Xiaoyang Gu

Learn More
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)
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)
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)
  • 1