Pine Continuous Functions and Computable Analysis
Pine Continuous Functions and Computable Analysis
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Pine 连续函数和可计算分析
DOI：
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发表时间：
2007
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通讯作者：
Takakazu Mori
中科院分区：
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作者：
Takakazu Mori
通过对可计算数、可计算函数、有效可积性等概念的有效定义，可计算分析被广泛认为是分析的“有效”构造。已经采取了许多这种尝试的方法。一个例子是由Weihrauch（[13]）开发的具有表示的II型可计算性。这种方法是基于编码理论。另一个例子是Tsujii，Yasugi和Mori（[8]，[15]）继承了Pour-El和理查兹（[9]）的工作而发展的具有可计算结构的可计算度量空间。粗略地说，后一种方法使用有效收敛而不是通常的收敛来模拟通常的分析。有效的方法是基于递归理论的方法。因此，我们假设递归理论的基础知识，如递归函数。我们从$sqrt{2}$的计算开始，以说明可计算的数字。
Computable Analysis is regarded widely as areconstruction of analysis “effectively” by defining every notions effectively such as computable numbers, computable functions and effective integrability. Many approaches of this attempt have taken place. An example is Type II computability with representation, developed by Weihrauch ([13]). This approach is based on the coding theory. Another example is computable metric spaces with acomputability structure, developed by Tsujii, Yasugi and Mori ([8], [15]) inheriting the preceding work of Pour-El and Richards ([9]). Roughly speaking, the latter approach simulates the usual analysis using effective convergence instead of usual convergence. Effective way means amethod based on the recursion theory. So, we assume the basic knowledge of recursion theory such as recursive functions. We start with the calculation of $sqrt{2}$ for the sake of the illustration of computable numbers.