Upward separations and weaker hypotheses in resource-bounded measure

Authors:
Ryan C. Harkins;John M. Hitchcock
Affiliations:
Department of Computer Science, University of Wyoming, United States;Department of Computer Science, University of Wyoming, United States
Venue:
Theoretical Computer Science
Year:
2007

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Abstract

We consider resource-bounded measure in double-exponential-time complexity classes. In contrast to complexity class separation translating downwards, we show that measure separation translates upwards. For example, @m"p(NP)0@?@m"e(NE)0@?@m"e"x"p(NEXP)0. We also show that if NE does not have e-measure 0, then the NP-machine hypothesis holds. We give oracles relative to which the converses of these statements do not hold. Therefore the hypothesis on the e-measure of NE is relativizably weaker than the often-investigated p-measure hypothesis on NP, but it has many of the same consequences.