Randomness vs. completeness: On the diagonalization strength of resource-bounded random sets

  • Klaus Ambos-Spies
  • Steffen Lempp
  • Gunther Mainhardt
Contributed Papers Structural Complexity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1450)


We show that the question of whether the p-tt-complete or p-T-complete sets for the deterministic time classes E and EXP have measure 0 in these classes in the sense of Lutz's resource-bounded measure cannot be decided by relativizable techniques. On the other hand, we obtain the following absolute results if we bound the norm, i.e., the number of oracle queries of the reductions: For r = tt, T, etse465-01etse and etse465-02etse

In the second part of the paper we investigate the diagonalization strength of random sets in an abstract way by relating randomness to a new genericity concept. This provides an alternative, quite elegant and powerful approach for obtaining results on resource-bounded measures like the ones in the first part of the paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Klaus Ambos-Spies
    • 1
  • Steffen Lempp
    • 2
  • Gunther Mainhardt
    • 1
  1. 1.Mathematisches InstitutUniversität HeidelbergGermany
  2. 2.Department of MathematicsUniversity of WisconsinMadison

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