Theory and applications of complexity theory for continuous systems

• Project/Area Number: 26700001
• Research Category: Grant-in-Aid for Young Scientists (A)
• Allocation Type: Partial Multi-year Fund
• Research Field: Theory of informatics
• Research Institution: Kyushu University (2017); The University of Tokyo (2014-2016)
• Principal Investigator: Kawamura Akitoshi 九州大学, システム情報科学研究院, 准教授 (20600117)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥8,320,000 (Direct Cost: ¥6,400,000、Indirect Cost: ¥1,920,000); Fiscal Year 2017: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000); Fiscal Year 2016: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000); Fiscal Year 2015: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2014: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
• Keywords: 計算量 / 計算可能性 / 実数計算 / 実効的解析学 / 精度保証 / 微分方程式 / 計算量理論 / アナログ計算 / 数値計算 / 函数解析 / ワイラオホ次数 / 力学系 / 計算可能解析 / アルゴリズム / 応用数理 / 実数表現

Outline of Final Research Achievements

Polynomial-time computability and other fundamental notions of computational complexity play a central role in discrete algorithm design and analysis. In this project we explored (further) extensions of such notions to problems involving continuous data. Some of the concepts and techniques that had been known to work at the level of computability were successfully refined to give practically meaningful analysis of time- and space-bounded computation.

