Computational complexity of continuous systems

• Project/Area Number: 18H03203
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Basic Section 60010:Theory of informatics-related
• Research Institution: Kyoto University (2019-2023); Kyushu University (2018)
• Principal Investigator: Kawamura Akitoshi 京都大学, 数理解析研究所, 准教授 (20600117)
• Co-Investigator(Kenkyū-buntansha): 立木 秀樹 京都大学, 人間・環境学研究科, 教授 (10211377)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Project Status: Completed (Fiscal Year 2023)
• Budget Amount: ¥17,030,000 (Direct Cost: ¥13,100,000、Indirect Cost: ¥3,930,000); Fiscal Year 2022: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2021: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2020: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2019: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2018: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
• Keywords: 計算可能解析 / 計算量 / 線形時間 / パラメタ計算量 / プログラム抽出 / 計算可能性 / 実数表現 / 連分数 / ホロノミック列 / 到達可能性 / フラクタル / 形式証明 / 実数計算 / プログラム理論 / 複素解析 / 厳密計算 / 精度保証 / 計算複雑度 / ランダム性 / 情報量規準 / コルモゴロフ量 / 平均計算量 / 厳密数値計算 / 微分方程式 / 複雑度 / 数値計算

Outline of Final Research Achievements

We studied several issues in formulating and applying notions and techniques in discrete computation theory to continuous systems. These include fixed parameter tractability, average-case feasibility, almost linear-time computability, program verification and extraction.

Academic Significance and Societal Importance of the Research Achievements

計算アルゴリズムの記述や計算困難さの解析のための基礎理論は、記号の機械的な処理を基礎に置く計算モデルに基づいて組み立てられており、離散的な問題の分析では広く役立っている。一方、現実世界の多くの問題は、実数などのように近似によってのみ捉えられる連続量を本質的に含む。本課題は、連続系を扱うアルゴリズムにも計算理論を数学的に自然な形で拡張し、計算の実現や困難さの理解に役立てるための研究である。

