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Research on computable structures of continuous spaces like the real number through representation in bottomed sequences

Research Project

Project/Area Number 18500013
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Fundamental theory of informatics
Research InstitutionKyoto University

Principal Investigator

TSUIKI Hideki  Kyoto University, 人間・環境学研究科, 准教授 (10211377)

Research Collaborator 服部 泰直  島根大学, 総合理工学部, 教授
大田 春外  静岡大学, 教育学部, 教授
山田 修司  京都産業大学, 理学部, 教授
八杉 真理子  京都産業大学, 名誉教授
辻井 芳樹  京都産業大学, 理学部, 教授
森 隆一  京都産業大学, 理学部, 教授
Project Period (FY) 2006 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥3,630,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥630,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
Keywords実数計算 / グレイコード / ドメイン理論 / 位相空間論 / 不定元 / 双曲位相 / Lawson位相 / independent subbase / 計算可能性解析学 / グレイコ-ド / 独立部分基 / 有限時間計算可能性 / 距離空間 / ボトム入り文字列表現 / 解析学における計算可能性 / 実数 / 位相構造 / 計算構造
Research Abstract

The computational structure of the reals and other topological spaces are studied mainly with the method of embedding a space into the set of infinite sequences with bottoms. Some computationally natural properties of an embedding, such as the recursiveness of the definition and the non-redundancy of each digit in a code sequence, are investigated through their characterization in general topological terms, and some characterizations of spaces with such an embedding are given. Other topics such as constant time computability preserving conversions, and the relation between the Lawson topology of the space of formal balls and the hyperbolic topology of a metric space, are also investigated.

Report

(6 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report   Self-evaluation Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (35 results)

All 2010 2009 2008 2007 2006 Other

All Journal Article (20 results) (of which Peer Reviewed: 14 results) Presentation (15 results)

  • [Journal Article] Independent Subbases of the Sierpinski Gasket2010

    • Author(s)
      Hideki Tsuiki, Shuji Yamada
    • Journal Title

      京都大学数理解析研究所講究録 (to appear)

    • Related Report
      2009 Final Research Report
  • [Journal Article] Random Iteration Algorithm for Graph-Directed Sets.2010

    • Author(s)
      Yoshiki Tsujii, Takakazu Mori, Mariko Yasugi, Hideki Tsuiki
    • Journal Title

      Schloss Dagstuhl-Leibniz Center for Informatics(Andrej Bauer, Peter Hertling, Ker-I Ko) (to appear)

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hyperbolic topology of normed linear spaces.2010

    • Author(s)
      Yasunao Hattori, Hideki Tsuiki
    • Journal Title

      Topology and its applications 157

      Pages: 77-82

    • Related Report
      2009 Annual Research Report 2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Random Iteration Algorithm for Graph-Directed Sets2010

    • Author(s)
      Yoshiki Tsujii, Takakazu Mori, Mariko Yasugi, Hideki Tsuiki
    • Journal Title

      6th International Conference on Computability and Complexity in Analysis Proceedings 2275

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Independent Subbases of the Sierpinski Gasket2010

    • Author(s)
      Hideki Tsuiki, Shuji Yamada
    • Journal Title

      京都大学数理解析研究所講究録 (印刷中)

    • Related Report
      2009 Annual Research Report
  • [Journal Article] On Finite-time Computability Preserving Conversions.2009

    • Author(s)
      Hideki Tsuiki, Shuji Yamada
    • Journal Title

      Journal of Universal Computer Science 15(6)

      Pages: 1365-1380

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Fine-Continuous Functions and Fractals Defined by Infinite Systems of Contractions.2009

    • Author(s)
      Yoshiki Tsujii, Takakazu Mori, Mariko Yasugi, Hideki Tsuiki
    • Journal Title

      Lecture Notes in Computer Science 5489

      Pages: 109-125

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Finite-time Computability Preserving Conversions2009

