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Sizes of Cohen-type forcing condition : Application to randomness and computational complexity

Research Project

Project/Area Number 17540131
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionTokyo Metropolitan University (2006-2007)
Osaka Prefecture University (2005)

Principal Investigator

SUZUKI Toshio  Tokyo Metropolitan University, Department of Mathematics and Information Sciences, Associate professor (30235973)

Co-Investigator(Kenkyū-buntansha) KUMABE Masahiro  The Open University of Japan, Faculty of Liberal Arts, Associate professor (70255173)
Project Period (FY) 2005 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥3,370,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywordsmathematical logic / foundation of computer sciences / algorithm / randomness / random number
Research Abstract

We improve the main theorem of the following paper. Toshio Suzuki, Archive for Mathematical Logic, vcol.44 (2005) pp. 751-762. The constant norm in the main theorem of the above paper is relaxed to multiple of constant and the norm. Summary of this result may be found in the following research report. M. Kumabe, T Suzuki and T. Yamazaki, "Truth-table reductions and minimum sizes of forcing conditions", Surikaisekikenkyusho-kokyuroku, vol. 1533 (2007), Research Institute of Mathematical Sciences, Kyoto University.
We study Boolean functions defined by copies of a Boolean decision tree connected in parallel. An input string is given to leaves, and an output string is given by roots. We investigate which kind of weak randomness property is conserved by this type of Boolean functions. We showed a necessary condition of Martin-Loef randomness is conserved by this type of Boolean functions. The necessary condition is that for every positive integer r, a give oracle is r-generic in the sense of Dowd. We report this result at the following conference talk. "Which weak-randomness property is preserved by Boolean decision trees?", Proof theory 2007 (2007 December 3-4), Tokyo Metropolitan-University.

Report

(4 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (30 results)

All 2007 2006 2005 Other

All Journal Article (14 results) (of which Peer Reviewed: 2 results) Presentation (13 results) Book (1 results) Remarks (2 results)

  • [Journal Article] Truth-table reductions and minimum sizes of forcing conditions2007

    • Author(s)
      M.Kumabe(T Suzuki、T.Yamazakiと連名)
    • Journal Title

      京都大学数理解析研究所講究録 1533

      Pages: 9-14

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Truth-table reductions and minimum sizes of forcing conditions2007

    • Author(s)
      M. Kumabe, (T. Suzuki, T. Yamazaki)
    • Journal Title

      Surikaisekikenkyusho-kokyuroku 1533

      Pages: 9-14

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Truth-table reductions and minimum sizes of forcing conditions (preliminary draft)2007

    • Author(s)
      M.Kumabe, T.Suzuki, T.Yamazaki
    • Journal Title

      数理解析研究所講究録 1533

      Pages: 9-14

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Resource bounded immunity and simplicity2005

    • Author(s)
      Tomoyuki Yamakami(Toshio Suzukiと連名)
    • Journal Title

      Theoretical Computer Science 347

      Pages: 90-129

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Bounded truth table does not reduce the one-query tautologies to a random oracle2005

    • Author(s)
      Toshio Suzuki
    • Journal Title

      Archive for Mathematical Logic 44

      Pages: 751-762

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary 2005 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 手描き曲線からの乱数抽出とそのセマンティクス(中間報告)2005

    • Author(s)
      川西 暁夫(鈴木 登志雄と連名)
    • Journal Title

      京都大学数理解析研究所講究録 1442

      Pages: 8-41

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Logarithmic truth-table reductions and minimum sizes of forcing conditions2005

    • Author(s)
      M.Kumabe(T Suzuki、T.Yamazakiと連名)
    • Journal Title

      京都大学数理解析研究所講究録 1442

      Pages: 42-47

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Bounded truth table does not reduce the one-query tautologies to a random oracle2005

    • Author(s)
      Toshio, Suzuki
    • Journal Title

      Archive for Mathematical Logic 44

      Pages: 751-762

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Random extraction from freehand drawings and its semantics (preliminary report) (in Japanese)2005

    • Author(s)
      A. Kawanishi (T. Suzuki)
    • Journal Title

      Surikaisekikenkyusho-kokyutoku 1422

      Pages: 8-41

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Logarithmic truth-table reductions and minimum sizes of forcing conditions2005

    • Author(s)
      M. Kumabe (T. Suzuki, T. Yamazaki)
    • Journal Title

      Surikaisekikenkyusho-kokyuroku 1422

      Pages: 42-47

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] 手描き曲線からの乱数抽出とそのセマンティクス(中間報告)2005

    • Author(s)
      川西暁夫, 鈴木登志雄
    • Journal Title

      京都大学数理解析研究所講究録 1442

      Pages: 8-41

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Logarithmic truth-table reductions and minimum sizes of forcing conditions2005

    • Author(s)
      M.Kumabe, T.Suzuki, T.Yamazaki
    • Journal Title

      京都大学数理解析研究所講究録 1442

      Pages: 42-47

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Resource bounded immunity and simplicity2005

