Randomness vs. Completeness: On the Diagonalization Strength of Resource-Bounded Random Sets

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 , p (fC : C p-r(kn)-complete for Eg) = 0 and p 2 (fC : C p-r(n k )-complete for EXPg) = 0: 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 rst part of the paper.