Skip to main content
Springer Nature Link
Log in

Nonuniform lowness and strong nonuniform lowness

  • Regular Papers
  • Published:
Journal of Computer Science and Technology Aims and scope Submit manuscript

Abstract

The concepts of the nonuniform and strong nonuniform lownesss are introduced. Those notions provide a uniform framework to study connections between the polynomial-time hierarchy and sparse sets.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Balcázar J, Book R, Schöning U. The polynomial-time hierarchy and sparse oracles.J. ACM., 1986, 33: 603–617.

    Article  MATH  Google Scholar 

  2. Balcázar J, Book R, Schöning U. Sparse sets, lowness, and highness.SIAM J. Comput., 1986, 15: 739–747.

    Article  MathSciNet  Google Scholar 

  3. Balcázar J, Dían J, Gabarró J. Structural complexity, Vol. I, II. Springer-Verlag, 1988 and 1990.

  4. Karp R, Lipton R. Some connections between nonuniform and uniform complexity classes. InProc. 12th ACM STOC., 1980, pp. 302–309.

  5. Ko K, Schöning U. On circuit-size complexity and the low hierarchy in NP.SIAM J. Comput., 1985, 14: 41–51.

    Article  MATH  MathSciNet  Google Scholar 

  6. Li Hongzhou. The polynomial-time hierarchy and oracle setA ∈ PH/poly. Chinese Sci. Bulletin, 1990/1991, 35/36: 322-325/17-20.

  7. Long T, Selman A. Relativizing complexity classes with sparse oracles.J. ACM., 1986, 33: 618–627.

    Article  MathSciNet  Google Scholar 

  8. Mahaney S. Sparse complete sets for NP: Solution of a conjecture of Berman and Hartmanis.J. Comput. System Sci., 1982, 25: 130–143.

    Article  MATH  MathSciNet  Google Scholar 

  9. Ogiwara M, Watanabe O. On polynomial-time bounded truth-table reducibility of NP sets to sparse sets.SIAM J. Comput., 1991, 20: 471–483.

    Article  MATH  MathSciNet  Google Scholar 

  10. Schöning U. A low and a high hierarchy within NP.J. Comput. System Sci., 1983, 27: 14–28.

    Article  MATH  MathSciNet  Google Scholar 

  11. Schöning U. On small generators.Theoretic Computer Science, 1983, 27: 14–28.

    MATH  Google Scholar 

  12. Schöning U. Complexity and structure. Lecture Notes in Computer Scince, Vol, 211, 1986.

  13. Yap C. Some consequences of nonuniform conditions on uniform classes.Theoretic Computer Science, 1983, 27: 287–300.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, South China Normal University, 510631, Guangzhou

    Li Hongzhou & Li Guanying

Authors
  1. Li Hongzhou
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Li Guanying
    View author publications

    You can also search for this author inPubMed Google Scholar

Additional information

This research is supported by the 863 High-Tech Program.

Li Hongzhou received his B.S. degrss from Guangxi Normal University in 1985 and his M.S. degree from Guizhou University in 1988, both in Mathematics. He has been an Associate Professor at Department of Computer Science at South China Normal University since 1992. His research interests are in computational complexity theory.

Li Guanying graduated from Department of Mathematics of South China Normal University in 1959. He has been a Professor of computer science at South China Normal University since 1987. His research interests are in theoretical computer science.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, H., Li, G. Nonuniform lowness and strong nonuniform lowness. J. of Compt. Sci. & Technol. 10, 253–259 (1995). https://doi.org/10.1007/BF02943492

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02943492

Keywords