Research Products

• [Int'l Joint Research] ダルムシュタット工科大学(ドイツ)
• [Int'l Joint Research] 仏国立情報学自動制御研究所（INRIA）(フランス)
• [Int'l Joint Research] 韓国科学技術院（KAIST）(韓国)
• [Int'l Joint Research] ダルムシュタット工科大学（TU Darmstadt）/トリール大学（Universität Trier）(ドイツ)
• [Int'l Joint Research] 韓国科学技術院（KAIST）(韓国)
• [Journal Article] Polynomial running times for polynomial-time oracle machines (2017)
  • Author(s): A. Kawamura and F. Steinberg
  • Journal Title: In Proc. Second International Conference on Formal Structures for Computation and Deduction (FSCD), Leibniz International Proceedings in Informatics Volume: 84 Pages: 23-23
  • DOI: 10.4230/LIPIcs.FSCD.2017.23
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] On the computational complexity of the Dirichlet Problem for Poisson's Equation (2016)
  • Author(s): KAWAMURA AKITOSHI、STEINBERG FLORIAN、ZIEGLER MARTIN
  • Journal Title: Mathematical Structures in Computer Science Volume: 27 Issue: 8 Pages: 1437-1465
  • DOI: 10.1017/s096012951600013x
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Complexity theory of (functions on) compact metric spaces (2016)
  • Author(s): A. Kawamura, F. Steinberg and M. Ziegler
  • Journal Title: Proc. 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Volume: - Pages: 837-846
  • DOI: 10.1145/2933575.2935311
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Towards computational complexity theory on advanced function spaces in analysis (2016)
  • Author(s): A. Kawamura, F. Steinberg and M. Ziegler
  • Journal Title: Proc. Computability in Europe (CiE), Lecture Notes in Computer Science Volume: 9709 Pages: 142-152
  • DOI: 10.1007/978-3-319-40189-8_15
  • ISBN: 9783319401881, 9783319401898
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Computational benefit of smoothness: Parameterized bit-complexity of numerical operators on analytic functions and Gevrey's hierarchy (2015)
  • Author(s): A. Kawamura, N. Müller, C. Rösnick and M. Ziegler
  • Journal Title: Journal of Complexity Volume: 31(5) Issue: 5 Pages: 689-714
  • DOI: 10.1016/j.jco.2015.05.001
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Small complexity classes for operators in analysis (2014)
  • Author(s): A. Kawamura and H. Ota
  • Journal Title: Mathematical Foundations of Computer Science 2014, Lecture Notes in Computer Science Volume: 8635 Pages: 432-444
  • DOI: 10.1007/978-3-662-44465-8_37
  • ISBN: 9783662444641, 9783662444658
  • Peer Reviewed / Open Access
• [Presentation] Applying ideas in discrete complexity theory to the continuous world (2018)
  • Author(s): A. Kawamura
  • Organizer: Second Workshop on Mathematical Logic and its Application
  • Int'l Joint Research / Invited
• [Presentation] 解析学における計算量 (2017)
  • Author(s): 河村彰星
  • Organizer: 日本数学会年会特別講演
  • Place of Presentation: 首都大学東京（東京都八王子市）
  • Year and Date: 2017-03-25
  • Invited
• [Presentation] Average Case Complexity for the N-body problem (2017)
  • Author(s): A. Kawamura, H. Thies and M. Ziegler
  • Organizer: Computability in Europe (CiE) 2017
  • Int'l Joint Research
• [Presentation] アナログ計算機と計算可能性 (2017)
  • Author(s): 河村彰星
  • Organizer: 第19回全脳アーキテクチャ勉強会
  • Invited
• [Presentation] 実数計算の理論と実践――連続世界の計算限界 (2016)
  • Author(s): 河村彰星
  • Organizer: オペレーションズリサーチ学会数理計画（RAMP）シンポジウム
  • Place of Presentation: 新潟大学（新潟県新潟市）
  • Year and Date: 2016-10-14
  • Invited
• [Presentation] Data-types for multidimensional functions in reliable numerics―Implementations inspired by Real Complexity Theory (2016)
  • Author(s): A. Kawamura, F. Steinberg and H. Thies
  • Organizer: 19th Japan-Korea Joint Workshop on Algorithms and Computation (WAAC)
  • Place of Presentation: 函館市民会館（北海道函館市）
  • Year and Date: 2016-08-31
  • Int'l Joint Research / Invited
• [Presentation] Reducibility in polynomial-time computable analysis (2015)
  • Author(s): A. Kawamura
  • Organizer: Dagstuhl Seminar, Joint Session of 15391 "Algorithms and Complexity for Continuous Problems" and 15392 "Measuring the Complexity of Computational Content: Weihrauch Reducibility and Reverse Analysis"
  • Place of Presentation: Wadern, Germany
  • Year and Date: 2015-09-24
  • Int'l Joint Research
• [Presentation] Towards computational complexity theory on advanced function spaces in analysis (2015)
  • Author(s): A. Kawamura, F. Steinberg and M. Ziegler
  • Organizer: Continuity, Computability, Constructivity―From Logic to Algorithms (CCC)
  • Place of Presentation: Kochel am See, Germany
  • Year and Date: 2015-09-17
  • Int'l Joint Research
• [Presentation] Invitation to real complexity theory: Algorithmic foundations to reliable numerics with bit-costs (2015)
  • Author(s): A. Kawamura and M. Ziegler
  • Organizer: 18th Korea-Japan Joint Workshop on Algorithms and Computation (WAAC)
  • Place of Presentation: Incheon, Korea
  • Year and Date: 2015-08-21
  • Int'l Joint Research
• [Presentation] On the image and length of polynomial-time computable curves (2015)
  • Author(s): T. Katayama and A. Kawamura
  • Organizer: Twelfth International Conference on Computability and Complexity in Analysis (CCA)
  • Place of Presentation: 明治大学駿河台キャンパス（東京都千代田区）
  • Year and Date: 2015-07-14
  • Int'l Joint Research
• [Presentation] Computational complexity of real functions (2015)
  • Author(s): A. Kawamura
  • Organizer: German-Japanese Workshop on Theory and Practice of Real Computation
  • Place of Presentation: 明治大学駿河台キャンパス（東京都千代田区）
  • Year and Date: 2015-07-12
  • Int'l Joint Research
• [Presentation] Weihrauch reducibility in polynomial-time computable analysis (2015)
  • Author(s): A. Kawamura
  • Organizer: Sixteenth International Workshop on Logic and Computational Complexity (LCC)
  • Place of Presentation: 京都大学吉田キャンパス（京都府京都市左京区）
  • Year and Date: 2015-07-04
  • Int'l Joint Research / Invited
• [Presentation] Computational complexity theory for classes of integrable functions (2015)
  • Author(s): A. Kawamura, F Steinberg and M. Ziegler
  • Organizer: Constructivism and Computability
  • Place of Presentation: 石川県金沢市
  • Year and Date: 2015-03-03
• [Presentation] 連続世界の計算量 (2015)
  • Author(s): 河村彰星
  • Organizer: 情報処理学会第百五十一回アルゴリズム研究会・人工知能学会第九十六回人工知能基本問題研究会
  • Place of Presentation: 愛知県名古屋市昭和区
  • Year and Date: 2015-01-14
  • Invited
• [Presentation] 解析函数の完全精度演算の計算量と実装について (2014)
  • Author(s): 河村彰星
  • Organizer: 平成26年度RIMS研究集会「証明論・計算論とその周辺」
  • Place of Presentation: 京都府京都市左京区
  • Year and Date: 2014-12-25
• [Presentation] Analytic functions in iRRAM (2014)
  • Author(s): A. Kawamura, F. Steinberg and H. Thies
  • Organizer: Eleventh International Conference on Computability and Complexity in Analysis (CCA)
  • Place of Presentation: Darmstadt, Germany
  • Year and Date: 2014-07-23
• [Remarks] 連続系計算量理論の深化と展開
  • URL: http://www.i.kyushu-u.ac.jp/~kawamura/26700001/
• [Remarks] 連続計算量理論の深化と展開
  • URL: http://www.graco.c.u-tokyo.ac.jp/~kawamura/26700001/
• [Remarks] 連続系計算量理論の深化と展開
  • URL: http://www.graco.c.u-tokyo.ac.jp/~kawamura/26700001/
• [Funded Workshop] Twelfth International Conference on Computability and Complexity in Analysis (2015)
  • Place of Presentation: 明治大学駿河台キャンパス（東京都千代田区）
  • Year and Date: 2015-07-13
• [Funded Workshop] German-Japanese Workshop on Theory and Practice of Real Computation (2015)
  • Place of Presentation: 明治大学駿河台キャンパス（東京都千代田区）
  • Year and Date: 2015-07-12