Multilateral Researches on Computability Problems on the Continuum

连续体可计算性问题的多边研究

基本信息

  • 批准号:
    12440031
  • 负责人:
  • 金额:
    $ 4.86万
  • 依托单位:
  • 依托单位国家:
    日本
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
  • 财政年份:
    2000
  • 资助国家:
    日本
  • 起止时间:
    2000 至 2002
  • 项目状态:
    已结题

项目摘要

The purpose of this project is the computability structure on the continuum in Pour-E1 style; its extension, application, and formalization. Most of the objectives have been steadily achieved. We here report our results.The major research target of this project is the computability problems of real discontinuous functions, especially piecewise continuous functions, that is, the foundations of computation of function values at discontinuous points.1. Limit computation: This is a computation method by taking the limits of recursive functions. We have shown that many of piecewise continuous functions are computable with this method.2. Effective uniform space: The theory of the computability structure on the uniform space obtained by isolating discontinuous points has been developed. Many of piecewise continuous functions have been shown to be computable in this theory. The equivalence of effective convergences of a function with regards to respectively uniformity and its metrization.3. Limit computation and uniform space: Under a certain condition, sequential computabilities of a piecewise continuous function with regards to respectively limit computation and uniformity.4. Method of Walsh analysis: The theory of representing computability notions in terms of Fine metric has been developed, and various notions of computability have been defined.5. A formal system of limit computable mathematics: A formal system in which limiting computable mathematics can be executed has been defined, and its functional interpretation has been carried out.6. Computability in functional analysis: Effectivity of solving the invisid partial differential equation and effectivity of some linear operators on the interpolation space have been solved affirmatively.7. Theories of representing real numbers: Theories of representing a complete uniform space by a uniform domain, and representations of real numbers by respectively Gray codes and a certain category have been developed.
本项目的目的是建立Pour-E1风格的连续体上的可计算性结构,并对其进行扩展、应用和形式化。大部分目标已经稳步实现。本课题的主要研究对象是实不连续函数,特别是分段连续函数的可计算性问题,即不连续点处函数值计算的基础。极限计算:这是一种利用递归函数的极限进行计算的方法。我们已经证明了许多分段连续函数是可以用这种方法计算的。有效均匀空间:通过隔离不连续点得到的均匀空间上的可计算性结构的理论已经得到发展。在这一理论中,许多分段连续函数已被证明是可计算的。函数关于一致性及其度量化的有效收敛的等价性。极限计算和一致空间:在一定条件下,分段连续函数关于极限计算和一致的序列可计算性。沃尔什分析方法:发展了用精细度量来表示可计算性概念的理论,并定义了各种可计算性概念。定义了极限可计算数学的形式系统:定义了可执行极限可计算数学的形式系统,并对其进行了函数解释。泛函分析中的可计算性:肯定地解决了隐式偏微分方程解的有效性和插值空间上某些线性算子的有效性问题。实数表示理论:用一致整环表示完全一致空间的理论,以及分别用格雷码和某一范畴表示实数的理论。

项目成果

期刊论文数量(74)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
V.Brattka: "Some notes on Fine Computability"JUCS. 8-3. 382-395 (2002)
V.Brattka:“关于精细可计算性的一些注释”JUCS。
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    0
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  • 通讯作者:
M. Yasugi, et al.: "Metrization of the uniform space and effective convergence"MLQ. 48-Suppl. 1. 123-130 (2002)
M. Yasugi 等人:“均匀空间的度量化和有效收敛”MLQ。
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    0
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Susumu Hayashi et.al: "Towards animation of proofs-testing proofs by examples"Theoretical Computer Science. (to appear).
Susumu Hayashi 等人:“走向证明动画 - 通过示例测试证明”理论计算机科学。
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    0
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M. Yasugi, et al.: "Two notions of sequential computability of a function with jumps"ENTCS (Proceedings of CCA2002). 66-1. 11 (2002)
M. Yasugi 等人:“带有跳转的函数的顺序可计算性的两个概念”ENTCS(CCA2002 论文集)。
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  • 影响因子:
    0
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Yasugi, Mariko 他: "A note on Rademacher functions and computability"ICWLC. (accepted).
Yasugi、Mariko 等人:“关于 Rademacher 函数和可计算性的说明”ICWLC(已接受)。
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    0
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YASUGI Mariko其他文献

YASUGI Mariko的其他文献

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{{ truncateString('YASUGI Mariko', 18)}}的其他基金

Multilateral research on the role of limiting recursive functions in the computability problem
限制递归函数在可计算性问题中的作用的多边研究
  • 批准号:
    20540143
  • 财政年份:
    2008
  • 资助金额:
    $ 4.86万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Computability of discontinuous functions-Towards its paradigm
不连续函数的可计算性——走向它的范式
  • 批准号:
    16340028
  • 财政年份:
    2004
  • 资助金额:
    $ 4.86万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)

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