Extended abstract
  • Uwe Schöning
  • Ronald V. Book
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 154)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baker, T., Gill, J. and Solovay, R., Relativizations of the P=? NP question. SIAM J. Computing, 4(1975), 431–442.Google Scholar
  2. 2.
    Balcázar, J., Simplicity for relativized complexity classes, submitted for publication.Google Scholar
  3. 3.
    Bennett, C. and Gill, J., Relative to a random oracle A, pA≠ NPA ≠ co-NPA with probability 1. SIAM J. Computing, 10(1981), 96–113.Google Scholar
  4. 4.
    Book, R., Bounded query machines: on NP and PSPACE. Theoret. Comput. Sci., 15(1981), 27–39.Google Scholar
  5. 5.
    Book, R., Long, T. and Selman, A., Controlled relativizations of P and NP. Theoret. Comput. Sci., Lecture Notes in Computer Science, 145(1983), 85–90.Google Scholar
  6. 6.
    Book, R., Wilson, C. and Xu Mei-rui, Relativizing time, space, and time space. SIAM J. Computing, 11(1982), 571–581.Google Scholar
  7. 7.
    Book, R. and Wrathall, C., Bounded query machines: on NP and NPQUERY. Theoret. Comput. Sci., 15(1981), 41–50.Google Scholar
  8. 8.
    Flajolet, P. and Steyaert, J., On sets having only hard subsets. 2nd International Colloquium on Automata, Languages, and Programming, Lecture Notes in Computer Science, 14(1974), 446–457. Also, Une généralization de la notion d'ensemble immune, R.A.I.R.O. Informatique Théorique, 8(1974), 37–48.Google Scholar
  9. 9.
    Homer, S. and Maass, W., Oracle dependent properties of the lattice of NP sets. Theoret. Comput. Sci., to appear.Google Scholar
  10. 10.
    Hopcroft, J. and Ullman, J., Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, 1979.Google Scholar
  11. 11.
    Kintala, C.M.R., Computations with a Restricted Number of Nondeter-ministic Steps. Ph.D. dissertation, Pennsylvania State University, 1977.Google Scholar
  12. 12.
    Kintala, C.M.R. and Fischer, P., Refining nondeterminism in relativized polynomial time-bounded computations. SIAM J. Computing, 9(1980), 46–53.Google Scholar
  13. 13.
    Ko, K and Moore, D., Completeness, approximation, and density. SIAM J. Computing, 10(1981), 787–796.Google Scholar
  14. 14.
    Long, T., Relativizing nondeterministic time. Unpublished manuscript, 1981.Google Scholar
  15. 15.
    Schöning, U., A low and a high hierarchy within NP. J. Comput. Syst. Sci., (1983), to appear.Google Scholar
  16. 16.
    Schöning, U., Relativization and infinite subsets of NP sets. Unpublished manuscript, 1982.Google Scholar
  17. 17.
    Schöning, U., Bi-immune sets for complexity classes, in preparation.Google Scholar
  18. 18.
    Selman, A., Xu Mei-rui and Book, R., Positive relativizations of complexity classes. SIAM J. Computing, 12(1983), to appear.Google Scholar
  19. 19.
    Xu Mei-rui, Doner, J. and Book, R., Refining nondeterminism in relativized complexity classes. J. Assoc. Comput. Mach., 30(1983), to appear.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Uwe Schöning
    • 1
  • Ronald V. Book
    • 2
  1. 1.Institut für InformatikUniversität StuttgartStuttgart 1West Germany
  2. 2.Department of MathematicsUniversity of California at Santa BarbaraSanta BarbaraUSA

Personalised recommendations