    • Author(s)
      Hideki Tsiki, Shuji Yamada
    • Journal Title

      Journal of Universal Computer Science 15

      Pages: 1365-1380

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fine-Continuous Functions and Fractals Defined by Infinite Systems of Contractions2009

    • Author(s)
      Yoshiki Tsujii, Takakazu Mori, Mariko Yasugi, Hideki Tsuiki
    • Journal Title

      Lecture Notes in Computer Science 5489

      Pages: 109-125

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The hyperbolic topology of L_p(\Omega, \Sigma, \mu)2009

    • Author(s)
      Yasunao Hattori, Hideki Tsuiki
    • Journal Title

      Topology and its applications (掲載予定確定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Finite-time Computability Preserving Conversions2009

    • Author(s)
      Hideki Tsuiki, Shuji Yamada
    • Journal Title

      Journal of Universal Computer Science (掲載予定確定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fine-continuous functions and fractals defined by infinite systems of contractions2009

    • Author(s)
      Yoshiki Tsujii, Takakazu Mori, Mariko Yasugi, Hideki Tsuiki
    • Journal Title

      Proceedings of IIC2007, LNCS series (掲載予定確定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Finite-time Computability Preserving Conversions2008

    • Author(s)
      Hideki Tsuiki, Shuji Yamada
    • Journal Title

      Electric Notes in Theoretical Computer Science 221

      Pages: 299-308

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Lawson topology of the space of formal balls and the hyperbolic topology.2008

    • Author(s)
      Hideki Tsuiki, Yasunao Hattori.
    • Journal Title

      Theoretical Computer Science 405(1-2)

      Pages: 198-205

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Lawson topology of the space of formal balls and the hyperbolic topology2008

    • Author(s)
      Hideki Tsuiki, Yasunao Hattori
    • Journal Title

      Theoretical Computer Science vol. 405

      Pages: 198-205

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Lawson topology of the space of formal balls and the hyperbolic topology2008

    • Author(s)
      Hideki Tsuiki, Yasunao Hattori
    • Journal Title

      Theoretical Computer Science 405

      Pages: 198-205

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Lawson topology of the space of formal balls and the hyperbolic topology2008

    • Author(s)
      Hideki Tsuiki, Yasunao Hattori
    • Journal Title

      Theoretical Computer Science (To appear)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The hyperbolic topology of L_p(\Omega, \Sigma, \mu)

    • Author(s)
      Yasunao Hattori, Hideki Tsuiki
    • Journal Title

      Topology and its applications (to Appear in)

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] On Finite-time Computability Preserving Conversions

    • Author(s)
      Hideki Tsuiki, Shuji Yamada
    • Journal Title

      Journal of Universal Computer Science (to appear)

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Fine-continuous functions and fractals defined by infinite systems of contractions

    • Author(s)
      Yoshiki Tsujii, Takakazu Mori, Mariko Yasugi, Hideki Tsuiki
    • Journal Title

      to appear in proceedings of ILC2007

    • Related Report
      2008 Self-evaluation Report
  • [Presentation] Domain Representations Derived from Dyadic Subbases2010

    • Author(s)
      Hideki Tsuiki
    • Organizer
      Workshop on Constructive Aspects of Logic and Mathematics
    • Place of Presentation
      Kanazawa, Japan
    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Presentation] Independent Subbases of the Sierpinski Gasket2009

    • Author(s)
      立木秀樹
    • Organizer
      RIMS研究集会「一般位相幾何学及び幾何学的トポロジーに関する研究」
    • Place of Presentation
      京都
    • Related Report
      2009 Final Research Report
  • [Presentation] Finite-time Computability Preserving Conversions2009

    • Author(s)
      Hideki Tsuiki
    • Organizer
      5th International Symposium on Domain Theory
    • Place of Presentation
      Shanghai, China
    • Related Report
      2009 Final Research Report
  • [Presentation] Random Iteration Algorithm for Graph-Directed Sets.2009

