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Search Results: 1 - 10 of 31386 matches for " Fu Bin "
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NE is not NP Turing Reducible to Nonexpoentially Dense NP Sets
Bin Fu
Computer Science , 2010,
Abstract: A long standing open problem in the computational complexity theory is to separate NE from BPP, which is a subclass of $NP_T(NP\cap P/poly)$. In this paper, we show that $NE\not\subseteq NP_(NP \cap$ Nonexponentially-Dense-Class), where Nonexponentially-Dense-Class is the class of languages A without exponential density (for each constant c>0,$|A^{\le n}|\le 2^{n^c}$ for infinitely many integers n). Our result implies $NE\not\subseteq NP_T({pad(NP, g(n))})$ for every time constructible super-polynomial function g(n) such as $g(n)=n^{\ceiling{\log\ceiling{\log n}}}$, where Pad(NP, g(n)) is class of all languages $L_B=\{s10^{g(|s|)-|s|-1}:s\in B\}$ for $B\in NP$. We also show $NE\not\subseteq NP_T(P_{tt}(NP)\cap Tally)$.
Multivariate Polynomial Integration and Derivative Are Polynomial Time Inapproximable unless P=NP
Bin Fu
Computer Science , 2010,
Abstract: We investigate the complexity of integration and derivative for multivariate polynomials in the standard computation model. The integration is in the unit cube $[0,1]^d$ for a multivariate polynomial, which has format $f(x_1,\cdots, x_d)=p_1(x_1,\cdots, x_d)p_2(x_1,\cdots, x_d)\cdots p_k(x_1,\cdots, x_d)$, where each $p_i(x_1,\cdots, x_d)=\sum_{j=1}^d q_j(x_j)$ with all single variable polynomials $q_j(x_j)$ of degree at most two and constant coefficients. We show that there is no any factor polynomial time approximation for the integration $\int_{[0,1]^d}f(x_1,\cdots,x_d)d_{x_1}\cdots d_{x_d}$ unless $P=NP$. For the complexity of multivariate derivative, we consider the functions with the format $f(x_1,\cdots, x_d)=p_1(x_1,\cdots, x_d)p_2(x_1,\cdots, x_d)\cdots p_k(x_1,\cdots, x_d),$ where each $p_i(x_1,\cdots, x_d)$ is of degree at most $2$ and $0,1$ coefficients. We also show that unless $P=NP$, there is no any factor polynomial time approximation to its derivative ${\partial f^{(d)}(x_1,\cdots, x_d)\over \partial x_1\cdots \partial x_d}$ at the origin point $(x_1,\cdots, x_d)=(0,\cdots,0)$. Our results show that the derivative may not be easier than the integration in high dimension. We also give some tractable cases of high dimension integration and derivative.
On the Complexity of Approximate Sum of Sorted List
Bin Fu
Computer Science , 2011,
Abstract: We consider the complexity for computing the approximate sum $a_1+a_2+...+a_n$ of a sorted list of numbers $a_1\le a_2\le ...\le a_n$. We show an algorithm that computes an $(1+\epsilon)$-approximation for the sum of a sorted list of nonnegative numbers in an $O({1\over \epsilon}\min(\log n, {\log ({x_{max}\over x_{min}})})\cdot (\log {1\over \epsilon}+\log\log n))$ time, where $x_{max}$ and $x_{min}$ are the largest and the least positive elements of the input list, respectively. We prove a lower bound $\Omega(\min(\log n,\log ({x_{max}\over x_{min}}))$ time for every O(1)-approximation algorithm for the sum of a sorted list of nonnegative elements. We also show that there is no sublinear time approximation algorithm for the sum of a sorted list that contains at least one negative number.
Derandomizing Polynomial Identity over Finite Fields Implies Super-Polynomial Circuit Lower Bounds for NEXP
Bin Fu
Computer Science , 2013,
Abstract: We show that derandomizing polynomial identity testing over an arbitrary finite field implies that NEXP does not have polynomial size boolean circuits. In other words, for any finite field F(q) of size q, $PIT_q\in NSUBEXP\Rightarrow NEXP\not\subseteq P/poly$, where $PIT_q$ is the polynomial identity testing problem over F(q), and NSUBEXP is the nondeterministic subexpoential time class of languages. Our result is in contract to Kabanets and Impagliazzo's existing theorem that derandomizing the polynomial identity testing in the integer ring Z implies that NEXP does have polynomial size boolean circuits or permanent over Z does not have polynomial size arithmetic circuits.
Sublinear Time Motif Discovery from Multiple Sequences
Bin Fu,Yunhui Fu
Computer Science , 2010,
Abstract: A natural probabilistic model for motif discovery has been used to experimentally test the quality of motif discovery programs. In this model, there are $k$ background sequences, and each character in a background sequence is a random character from an alphabet $\Sigma$. A motif $G=g_1g_2...g_m$ is a string of $m$ characters. Each background sequence is implanted a probabilistically generated approximate copy of $G$. For a probabilistically generated approximate copy $b_1b_2...b_m$ of $G$, every character $b_i$ is probabilistically generated such that the probability for $b_i\neq g_i$ is at most $\alpha$. We develop three algorithms that under the probabilistic model can find the implanted motif with high probability via a tradeoff between computational time and the probability of mutation. The methods developed in this paper have been used in the software implementation. We observed some encouraging results that show improved performance for motif detection compared with other softwares.