Research Products

• [Int'l Joint Research] アストン大学(英国)
• [Int'l Joint Research] リュブリャナ大学(スロベニア)
• [Int'l Joint Research] 国立情報学自動制御研究所 （INRIA）(フランス)
• [Int'l Joint Research] 国立情報学自動制禦研究所（INRIA）/リヨン高等師範学校（ENS Lyon）(フランス)
• [Int'l Joint Research] 韓国科学技術院（KAIST）(韓国)
• [Journal Article] Elementarily Traceable Irrational Numbers (2023)
  • Author(s): Hiroshima Keita、Kawamura Akitoshi
  • Journal Title: Lecture Notes in Computer Science Volume: 13967 Pages: 135-140
  • DOI: 10.1007/978-3-031-36978-0_11
  • ISBN: 9783031369773, 9783031369780
  • Peer Reviewed
• [Journal Article] Certified Computation of Nondeterministic Limits (2022)
  • Author(s): Konecny Michal、Park Sewon、Thies Holger
  • Journal Title: Lecture Notes in Computer Science book series (LNCS) Volume: 13260 Pages: 771-789
  • DOI: 10.1007/978-3-031-06773-0_41
  • ISBN: 9783031067723, 9783031067730
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Second-Order Linear-Time Computability with Applications to Computable Analysis (2019)
  • Author(s): Kawamura Akitoshi、Steinberg Florian、Thies Holger
  • Journal Title: Proc. of the 15th Annual Conference on Theory and Applications of Models of Computation (TAMC 2019), April 13-16, 2019, Kitakyushu, Japan Volume: 11436 Pages: 337-358
  • DOI: 10.1007/978-3-030-14812-6_21
  • ISBN: 9783030148119, 9783030148126
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Parameterized complexity for uniform operators on multidimensional analytic functions and ODE solving (2018)
  • Author(s): A. Kawamura, F. Steinberg and H. Thies
  • Journal Title: Proc. 25th Workshop on Logic, Language, Information and Computation (WoLLIC), Lecture Notes in Computer Science (LNCS) Volume: 10944 Pages: 223-236
  • DOI: 10.1007/978-3-662-57669-4_13
  • ISBN: 9783662576687, 9783662576694
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Average-case polynomial-time computability of Hamiltonian dynamics (2018)
  • Author(s): A. Kawamura, H. Thies and M. Ziegler
  • Journal Title: Proc. 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS), Leibniz International Proceedings in Informatics (LIPIcs) Volume: 117 Pages: 30-30
  • DOI: 10.4230/LIPICS.MFCS.2018.30
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Presentation] 初等的に追跡される数 (2024)
  • Author(s): 河村彰星，廣島佳汰
  • Organizer: 日本数学会年会
• [Presentation] 初等的に追跡される無理数 (2024)
  • Author(s): 廣島佳汰
  • Organizer: 第9回山陰数学と基礎論研究集会
• [Presentation] Computational complexity of differential equations (2023)
  • Author(s): A. Kawamura
  • Organizer: 17th Asian Logic Conference (ALC)
  • Int'l Joint Research / Invited
• [Presentation] Subrecursive translations between irrational number representations (2023)
  • Author(s): A. Kawamura
  • Organizer: Fifth Workshop on Digitalization and Computable Models (WDCM)
  • Int'l Joint Research / Invited
• [Presentation] A number that has an elementary contractor and no elementary sum approximation (2023)
  • Author(s): K. Hiroshima
  • Organizer: Continuity, Computability, Constructivity (CCC)
  • Int'l Joint Research
• [Presentation] The ultimate signs of second-order holonomic sequences (2023)
  • Author(s): F. Hagihara and A. Kawamura
  • Organizer: 23rd Japan-Korea Joint Workshop on Algorithms and Computation
  • Int'l Joint Research
• [Presentation] 初等的に追跡される無理数 (2023)
  • Author(s): 廣島佳汰，河村彰星
  • Organizer: 情報処理学会第192回アルゴリズム研究会
• [Presentation] 2階ホロノミック列の極限符号 (2023)
  • Author(s): 萩原普賢
  • Organizer: 群・環・言語と計算機科学の周辺領域
  • Int'l Joint Research
• [Presentation] 2階ホロノミック列の極限符号 (2023)
  • Author(s): 河村彰星，萩原普賢
  • Organizer: 冬のLAシンポジウム
• [Presentation] Induction and coindution for computing exact overlaps of fractals (2022)
  • Author(s): H. Tsuiki
  • Organizer: Continuity, Computability, Constructivity (CCC)
  • Int'l Joint Research
• [Presentation] Some steps toward program extraction in a type-theoretical interpretation of IFP (2022)
  • Author(s): U. Berger, S. Park, H. Thies and H. Tsuiki
  • Organizer: Continuity, Computability, Constructivity (CCC)
  • Int'l Joint Research
• [Presentation] Induction / coinduction and projections of fractals (2022)
  • Author(s): H. Tsuiki
  • Organizer: Proof and Computation
  • Int'l Joint Research
• [Presentation] Polynomial-time equivalent representations of compact sets in Euclidean spaces (2022)
  • Author(s): A. Kawamura
  • Organizer: Continuity, Computability, Constructivity (CCC)
  • Int'l Joint Research
• [Presentation] A number that has an elementary trace function and no elementary sum approximation (2022)
  • Author(s): K. Hiroshima
  • Organizer: Continuity, Computability, Constructivity (CCC)
  • Int'l Joint Research
• [Presentation] 実函数の計算理論 (2022)
  • Author(s): 河村彰星
  • Organizer: 組合せ最適化セミナー
  • Invited
• [Presentation] Verified computation over real numbers and other continuous objects (2022)
  • Author(s): S. Park
  • Organizer: Second Japan-Russia Workshop on Effective Descriptive Set Theory, Computable Analysis and Automata
  • Int'l Joint Research / Invited
• [Presentation] Analog characterization of complexity classes (2022)
  • Author(s): R. Gozzi
  • Organizer: Second Japan-Russia Workshop on Effective Descriptive Set Theory, Computable Analysis and Automata
  • Int'l Joint Research
• [Presentation] Average-case polynomial-time computability of Hamiltonian dynamics (2021)
  • Author(s): A. Kawamura
  • Organizer: First Japan-Russia Workshop on Effective Descriptive Set Theory, Computable Analysis and Automata
  • Int'l Joint Research
• [Presentation] 時間限定の下での中間次数について (2020)
  • Author(s): 河村彰星
  • Organizer: 第7回山陰基礎論・解析学研究集会
• [Presentation] グレー符号と乱択近似可能実数 (2019)
  • Author(s): 河村，レシーヌ
  • Organizer: 情報処理学会第172回アルゴリズム研究会
• [Presentation] On randomized polynomial-time approximability of real numbers and sets (2019)
  • Author(s): A. Kawamura and U. Lechine
  • Organizer: Third Workshop on Mathematical Logic and its Applications (MLA)
  • Int'l Joint Research
• [Presentation] Gray code representation and polynomial-time approximability (2019)
  • Author(s): A. Kawamura
  • Organizer: Computability Theory and Foundations of Mathematics (CTFM) 2019
  • Int'l Joint Research / Invited
• [Presentation] Applications of average-case complexity to problems in analysis (2018)
  • Author(s): A. Kawamura, H. Thies and M. Ziegler
  • Organizer: 夏のエルエーシンポジウム
• [Presentation] Average-case polynomial-time computability of the three-body problem (2018)
  • Author(s): A. Kawamura
  • Organizer: Dagstuhl Seminar 18361: Measuring the Complexity of Computational Content: From Combinatorial Problems to Analysis
  • Int'l Joint Research
• [Presentation] Computable analysis and computability in linear time (2018)
  • Author(s): A. Kawamura, F. Steinberg and H. Thies
  • Organizer: Computability Theory and Foundations of Mathematics (CTFM) 2018
  • Int'l Joint Research
• [Presentation] On proving parameterized polynomial time computability of compositions of fundamental functions (2018)
  • Author(s): H. Hamamoto, A. Kawamura and M. Ziegler
  • Organizer: Computability Theory and Foundations of Mathematics (CTFM) 2018
  • Int'l Joint Research
• [Presentation] Applying ideas in discrete complexity theory to the continuous world (2018)
  • Author(s): A. Kawamura
  • Organizer: Continuity, Computability, Constructivity (CCC) 2018
  • Int'l Joint Research / Invited
• [Presentation] A class for second-order linear-time computability (2018)
  • Author(s): A. Kawamura, F. Steinberg and H. Thies
  • Organizer: Continuity, Computability, Constructivity (CCC) 2018
  • Int'l Joint Research
• [Presentation] グレー符号と乱択近似可能数 (2018)
  • Author(s): 河村
  • Organizer: 数学基礎論若手の会
• [Remarks] 連続系の複雑さを解明する計算理論
  • URL: https://www.kurims.kyoto-u.ac.jp/~kawamura/18H03203/
• [Remarks] 連続系の複雑さを解明する計算理論
  • URL: http://www.fc.inf.kyushu-u.ac.jp/~kawamura/18H03203/
• [Funded Workshop] Workshop on Computability Theory and Foundations of Mathematics (CTFM) 2018 (2018)