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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Introduction,orial optimization, graph theory, number theory and cryptography. As a consequence, many researchers have begun to re-examine various branches of classical mathematics from the complexity point of view. For a given nonconstructive existence theorem in classical mathematics, one would like to find a

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Maximization,tion . on [0,1]. It is to be shown that these maximum values axe exactly the real numbers which have a (general) left cut in . (called left . real numbers). For two-dimensional, polynomial-time computable functions . on [0, l]., the maximum functions .) = max{., .)| 0 ≤ . ≤ 1} coincide with . real f

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Ordinary Differentiation Equations,on the solution . (for example, by the use of the Euler method). The main result of this chapter proves that polynomial space is also a lower bound for the solution . of equation (7.1) if the function . is polynomial-time computable and satisfies a weak form of local Lipschitz condition in the neigh

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Book 1991ng combinatorial optimization, graph theory, number theory and cryptography. As a consequence, many researchers have begun to re-examine various branches of classical mathematics from the complexity point of view. For a given nonconstructive existence theorem in classical mathematics, one would like