Pastoral Investigation on the Form and Usage of Local-Style Dwelling Houses in Jiarong Tibetan Traditional Village of Danba County  [PDF]
Bin Cheng, Libin Duan, Yangliu Fu
Journal of Building Construction and Planning Research (JBCPR) , 2018, DOI: 10.4236/jbcpr.2018.62004
Abstract: Under the dual background of rapid development and urbanization, the research is of practical significance for the construction and development of new rural harmonious society on the traditional villages, residential forms and ways of using. The purpose of this study is to learn the characteristics of the local residential forms and their usage, reveal the relationship between these characteristics and villagers’ lifestyles, and grasp the villagers’ evaluation of the satisfaction on living space, by the investigation of 168 questionnaires, 16 families in-depth interviews and survey mapping in the W, Y and Z villages of Suopo Township, Danba County, Sichuan Province. The resulted showed that: 1) Residents have obvious uniform features, mostly 3 - 5 layers of single-family residences, mostly in the area of 400 - 500 m2. The height of the house and the rooms has a relatively fixed modulus. 2) In the survey of the usage of local dwelling houses, it was found that farmers have a fixed model for the use of residential buildings. Most of the living activities are gathered in their own courtyards, and the utilization of the living room is usually limited. The floors above the second floor often have the terrace formed by the retreat to dry the food. There are often more bedrooms for spare, more than 90% of the family of four or more have two or more living rooms. 3) The residential area is embodied in both horizontal and vertical directions: the first floor of the indoor room from the courtyard to the dining room has the property of semi-open and semi-private space, and it is the main place for neighborhood interaction; and the rooms of the second and above are more private. 4) In the long process of life, the form and usage of houses will change with the changes of external factors. The traditional dwelling houses will be built or renovated, accounting for about 36% of the total amount surveyed.
Measurable nonlocal effect of bipartite system during a local cyclic evolution of its subsystem
Li-Bin Fu
Physics , 2004, DOI: 10.1209/epl/i2005-10598-7
Abstract: In this letter, a nonlocal effect for a bipartite system which is induced by a local cyclic evolution of one of its subsystem is suggested. This effect vanishes when the system is at a disentangled pure state but can be observed for some disentangled mixed states. As a paradigm, we study the effect for the system of two qubits in detail. It is interesting that the effect is directly related to the degree of entanglement for pure state of qubit pairs. Furthermore, we suggest a Bell-type experiment to measure this nonlocal effect for qubit pairs.
General correlation functions of the Clauser-Horne-Shimony-Holt inequality for arbitrarily high-dimensional systems
Li-Bin Fu
Physics , 2003, DOI: 10.1103/PhysRevLett.92.130404
Abstract: We generalize the correlation functions of the Clauser-Horne-Shimony-Holt (CHSH) inequality to arbitrarily high-dimensional systems. Based on this generalization, we construct the general CHSH inequality for bipartite quantum systems of arbitrarily high dimensionality, which takes the same simple form as CHSH inequality for two-dimension. This inequality is optimal in the same sense as the CHSH inequality for two dimensional systems, namely, the maximal amount by which the inequality is violated consists with the maximal resistance to noise. We also discuss the physical meaning and general definition of the correlation functions. Furthermore, by giving another specific set of the correlation functions with the same physical meaning, we realize the inequality presented in [Phys. Rev. Lett. {\bf 88,}040404 (2002)].
The Complexity of Testing Monomials in Multivariate Polynomials
Zhixiang Chen,Bin Fu
Computer Science , 2010,
Abstract: The work in this paper is to initiate a theory of testing monomials in multivariate polynomials. The central question is to ask whether a polynomial represented by certain economically compact structure has a multilinear monomial in its sum-product expansion. The complexity aspects of this problem and its variants are investigated with two folds of objectives. One is to understand how this problem relates to critical problems in complexity, and if so to what extent. The other is to exploit possibilities of applying algebraic properties of polynomials to the study of those problems. A series of results about $\Pi\Sigma\Pi$ and $\Pi\Sigma$ polynomials are obtained in this paper, laying a basis for further study along this line.
A Dense Hierarchy of Sublinear Time Approximation Schemes for Bin Packing
Richard Beigel,Bin Fu
Computer Science , 2010,
Abstract: The bin packing problem is to find the minimum number of bins of size one to pack a list of items with sizes $a_1,..., a_n$ in $(0,1]$. Using uniform sampling, which selects a random element from the input list each time, we develop a randomized $O({n(\log n)(\log\log n)\over \sum_{i=1}^n a_i}+({1\over \epsilon})^{O({1\over\epsilon})})$ time $(1+\epsilon)$-approximation scheme for the bin packing problem. We show that every randomized algorithm with uniform random sampling needs $\Omega({n\over \sum_{i=1}^n a_i})$ time to give an $(1+\epsilon)$-approximation. For each function $s(n): N\rightarrow N$, define $\sum(s(n))$ to be the set of all bin packing problems with the sum of item sizes equal to $s(n)$. For a constant $b\in (0,1)$, every problem in $\sum(n^{b})$ has an $O(n^{1-b}(\log n)(\log\log n)+({1\over \epsilon})^{O({1\over\epsilon})})$ time $(1+\epsilon)$-approximation for an arbitrary constant $\epsilon$. On the other hand, there is no $o(n^{1-b})$ time $(1+\epsilon)$-approximation scheme for the bin packing problems in $\sum(n^{b})$ for some constant $\epsilon>0$.
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