2023 Fiscal Year Final Research Report
Experimental Computational Complexity Theory - Its Establishment and Development
| Project/Area Number |
18K11152
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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 60010:Theory of informatics-related
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| Research Institution | Gunma University |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2024-03-31
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| Keywords | 計算量理論 / 計算複雑さ / P vs. NP問題 / 回路計算量 / 計算機援用 / しきい値回路 |
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| Outline of Final Research Achievements |
Computational complexity theory, which aims to develop methods for estimating the amount of resources required to achieve the desired computation on various computational models, is an important yet challenging field in which new advances are difficult to achieve. We have pursued an approach that employs computational analysis, which we named Experimental Computational Complexity Theory, and conducted research aimed at its broader application. As a result, significant advancements were made, particularly in constructing Boolean functions and establishing upper and lower bounds on the size of a small depth Boolean circuit. All these achievements were made possible for the first time through the approach pursued in this research, confirming its methodological effectiveness.
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| Free Research Field |
理論計算機科学
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| Academic Significance and Societal Importance of the Research Achievements |
近年の計算機の高速化は著しいが，要求される計算の大規模化はこれを上回るスピードで進んでいる．それゆえ，これら計算の効率化の限界点を明らかにすることのできる手法の開発は非常に重要である．本研究では，このような計算量理論分野のさまざまな問題に対して，計算機による大規模計算による解析を中核的に含む手法を追求し，その広範な有用性を確認することができた．また，得られた成果の多くは，その核心的部分に，人間には着想困難な発見が含まれるものとなっており，計算機と人間の協調による数学の更なる発展をも予感させるものである．
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