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Computational complexity of continuous systems

Research Project

Project/Area Number 18H03203
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Review Section Basic Section 60010:Theory of informatics-related
Research InstitutionKyoto University (2019-2022)
Kyushu University (2018)

Principal Investigator

河村 彰星  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 Granted (Fiscal Year 2022)
Budget Amount *help
¥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計算可能性 / 計算量 / 実数計算 / プログラム理論 / 複素解析 / 厳密計算 / 精度保証 / 計算可能解析 / 線形時間 / 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 Annual Research Achievements

令和2年度中にコロナ禍により大きな影響を受けたため、計画の大部分を令和3年度中に実施することとなった。特に、先に中止となった研究員の採用・来日は、繰越後の令和3年度の秋に実現した。博士号取得直後の若手研究者である朴世原氏(研究課題「高階函数の保証つき厳密計算に関する研究」)、リッカルド・ゴッツィ氏(研究課題「複素函数の計算可能解析に関する研究」)を採用し、共同研究を行った。それぞれ一定の成果が得られつつあり、論文としては次年度に発表を目指している。また両研究員が来てからは、京都大学内で定期的に人間・環境学研究科のグループと協力して「計算可能解析セミナー」を開催し、議論を深めている。連続系計算のプログラム言語と形式的検証に関する新たな課題が明らかになったため、令和4年度にはこのグループから分担者を加えて共同研究をする計画である。現時点までの結果の一部は、令和3年度末に遠隔開催された日露ワークショップで発表した。

またこの期間に研究代表者は関連する国際研究活動として、第14回「到達可能性問題国際会議」(RP 2020)プログラム委員、第4回「数理論理学とその応用」研究集会(MLA 2021)プログラム委員、第18回「解析学における計算可能性と計算量に関する国際会議」(CCA 2021)、第33回「カナダ計算幾何会議」(CCCG 2021)のプログラム委員を務めた。

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

前年度に予定していた研究員が来られなくなったこと、および令和2~3年度全体にわたりコロナ禍で往来が制限されたことにより、対面による成果発表や共同研究に関しては大きな影響を受けた。しかし、計画を変更して遠隔共同研究の態勢を整えたり、繰越後の令和3年度には新たな研究員を採用して活発な研究活動ができ、一定の進展を得たとともに今後の見通しも立っている。

Strategy for Future Research Activity

当年度中には大きく制限されていた対面での発表を目指すが、状況に応じて遠隔での発表・討論も活用する。

Report

(3 results)
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • 2018 Annual Research Report

Research Products

(23 results)

All 2022 2021 2020 2019 2018 Other

All Int'l Joint Research (3 results) Journal Article (3 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 3 results,  Open Access: 1 results) Presentation (14 results) (of which Int'l Joint Research: 10 results,  Invited: 3 results) Remarks (2 results) Funded Workshop (1 results)

  • [Int'l Joint Research] 国立情報学自動制御研究所 (INRIA)(フランス)

    • Related Report
      2019 Annual Research Report
  • [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)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] 韓国科学技術院(KAIST)(韓国)

    • Related Report
      2018 Annual Research Report
  • [Journal Article] Second-Order Linear-Time Computability with Applications to Computable Analysis2019

    • Author(s)
      Kawamura Akitoshi、Steinberg Florian、Thies Holger
    • Journal Title

      Proceedings of the 15th Annual Conference on Theory and Applications of Models of Computation (TAMC), Lecture Notes in Computer Science

      Volume: 11436 Pages: 337-358

    • DOI

      10.1007/978-3-030-14812-6_21

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Parameterized complexity for uniform operators on multidimensional analytic functions and ODE solving2018

    • Author(s)
      A. Kawamura, F. Steinberg and H. Thies
    • Journal Title

      Proc. of the 25th International Workshop on Logic, Language, Information, and Computation (WoLLIC 2018), July 24-27, 2018, Bogota, Colombia

      Volume: 10944 Pages: 223-236

    • DOI

      10.1007/978-3-662-57669-4_13

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Average-case polynomial-time computability of Hamiltonian dynamics2018

    • Author(s)
      A. Kawamura, H. Thies and M. Ziegler
    • Journal Title

      Proc. of the 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018), August 27-31, 2018, Liverpool, UK

      Volume: 117 Pages: 30-30

    • DOI

      10.4230/LIPICS.MFCS.2018.30

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Presentation] Verified computation over real numbers and other continuous objects2022

    • Author(s)
      S. Park
    • Organizer
      Second Japan-Russia Workshop on Effective Descriptive Set Theory, Computable Analysis and Automata
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Analog characterization of complexity classes2022

    • Author(s)
      R. Gozzi
    • Organizer
      Second Japan-Russia Workshop on Effective Descriptive Set Theory, Computable Analysis and Automata
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Average-case polynomial-time computability of Hamiltonian dynamics2021

    • Author(s)
      A. Kawamura
    • Organizer
      First Japan-Russia Workshop on Effective Descriptive Set Theory, Computable Analysis and Automata
    • Related Report
      2019 Annual Research Report
    • 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
    • Related Report
      2019 Annual Research Report
  • [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
    • Related Report
      2018 Annual Research Report
  • [Presentation] On randomized polynomial-time approximability of real numbers and sets2019

    • Author(s)
      A. Kawamura and U. Lechine
    • Organizer
      Third Workshop on Mathematical Logic and its Applications (MLA)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Gray code representation and polynomial-time approximability2019

    • Author(s)
      A. Kawamura
    • Organizer
      Computability Theory and Foundations of Mathematics (CTFM) 2019
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Applications of average-case complexity to problems in analysis2018

    • Author(s)
      A. Kawamura, H. Thies and M. Ziegler
    • Organizer
      夏のエルエーシンポジウム
    • Related Report
      2018 Annual Research Report
  • [Presentation] Average-case polynomial-time computability of the three-body problem2018

    • Author(s)
      A. Kawamura
    • Organizer
      Dagstuhl Seminar 18361: Measuring the Complexity of Computational Content: From Combinatorial Problems to Analysis
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Computable analysis and computability in linear time2018

    • Author(s)
      A. Kawamura, F. Steinberg and H. Thies
    • Organizer
      Computability Theory and Foundations of Mathematics (CTFM) 2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] On proving parameterized polynomial time computability of compositions of fundamental functions2018

    • Author(s)
      H. Hamamoto, A. Kawamura and M. Ziegler
    • Organizer
      Computability Theory and Foundations of Mathematics (CTFM) 2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Applying ideas in discrete complexity theory to the continuous world2018

    • Author(s)
      A. Kawamura
    • Organizer
      Continuity, Computability, Constructivity (CCC) 2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A class for second-order linear-time computability2018

    • Author(s)
      A. Kawamura, F. Steinberg and H. Thies
    • Organizer
      Continuity, Computability, Constructivity (CCC) 2018
    • Related Report
      2018 Annual Research Report
    • 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
    • Related Report
      2018 Annual Research Report
  • [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/

    • Related Report
      2020 Annual Research Report 2019 Annual Research Report
  • [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/

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] Workshop on Computability Theory and Foundations of Mathematics (CTFM) 20182018

    • Related Report
      2018 Annual Research Report

URL: 

Published: 2018-04-23   Modified: 2022-12-28  

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