Measure Theoretic Completeness Notions for the Exponential Time Classes
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Theoretical Computer Science
Theoretical Computer Science
Weak completeness notions for exponential time
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Nontriviality for exponential time w.r.t weak reducibilities
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Nontriviality for exponential time w.r.t. weak reducibilities
Theoretical Computer Science
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We compare the weak completeness notions for E in the sense of Lutz's resource-bounded measure theory with respect to the standard polynomial time reducibilities. Our results parallel results for classical completeness by Watanabe and others. We show that the weak completeness notions for 1-query reductions coincide: A set is weakly complete for E under 1-truth-table reducibility iff it is weakly complete for length-increasing one-one reducibility. For most of the other polynomial reducibilities, however, we obtain separations of the weak completeness notions where these reducibilities differ on E. In fact our separations simultaneously hold for the corresponding weak completeness notions for E and E, for the classical completeness notions, and for the weak completeness notions in the sense of the resource-bounded Baire category concepts of Ambos-Spies et al.