2010 Fiscal Year Final Research Report
Multilateral research on the role of limiting recursive functions in the computability problem
| Project/Area Number |
20540143
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Kyoto Sangyo University |
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Principal Investigator |
YASUGI Mariko Kyoto Sangyo University, 名誉教授 (90022277)
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| Co-Investigator(Kenkyū-buntansha) |
MORI Takakazu 京都産業大学, 理学部, 教授 (00065880)
KOBAYASHI Satoshi 京都産業大学, コンピュータ理工学部, 教授 (70234820)
TSUJII Yoshiki 京都産業大学, 理学部, 教授 (90065871)
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| Co-Investigator(Renkei-kenkyūsha) |
HAYASHI Susumu 京都大学, 大学院・文学研究科, 教授 (40156443)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 極限再帰関数 / 実効的一様位相 / 計算可能確率分布 / Fine計算可能関数 / 数学基礎論 |
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| Research Abstract |
A function whose value is obtained somewhere in the course of an infinite process of computations is called a limiting recursive function. The theory of limiting recursive functions plays an important role when one observes mathematics from the standpoint of "computation". We have applied it to the computability theory in mathematics, and compared this method with the method of uniform topology, in which a Euclidean discontinuous function turns continuous. We have further devised how to implement a part of this theory on the computer.
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