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This paper presents the following results on sets that are complete for NP. (i) If there is a problem in NP that requires $2^{n^{\Omega(1)}}$ time at almost all lengths, then every many-one NP-complete set is complete under length-increasing reductions that are computed by polynomial-size circuits. (ii) If there is a problem in co-NP that cannot be solved… (More)

- Xiaoyang Gu, Jack H Lutz, Pavan Aduri, Soumendra N Lahiri, Roger D Maddux, Elvira Mayordomo +1 other
- 2015

- David Doty, Xiaoyang Gu, Jack H Lutz, Elvira Mayordomo, Philippe Moser
- 2005

The zeta-dimension of a set A of positive integers is Dim ζ (A) = inf{s | ζ A (s) < ∞}, where ζ A (s) = n∈A n −s. Zeta-dimension serves as a fractal dimension on Z + that extends naturally and usefully to discrete lattices such as Z d , where d is a positive integer. This paper reviews the origins of zeta-dimension (which date to the eighteenth and… (More)

- David Doty, Xiaoyang Gu, Jack H Lutz, Elvira Mayordomo, Philippe Moser
- 2005

The zeta-dimension of a set A of positive integers is Dim ζ (A) = inf{s | ζA(s) < ∞}, where ζA(s) = n∈A n −s. Zeta-dimension serves as a fractal dimension on Z + that extends naturally and usefully to discrete lattices such as Z d , where d is a positive integer. This paper reviews the origins of zeta-dimension (which date to the eighteenth and nineteenth… (More)

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