    • Author(s)
      Yoshiki Tsujii, Takakazu Mori, Mariko Yasugi, Hideki Tsuiki
    • Organizer
      6th International Conference on Computability and Complexity in Analysis
    • Place of Presentation
      Ljubljana, Slovenia
    • Related Report
      2009 Final Research Report
  • [Presentation] {0, 1, ⊥}ω-codings Derived from Dynamical Systems.2009

    • Author(s)
      Hideki Tsuiki
    • Organizer
      Continuity, Computability, Constructivity Workshop
    • Place of Presentation
      Koeln, Germany
    • Related Report
      2009 Final Research Report
  • [Presentation] On Finite-time Computability Preserving Conversions.2009

    • Author(s)
      立木秀樹, 山田修司
    • Organizer
      題11回日本ソフトウェア科学会プログラミング及びプログラミング言語ワークショップ(PPL2009)
    • Place of Presentation
      高山
    • Related Report
      2009 Final Research Report
  • [Presentation] Finite-time Computability Preserving Conversions2009

    • Author(s)
      Hideki Tsuiki
    • Organizer
      5^<th> International Symposium on Domain Theory
    • Place of Presentation
      Shanghai, Chaina
    • Related Report
      2009 Annual Research Report
  • [Presentation] {0, 1, ⊥} ω-Codings Derived from Dynamical Systems2009

    • Author(s)
      Hideki Tsuiki
    • Organizer
      Continuity, Computability, Constructivity Workshop.
    • Place of Presentation
      Koeln, Germany
    • Related Report
      2009 Annual Research Report
  • [Presentation] On Finite-time Computability Preserving Conversions2008

    • Author(s)
      Hideki Tsuiki, Shuji Yamada
    • Organizer
      5th International conference on Computability and Complexity in Analysis
    • Place of Presentation
      Hagen, Germany
    • Year and Date
      2008-08-23
    • Related Report
      2008 Annual Research Report
  • [Presentation] On Finite-time Computability Preserving Conversions.2008

    • Author(s)
      Hideki Tsuiki, Shuji Yamada
    • Place of Presentation
      Hagen, Germany
    • Related Report
      2009 Final Research Report
  • [Presentation] Fractals Defined by Infinite Contractions and Mutual-Recursive Sets2007

    • Author(s)
      Yoshiki Tsujii, Takakazu Mori, Mariko Yasugi, Hideki Tsuiki
    • Place of Presentation
      Cape Town, South Africa University of Cape Town
    • Related Report
      2009 Final Research Report
  • [Presentation] On Finite-time Computable Functions2007

    • Author(s)
      Hideki Tsuiki, Shuji Yamada
    • Organizer
      International Conference on Infinity in Logic & Computation
    • Place of Presentation
      Cape Town, South Africa University of Cape Town
    • Related Report
      2009 Final Research Report 2007 Annual Research Report
  • [Presentation] Lawson Topology of the space of formal balls and the hyperbolic subbase2006

    • Author(s)
      Hideki Tsuiki
    • Organizer
      Dagstuhl Seminar 06341, Computational Structures for Modelling Space
    • Place of Presentation
      Time and Causality Dagstuhl, Germany
    • Related Report
      2009 Final Research Report
  • [Presentation] Lawson Topology of the space of formal balls and the hyperbolic subbase2006

    • Author(s)
      Hideki Tsuiki
    • Organizer
      International Conference on Topology and its Applications
    • Place of Presentation
      Aegion, Greece
    • Related Report
      2009 Final Research Report
  • [Presentation] Lawson topology of the space of formal balls and the hyperbolic subbase2006

    • Author(s)
      Hideki Tsuiki
    • Organizer
      International Conference on Topology and its application
    • Place of Presentation
      Aegion, Greece
    • Related Report
      2008 Self-evaluation Report

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Published: 2006-04-01   Modified: 2016-04-21  

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