Titlebook: Complexity Theory of Real Functions; Ker-I Ko Book 1991 Birkh?user Boston 1991 Approximation.NP-completeness.Notation.algorithm.algorithms

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Progress in Theoretical Computer Sciencehttp://image.papertrans.cn/c/image/231657.jpg

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Sergey V. Stasenko,Victor B. Kazantsevn logarithmic space and exponential space. Some results on complexity classes of sparse sets and tally sets are included because they are closely related to the structure of the representations of real numbers under our formal definition. Other results in discrete complexity theory, not directly rel

Chronic

Smart Innovation, Systems and Technologiesnumbers and computable real functions and their basic properties. Then, the oracle Turing machine is introduced as the formal model for computing real functions. This model allows us to define the complexity measures for computing real functions in a natural way. The class of polynomial time computa

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Model Complexity Control in Clusteringoptimization and nondeterminism have been observed, as many combinatorial optimization problems have been shown to be .-complete (cf. Garey and Johnson [1979]). On the other hand, optimization of a continuous function can often be solved in polynomial time. As an example, the linear programming prob

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https://doi.org/10.1007/978-3-319-59072-1mputational viewpoint, we may define a recursively measurable set to be one that can be approximated by simple open sets such that the measures of the approximation errors converge to zero recursively. A polynomial-time measurable set, or, more appropriately, a polynomial-time approximable set then

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Advances in Neural Networks - ISNN 2017rd to compute from the approximation of the function. However, if some nice properties about the function is known (such as the differentiability of the derivative itself) then the derivative may be easy to compute. Formally, we prove that the derivative of a polynomial-time computable function is p

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https://doi.org/10.1007/978-3-319-12436-0by a polynomial-time computable function . on the rectangle [0,1] × [-1,1]. We consider only ordinary differential equations of the first order, and only equations with initial conditions. The complexity of the solutions . of equation (7.1) depends on certain properties of the function .. First, if

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Biao Luo,Derong Liu,Xiong Yang,Hongwen Mamial function . such that .(.(. 2. for all . ∈ [0, 1], In this chapter we investigate the polynomial-time version of the Weierstrass approximation theorem: Is the sequence |.} polynomial-time computable, if . is known to be polynomial-time computable? Pour-El and Caldwell [1975] proved that the recu