Number theory, geometry and their application to algorithm
| Project/Area Number |
18K03213
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Hiroshima University |
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Principal Investigator |
MATSUMOTO Makoto 広島大学, 先進理工系科学研究科(理), 教授 (70231602)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2022: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 擬似乱数 / 代数 / 統計的検定 / xorshift / 差集合 / Difference set / association scheme / relation partition / 疑似乱数 / 代数系 / アルゴリズム / xorshift128+ / TinyMT / dynamic creator / 64 bit MT / モンテカルロ法 / 準モンテカルロ法 |
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| Outline of Final Research Achievements |
1. Proposal on a test on statistical tests for pseudorandom numbers. Some statistical tests reject even good pseudorandom numbers. Often, it is due to the accumulation of errors in approximating theoretical distribution by analytic functions. We proposed a method to avoid computing the approximation error to test problematic approximation and to judge statistical tests' flaws. 2. Find a flaw in xorshift128+ generators. Because of its mixed nature, xorshift128+ is hard to analyze. We pointed out its lattice structure by approximating two-element field arithmetics by integer arithmetic. 3. Generalize the notion of difference sets from finite groups to association schemes, and give non-existence and existence results.
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| Academic Significance and Societal Importance of the Research Achievements |
1. 擬似乱数の検定法に問題がある場合、ユーザーは全く対処のしようがない。本研究で提唱した「検定法のテスト」を用いれば、問題のある検定法の多くを発見することができ、実用上の意義は高い。2. 近年広く使われるようになったxorshift128+生成法の出力の格子構造を明らかにしたことは、こういった「統計的検定により乱数性を保証された擬似乱数」の隠された脆弱さを明らかにしたという点で意義がある。3.差集合の概念をassociation schemeに一般化することで、差集合の探索が容易になるケースがある。また、この一般化は自然で、純粋数学的に興味深い。
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Report
(6 results)
Research Products
(3 results)