    • Author(s)
      Tomoyuki Yamakami, Toshio Suzuki
    • Journal Title

      Theoretical Computer Science 347

      Pages: 90-129

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Resource bounded immunity and simplicity

    • Author(s)
      Tomoyuki, Yamakami (Toshio, Suzuki)
    • Journal Title

      Theoretical Computer Science 347

      Pages: 90-129

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Which weak-randomness property is preserved by Boolean decision trees2007

    • Author(s)
      鈴木 登志雄
    • Organizer
      2007年度証明論研究集会
    • Place of Presentation
      首都大学東京国際交流会館
    • Year and Date
      2007-12-04
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Which weak-randomness property is preserved by Boolean decision trees?2007

    • Author(s)
      Toshio, Suzuki
    • Organizer
      Proof theory 2007
    • Place of Presentation
      Tokyo Metropolitan University
    • Year and Date
      2007-12-04
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Which weak-randomness property is preserved by Boolean decision trees?2007

    • Author(s)
      鈴木登志雄
    • Organizer
      2007年度証明論研究集会
    • Place of Presentation
      首都大学東京国際交流会館
    • Year and Date
      2007-12-04
    • Related Report
      2007 Annual Research Report
  • [Presentation] 算術的フォーシングとフォーシング条件:クエリー記号付きプール式・計算量およびランダム性との関連2006

    • Author(s)
      鈴木 登志雄
    • Organizer
      数学基礎論と計算量理論
    • Place of Presentation
      電気通信大学
    • Year and Date
      2006-12-22
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Arithmetical forcing and forcing conditions2006

    • Author(s)
      Toshio, Suzuki
    • Organizer
      Mathematical logic and computational complexity
    • Place of Presentation
      The University of Electro-Communication
    • Year and Date
      2006-12-22
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Truth-table reduction and minimum sizes of forcing conditions2006

    • Author(s)
      鈴木 登志雄(隈部 正博、山崎 武と連名)
    • Organizer
      2006年度日本数学会秋季総合分科会
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2006-09-22
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Truth-table reduction and minimum sizes of forcing conditions2006

    • Author(s)
      Toshio, Suzuki (M. Kumabe, T. Yamazaki)
    • Organizer
      Mathematical Society of Japan
    • Place of Presentation
      Osaka City University
    • Year and Date
      2006-09-22
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Truth-table reductions and minimum sizes of forcing conditions2006

    • Author(s)
      鈴木 登志雄(隈部 正博、山崎 武と連名)
    • Organizer
      算術体系の証明論
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2006-08-23
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Truth-table reduction and minimum sizes of forcing conditions2006

    • Author(s)
      Toshio, Suzuki (M. Kumabe, T. Yamazaki)
    • Organizer
      Proof theory of arithmetic
    • Place of Presentation
      Research Institute of Mathematical Sciences, Kyoto University
    • Year and Date
      2006-08-23
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Random extraction from freehand drawings and its semantics based on forcing complexity2005

    • Author(s)
      鈴木 登志雄(川西 暁夫と連名)
    • Organizer
      第6回「代数学と計算」研究集会(AC2005)
    • Place of Presentation
      首都大学東京国際交流会館
    • Year and Date
      2005-11-18
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Random extraction from freehand drawings and its semantics based on forcing complexity2005

    • Author(s)
      Toshio, Suzuki (A. Kawanishi)
    • Organizer
      Algebra and computation 2005 (AC2005)
    • Place of Presentation
      Tokyo Metropolitan University
    • Year and Date
      2005-11-18
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Random extraction from freehand drawings and its semantics based on forcing complexity2005

    • Author(s)
      鈴木 登志雄(川西 暁夫と連名)
    • Organizer
      Franco-Canadian Workshop on Combinatorial Algo rithm(COMAL 2005)
    • Place of Presentation
      McMaster University(カナダ、オンタリオ州)
    • Year and Date
      2005-08-18
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Random extraction from freehand drawings and its semantics based on forcing complexity2005

    • Author(s)
      Toshio, Suzuki (A. Kawanishi)
    • Organizer
      Franco-Canadian workshop on combinatorial algorithm (COMAL 2005)
    • Place of Presentation
      McMaster University.(Canada)
    • Year and Date
      2005-08-18
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] ゲーデルと20世紀の論地学(1) ゲーデルの20世紀2007

    • Author(s)
      田中一之 編, 田中一之, 田中尚夫, 鈴木登志雄 ほか著
    • Total Pages
      240
    • Publisher
      東京大学出版会
    • Related Report
      2006 Annual Research Report
  • [Remarks] 「研究成果報告書概要(和文)」より

    • URL

      http://www.ac.auone-net.jp/~bellp/papers.html

    • Related Report
      2007 Final Research Report Summary
  • [Remarks]

    • URL

      http://www.ac.auone-net.jp/~bellp/papers.html

    • Related Report
      2007 Annual Research Report

URL: 

Published: 2005-04-01   Modified: 2016-04-21  

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