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Gray-code representation of real number and the induced computability structure

Gray-code representation of real number and the induced computability structure
实数的格雷码表示和导出的可计算性结构
批准号:
15500010
负责人:
TSUIKI Hideki
金额:
$1.6万
依托单位:
依托单位国家:
日本
项目类别:
Grant-in-Aid for Scientific Research (C)
财政年份:
2003
资助国家:
日本
项目状态:
已结题
起止时间:
2003 至 2005

项目摘要

项目成果

TSUIKI Hideki的其他基金

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中文摘要
翻译
研究了由{0,1,bot}-无限序列表示(格雷码表示)导出的真实的数的可计算结构及其上的不确定多头机(IM 2-machine)的计算、拓扑和Domain理论问题。当我们考虑{0,1,bot}-无限序列上的函数时,GHC中可表示的函数集大于IM 2-可计算函数集,但当只考虑真实的数表示时,它们是相等的。2. IM 2-机不能用函数语言实现,但通过扩展一个带有限制amb算子的函数语言,该算子是用顺序图归约规则而不是项归约规则实现的,可以实现IM 2机器的能力。3.表示拓扑空间所需的底数与拓扑维数相等。在代数整环上得到了一个更一般的结果,并从整环理论上证明了这个结果。引入自然计算结构的编码将引入基于正则开集对的并矢子基。格雷码表示的效率可以通过相应的子基,这是拓扑研究的性质来表征。
英文摘要
We studied computational, topological, and domain-theoretic problems related to the computable structure of real numbers derived form representation with {0,1,bot}-infinite sequences (Gray-code representation) and indeterministic multi-head machine (IM2-machine) operating on them.1.IM2-machines can be realized with logic programming languages with guards like GHC (Guarded Horn Clauses). The set of functions expressible in GHC is larger than the set of IM2-computable functions when we consider functions over {0,1,bot}-infinite sequences but they are equal when only real number representation is considered.2.IM2-machines cannot be realized with functional languages, but by extending a functional language with a restricted amb operator which is realized with sequential graph reduction rules instead of term reduction rules, one can implement the ability of IM2-machines. We have implemented it as an extension of the Haskell language.3.The number of bottoms required to represent a topological space and the topological dimension of the space is equal. We have a more general result on an algebraic domain, which is proved domain-theoretically.4.Codings and subbases of a topological space are closely related. Codings which induce natural computational structure will induce a dyadic subbase, which is based on pairs of regular open sets. The efficiency of the Gray-code representation can be characterized through properties of the corresponding subbase, which are studied topologically.
期刊论文(29)
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科研奖励(0)
会议论文
Compact metric spaces as minimal-limit sets in domains of bottomed sequences
紧致度量空间作为有底序列域中的最小极限集
DOI: --
发表时间: 2004
期刊: Mathematical Structures in Computer Science 14(6)
影响因子: --
作者: [M.Oyamaguchi, Y.Ohta, Hideki Tsuiki]
通讯作者: Hideki Tsuiki
Dyadic subbases and efficiency properties of the induced (0, 1, bot) ^omega-representations
诱导的 (0, 1, bot) ^omega 表示的二元底基和效率特性
DOI: --
发表时间: 2004
期刊: Topology Proceedings 28(2)
影响因子: --
作者: [Chika Oshima, Naoki Itou, Kazushi Nishimoto, Masahide Naemura, Hideki Tsuiki]
通讯作者: Hideki Tsuiki
A Domain-theoretic Semantics of Lax Generic Functions
宽松泛型函数的领域理论语义
DOI: --
发表时间: 2003
期刊: Theoretical Computer Science 294
影响因子: --
作者: [Hideki Tsuiki, Keiji Sugihara, Hideki Tsuiki, Hideki Tsuiki, Hideki Tsuiki, Hideki Tsuiki, Hideki Tsuiki, Hideki Tsuiki, Hideki Tsuiki, Hideki Tsuiki, Hideki Tsuiki]
通讯作者: Hideki Tsuiki
Embedding Compact Metric Spaces as Minimal-limit Sets in Domains of Bottomed Sequences
将紧度量空间嵌入为有底序列域中的最小极限集
DOI: --
发表时间: 2004
期刊: Mathematical Structures in Computer Science 14(6)
影响因子: --
作者: [有村光晴, 長岡浩司, Hideki Tsuiki]
通讯作者: Hideki Tsuiki
13
    Studies on representation-based computational structures of spaces and figures, and on related structures like fractals
    • 批准号:
      22500014
    • 项目类别:
      Grant-in-Aid for Scientific Research (C)
    • 资助金额:
      $2.41万
    • 财政年份:
      2010
    • 负责人:
      TSUIKI Hideki
    • 依托单位:
    Research on computable structures of continuous spaces like the real number through representation in bottomed sequences
    • 批准号:
      18500013
    • 项目类别:
      Grant-in-Aid for Scientific Research (C)
    • 资助金额:
      $2.32万
    • 财政年份:
      2006
    • 负责人:
      TSUIKI Hideki
    • 依托单位:
    海外基金