Skip to main content
SpringerLink
Log in

Two remarks on the power of counting

  • Contributed Papers
  • Conference paper
  • First Online:
Theoretical Computer Science

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 145))

Abstract

The relationship between the polynomial hierarchy and Valiant's class #P is at present unknown. We show that some low portions of the polynomial hierarchy, namely deterministic polynomial algorithms using an NP oracle at most a logarithmic number of times, can be simulated by one #P computation. We also show that the class of problems solvable by polynomial-time nondeterministic Turing machines which accept whenever there is an odd number of accepting computations is idempotent, that is, closed under usage of oracles from the same class.

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. D. Angluin "On counting problems and the polynominal-time hierarchy", Theoretical Computer Science 12 (1980), pp. 161–173

    Google Scholar 

  2. M.R. Garey, D.S. Johnson Computers and Intractability: A Guide to the Theory of NP-completeness, Freeman, 1979.

    Google Scholar 

  3. J. Gill "Computational complexity of probabilistic Turing machines", SIAM J. Computing 6 (1977), pp. 675–695.

    Google Scholar 

  4. H.R. Lewis, C.H. Papadimitriou Elements of the Theory of Computation, Prentice-Hall, 1981.

    Google Scholar 

  5. C.H. Papadimitriou "The complexity of unique solutions", Proc. 13th FOCS Conference, 1982, to appear.

    Google Scholar 

  6. C.H. Papadimitriou, M. Yannakakis "The complexity of facets (and some facets of complexity", Proc. 14th STOC, pp. 255–260, 1982. Also to appear in JCSS.

    Google Scholar 

  7. J. Simon "On the difference between one and many" Proc. 4th Intern. Colloguium on Automata, Languages and Programming, pp. 480–491, 1977.

    Google Scholar 

  8. L.J. Stockmeyer "The polynamial-time hierarchy", Theoretical Computer Science, 3 (1977), pp. 1–22.

    Google Scholar 

  9. L.G. Valiant "The complexity of computing the permanent", Theoretical Computer Science, 8 (1979), pp. 181–201.

    Google Scholar 

  10. L.G. Valiant, private communication, August 1982.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Computer Science, M.I.T., Cambridge, USA

    Christos H. Papadimitriou & Stathis K. Zachos

Authors
  1. Christos H. Papadimitriou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stathis K. Zachos
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Armin B. Cremers Hans-Peter Kriegel

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Papadimitriou, C.H., Zachos, S.K. (1982). Two remarks on the power of counting. In: Cremers, A.B., Kriegel, HP. (eds) Theoretical Computer Science. Lecture Notes in Computer Science, vol 145. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036487

Download citation

  • DOI: https://doi.org/10.1007/BFb0036487

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11973-9

  • Online ISBN: 978-3-540-39421-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation