Xiaoyang Gu

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  • Xiaoyang Gu
  • 2004
In this paper, we use resource-bounded dimension theory to investigate polynomial size circuits. We show that for every i ≥ 0, P/poly has ith order scaled p 3-strong dimension 0. We also show that P/poly i.o. has p 3-dimension 1/2, p 3-strong dimension 1. Our results improve previous measure results of Lutz (1992) and dimension results of Hitchcock and(More)
We exhibit a polynomial time computable plane curve Γ that has finite length, does not intersect itself, and is smooth except at one endpoint, but has the following property. For every computable parametrization f of Γ and every positive integer n, there is some positive-length subcurve of Γ that f retraces at least n times. In contrast, every computable(More)
We use derandomization to show that sequences of positive pspace-dimension – in fact, even positive ∆ p k-dimension for suitable k – have, for many purposes, the full power of random oracles. For example, we show that, if S is any binary sequence whose ∆ p 3-dimension is positive, then BPP ⊆ P S and, moreover, every BPP promise problem is P S-separable. We(More)
BACKGROUND Human bocavirus (HBoV) is a newly discovered parvovirus and increasing evidences are available to support its role as an etiologic agent in lower respiratory tract infection (LRTI). The objective of this study is to assess the impact of HBoV viral load on clinical characteristics in children who were HBoV positive and suffered severe LRTI. (More)
The "analyst's traveling salesman theorem" of geometric measure theory characterizes those subsets of Euclidean space that are contained in curves of finite length. This result, proven for the plane by Jones (1990) and extended to higher-dimensional Euclidean spaces by Okikiolu (1992), says that a bounded set K is contained in some curve of finite length if(More)
The dimension of a point x in Euclidean space (meaning the constructive Hausdorff dimension of the singleton set {x}) is the algorithmic information density of x. Roughly speaking, this is the least real number dim(x) such that r × dim(x) bits suffice to specify x on a general-purpose computer with arbitrarily high precision 2 −r. The dimension spectrum of(More)
Consider the problem of calculating the fractal dimension of a set X consisting of all infinite sequences S over a finite alphabet Σ that satisfy some given condition P on the asymptotic frequencies with which various symbols from Σ appear in S. Solutions to this problem are known in cases where (i) the fractal dimension is classical (Hausdorff or packing(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)
Resource-bounded measure is a generalization of classical Lebesgue measure that is useful in computational complexity. The central parameter of resource-bounded measure is the resource bound ∆, which is a class of functions. When ∆ is unrestricted, i.e., contains all functions with the specified domains and codomains, resource-bounded measure coincides with(More)