Computational Complexity in Analysis and Geometry

• Project/Area Number: 23700009
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Fundamental theory of informatics
• Research Institution: The University of Tokyo
• Principal Investigator: KAWAMURA Akitoshi 東京大学, 情報理工学(系)研究科, 助教 (20600117)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 計算量 / 数値計算 / 計算可能解析 / 計算可能解析学 / 帰納解析学

Outline of Final Research Achievements

(1) Foundation of computational complexity in mathematical analysis using type-two complexity and theory of representations
(2) Computational complexity of problems involving analytic functions and some slightly larger classes of functions

Research Products

• [Journal Article] Computational Complexity of Smooth Differential Equations (2014)
  • Author(s): Akitoshi Kawamura , Hiroyuki Ota, Carsten Rosnick Martin Ziegler
  • Journal Title: Logical Methods in Computer Science Volume: 10 Pages: 1-15
  • DOI: 10.2168/lmcs-10(1:6)2014
  • Peer Reviewed / Open Access
• [Journal Article] The distance 4-sector of two points is unique (2013)
  • Author(s): R. Fraser, M. He, A. Kawamura, A. López-Ortiz, J. I. Munro, P. K. Nicholson
  • Journal Title: Proc. Twenty-Fourth International Symposium on Algorithms and Computation (ISAAC) Volume: LNCS 8283 Pages: 612-622
  • DOI: 10.1007/978-3-642-45030-3_57
  • ISBN: 9783642450297, 9783642450303
  • Peer Reviewed
• [Journal Article] Complexity theory for operators in analysis (2012)
  • Author(s): Akitoshi Kawamura and Stephen Cook
  • Journal Title: ACM Transactions on Computation Theory Volume: 4 Issue: 2 Pages: 1-24
  • DOI: 10.1145/2189778.2189780
  • NAID: 110008900059
  • Peer Reviewed
• [Journal Article] Parameterized Uniform Complexity in Numerics: from Smooth to Analytic, from NP-hard to Polytime (2012)
  • Author(s): Akitoshi Kawamura, Norbert Th. Müller, Carsten Rösnick, Martin Ziegler
  • Journal Title: arXiv:1211.4974 Volume: arXiv:1211.4974
• [Journal Article] Computational Complexity of Smooth Differential Equations (2012)
  • Author(s): A. Kawamura, H. Ota, C. Rosnick, and M. Ziegler
  • Journal Title: Lecture Notes in Computer Science Volume: 7464 Pages: 578-589
  • DOI: 10.1007/978-3-642-32589-2_51
  • ISBN: 9783642325885, 9783642325892
  • Peer Reviewed
• [Presentation] Applying higher-type complexity to analysis (2014)
  • Author(s): Akitoshi Kawamura
  • Organizer: Fifth Workshop on Developments in Implicit Computational Complexity (DICE)
  • Place of Presentation: Grenoble, France
  • Year and Date: 2014-04-05
  • Invited
• [Presentation] On small complexity classes for computable analysis
  • Author(s): A. Kawamura
  • Organizer: Continuity, Computability, Constructivity -- From Logic to Algorithms (CCC)
  • Place of Presentation: Gregynog, Swansea University, Wales, UK
  • Invited
• [Presentation] Polynomial-time randomness and differentiability
  • Author(s): A. Kawamura, K. Miyabe
  • Organizer: Computability in Europe (CiE)
  • Place of Presentation: Milan, Italy
• [Presentation] On the Computational Complexity of Laplace's and Poisson's Equations
  • Author(s): A. Kawamura, F. Steinberg, M. Ziegler
  • Organizer: Logic Colloquium (LC)
  • Place of Presentation: Évora, Portugal
• [Presentation] 連続系の計算量
  • Author(s): 河村彰星
  • Organizer: 新学術領域研究「計算限界解明」計算量理論秋学校
  • Place of Presentation: 長野県北佐久郡軽井沢町
  • Invited
• [Presentation] 計算資源としての乱択
  • Author(s): 河村彰星
  • Organizer: 京都大学大学院人間環境学研究科 数理科学講座談話会
  • Place of Presentation: 京都府京都市左京区
  • Invited
• [Presentation] Polynomial-time computability on the space of real functions
  • Author(s): A. Kawamura
  • Organizer: Dagstuhl-seminar 11411: Computing with Infinite Data
  • Place of Presentation: 独国ザールラント州ワーデルン市
• [Presentation] 解析学における高階計算量
  • Author(s): 河村、クック
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 宮城県仙台市青葉区
• [Presentation] 滑らかな常微分方程式の計算量
  • Author(s): 太田、河村、ツィーグラー、レースニク
  • Organizer: 冬のエルエーシンポジウム
  • Place of Presentation: 京都府京都市左京区