFb0030341

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13372-8

  • Online ISBN: 978-3-540-38929-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation