P-generic sets

  • Klaus Ambos-Spies
  • Hans Fleischhack
  • Hagen Huwig
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 172)


We introduce the notion of a p-generic set. P-generic sets automatically have all properties which can be enforced by usual diagonalizations over polynomial time computable sets and functions. We prove that there are recursive — in fact exponential time computable — p-generic sets. The existence of p-generic sets in NP is shown to be oracle dependent, even under the assumption that PNP.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Ambos-Spies,K., P-mitotic sets, in: E.Börger, G.Hasenjaeger and D.Rödding, Eds., Logic and machines: Decision problems and complexity, SLNCS (to appear in 1984). Preprint: Techn. Report Nr. 167 (1983) Universität Dortmund.Google Scholar
  2. [2]
    Ambos-Spies,K., Fleischhack,H., and Huwig,H., Diagonalizations over polynomial time computable sets, submitted for publication. Preprint: Techn. Report Nr. 177 (1984) Universität Dortmund.Google Scholar
  3. [3]
    Benett, C.H. and J. Gill, Relative to a random oracle A,PA≠NPA≠CO-NPA with probability 1, SIAM Comp. 10 (1981) 96–113.Google Scholar
  4. [4]
    Homer, S. and W. Maass, Oracle dependent properties of the lattice of NP-sets, TCS 24(1983) 279–289Google Scholar
  5. [5]
    Jockusch, C., Notes on genericity for r.e. sets, handwritten notes.Google Scholar
  6. [6]
    Ladner, R.E., Lynch, N.A., and Selman, A.L., A comparison of polynomial time reducibilities, TCS 1 (1975) 103–123.Google Scholar
  7. [7]
    Maass, W., Recursively enumerable generic sets, J.Symb.Logic 47 (1982) 809–823.Google Scholar
  8. [8]
    Selman, A.L., P-selective sets, tally languages, and the behaviour of polynomial time reducibilities on NP, Math. Systems Theory 13 (1979) 55–65.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Klaus Ambos-Spies
    • 1
  • Hans Fleischhack
    • 1
  • Hagen Huwig
    • 1
  1. 1.Lehrstuhl Informatik IIUniversität DortmundDortmund 50

Personalised recommendations