Computational Aspects of Randomness and Their Structural Analysis via Nonstandard Methods
| Project/Area Number |
23340020
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tohoku University |
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Principal Investigator |
TANAKA Kazuyuki 東北大学, 理学(系)研究科(研究院), 教授 (70188291)
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| Co-Investigator(Kenkyū-buntansha) |
YAMAZAKI Takeshi 東北大学, 大学院理学研究科, 准教授 (30336812)
SUZUKI Toshio 首都大学東京, 大学院理学研究院, 准教授 (30235973)
TADAKI Kohtaro 中央大学, 研究開発機構, 機構准教授 (70407881)
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| Co-Investigator(Renkei-kenkyūsha) |
KURODA Satoru 群馬県立女子大学, 文学部, 准教授 (30300586)
YOKOYAMA Keita 北陸先端科学技術大学院大学, 情報科学研究科, 助教 (10534430)
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| Project Period (FY) |
2011-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥17,940,000 (Direct Cost: ¥13,800,000、Indirect Cost: ¥4,140,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥7,410,000 (Direct Cost: ¥5,700,000、Indirect Cost: ¥1,710,000)
Fiscal Year 2012: ¥5,720,000 (Direct Cost: ¥4,400,000、Indirect Cost: ¥1,320,000)
Fiscal Year 2011: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
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| Keywords | 計算可能性理論 / 超準モデル / ランダム性 / 数学基礎論 |
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| Outline of Final Research Achievements |
The main aim of this research is to cultivate systematic understanding of randomness via various logical methods such as non-standard analysis so that computational aspects of basic concepts about probability and games deeply correlated to randomness should be clarified. We focus on the following five topics. (1) Setting a logical framework of nonstandard arguments for constructive measure theory. (2) Investigating computational structures by randomness notions. (3) Determining the equilibrium points of game trees. (4) Elucidating physical meaning of Chaitin’s Omega. (5) Logical treatments for determinacy of games.
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Report
(5 results)
Research Products
(28 results)
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[Presentation] 決定問題の相転移2015
Author(s)
田中一之
Organizer
情報処理学会第７７回全国大会
Place of Presentation
京都大学
Year and Date
2015-03-17
Related Report
Invited
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