Abstract
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.
Research supported in part by the Human Capital and Mobility Program of the European Community under grant CHRX-CT93-0415 (COLORET). The second author would like to acknowledge partial support by National Science Foundation grant DMS-9504474 and a grant of the British Engineering and Physical Sciences Research Council. The main results of Section 3 were obtained by the first and second author when they visited the University of Leeds in the spring of 1996. In Section 4 some recent work by the first and third author is reported.
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Ambos-Spies, K., Lempp, S., Mainhardt, G. (1998). Randomness vs. completeness: On the diagonalization strength of resource-bounded random sets. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055796
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DOI: https://doi.org/10.1007/BFb0055796
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