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  1.  10
    On the Computability of Fractal Dimensions and Hausdorff Measure.Ker-I. Ko - 1998 - Annals of Pure and Applied Logic 93 (1-3):195-216.
    It is shown that there exist subsets A and B of the real line which are recursively constructible such that A has a nonrecursive Hausdorff dimension and B has a recursive Hausdorff dimension but has a finite, nonrecursive Hausdorff measure. It is also shown that there exists a polynomial-time computable curve on the two-dimensional plane that has a nonrecursive Hausdorff dimension between 1 and 2. Computability of Julia sets of computable functions on the real line is investigated. It is shown (...)
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  2.  32
    On the Complexity of Finding Paths in a Two‐Dimensional Domain I: Shortest Paths.Arthur W. Chou & Ker-I. Ko - 2004 - Mathematical Logic Quarterly 50 (6):551-572.
    The computational complexity of finding a shortest path in a two-dimensional domain is studied in the Turing machine-based computational model and in the discrete complexity theory. This problem is studied with respect to two formulations of polynomial-time computable two-dimensional domains: domains with polynomialtime computable boundaries, and polynomial-time recognizable domains with polynomial-time computable distance functions. It is proved that the shortest path problem has the polynomial-space upper bound for domains of both type and type ; and it has a polynomial-space lower (...)
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  3.  12
    Approximation to Measurable Functions and its Relation to Probabilistic Computation.Ker-I. Ko - 1986 - Annals of Pure and Applied Logic 30 (2):173-200.
    A theory of approximation to measurable sets and measurable functions based on the concepts of recursion theory and discrete complexity theory is developed. The approximation method uses a model of oracle Turing machines, and so the computational complexity may be defined in a natural way. This complexity measure may be viewed as a formulation of the average-case complexity of real functions—in contrast to the more restrictive worst-case complexity. The relationship between these two complexity measures is further studied and compared with (...)
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  4.  14
    Editorial: Math. Log. Quart. 4–5/2007.Ker-I. Ko, Klaus Weihrauch & Xizhong Zheng - 2007 - Mathematical Logic Quarterly 53 (4‐5):325-325.
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  5.  11
    On the Computational Complexity of Integral Equations.Ker-I. Ko - 1992 - Annals of Pure and Applied Logic 58 (3):201-228.
    Ko, K., On the computational complexity of integral equations, Annals of Pure and Applied Logic 58 201–228. The computational complexity of Volterra integral equations of the second kind and of the first kind is investigated. It is proved that if the kernel functions satisfy the Lipschitz condition, then the solutions of Volterra equations of the second kind are polynomial-space computable. If, one the other hand, the kernel functions only satisfy the local Lipschitz condition with the Lipschitz constants growing in an (...)
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  6.  10
    Preface: MLQ - Math. Log. Quart. 4–5/2004.Vasco Brattka, Peter Hertling, Ker-I. Ko & Ning Zhong - 2004 - Mathematical Logic Quarterly 50 (45):327-328.
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  7.  9
    Preface: MLQ ‐ Math. Log. Quart. 4–5/2004.Vasco Brattka, Peter Hertling, Ker-I. Ko & Ning Zhong - 2004 - Mathematical Logic Quarterly 50 (4‐5):327-328.
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  8.  7
    On the Complexity of Finding Paths in a Two-Dimensional Domain I: Shortest Paths.Arthur W. Chou & Ker-I. Ko - 2004 - Mathematical Logic Quarterly 50 (6):551-572.
    The computational complexity of finding a shortest path in a two-dimensional domain is studied in the Turing machine-based computational model and in the discrete complexity theory. This problem is studied with respect to two formulations of polynomial-time computable two-dimensional domains: domains with polynomialtime computable boundaries, and polynomial-time recognizable domains with polynomial-time computable distance functions. It is proved that the shortest path problem has the polynomial-space upper bound for domains of both type and type ; and it has a polynomial-space lower (...)
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