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Automated Generation of No Logical Gap Readable Proof for Information Theory

Research Project

Project/Area Number 16K12391
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Theory of informatics
Research InstitutionChiba University

Principal Investigator

Hagiwara Manabu  千葉大学, 大学院理学研究院, 准教授 (80415728)

Co-Investigator(Kenkyū-buntansha) 葛岡 成晃  和歌山大学, システム工学部, 准教授 (60452538)
Research Collaborator Garrigue Jacques  
Nakano Kyosuke  
Kong Justin  
Project Period (FY) 2016-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords情報理論 / 形式化 / Coq / Coqtop / Proviola / Python / 定理証明 / 情報源符号化 / シャノン理論 / SSReflect / 自動翻訳
Outline of Final Research Achievements

As an application of the library InfoTheo on Coq / MathComp for information theory, we challenged the implementation of software that converts .v files of the library into human readable natural language. The approach is based on customization of the software Proviolla and creating completely original source code on Python, and replacing MathComp tactics and Coq commands with human readable natural language.

Academic Significance and Societal Importance of the Research Achievements

情報理論の著名な諸定理を論理的な隙間なしに解説する文書が作成されることは、情報理論の基礎理論を頑健たるものにするだけでなく、初学者が誤解なく自主学習できる文献を提供できる。論理的に隙間のない証明として、計算機向けに形式化された証明が存在する。しかしこれは、人間にとってのReadabilityが欠如している。
本研究の目標が達成されれば、隙間なくReadabilityのある証明が得られることになる。

Report

(4 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (24 results)

All 2018 2017 2016

All Journal Article (16 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 14 results,  Acknowledgement Compliant: 4 results) Presentation (6 results) (of which Int'l Joint Research: 2 results,  Invited: 1 results) Book (2 results)

  • [Journal Article] Formalization of Insertion/Deletion Codes and the Levenshtein Metric in Lean2018

    • Author(s)
      Justin Kong, David Webb, Manabu Hagiwara
    • Journal Title

      Proceeding of ISITA 2018

      Volume: 1 Pages: 1-6

    • DOI

      10.23919/isita.2018.8664354

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] An application of universal FV codes to source coding allowing errors2017

    • Author(s)
      Shigeaki Kuzuoka
    • Journal Title

      IEICE Technical Report

      Volume: 2017-5 Pages: 25-30

    • Related Report
      2017 Research-status Report
  • [Journal Article] Network, Permutation, Formalization towards Post Modern Coding Theory, Vol. 4: Formalization on Coding Theory2016

    • Author(s)
      萩原学
    • Journal Title

      Bulletin of the Japan Society for Industrial and Applied Mathematics

      Volume: 26 Issue: 4 Pages: 28-33

    • DOI

      10.11540/bjsiam.26.4_28

    • NAID

      130007042676

    • ISSN
      2432-1982
    • Year and Date
      2016-12-22
    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Network, Permutation, Formalization towards Post Modern Coding Theory, Vol. 3: Permutation Codes2016

    • Author(s)
      萩原学
    • Journal Title

      Bulletin of the Japan Society for Industrial and Applied Mathematics

      Volume: 26 Issue: 3 Pages: 29-34

    • DOI

      10.11540/bjsiam.26.3_29

    • NAID

      130007043100

    • ISSN
      2432-1982
    • Year and Date
      2016-09-26
    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Network, Permutation, Formalization towards Post Modern Coding Theory, Vol. 2: Network Coding2016

    • Author(s)
      萩原学
    • Journal Title

      Bulletin of the Japan Society for Industrial and Applied Mathematics

      Volume: 26 Issue: 2 Pages: 27-32

    • DOI

      10.11540/bjsiam.26.2_27

    • NAID

      130005267460

    • ISSN
      2432-1982
    • Year and Date
      2016-06-24
    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Consolidation for compact constraints and Kendall tau LP decodable permutation codes2016

    • Author(s)
      Manabu Hagiwara and Justin Kong
    • Journal Title

      Designs, Codes and Cryptography

      Volume: 1 Issue: 3 Pages: 1-39

    • DOI

      10.1007/s10623-016-0313-5

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Formalization of Bing's shrinking method in geometric topology2016

    • Author(s)
      Ken'ichi Kuga, Manabu Hagiwara, Mitsuharu Yamamoto
    • Journal Title

      Lecture Notes in Artificial Intelligence

      Volume: 9791 Pages: 18-21

    • DOI

      10.1007/978-3-319-42547-4_2

    • ISBN
      9783319425467, 9783319425474
    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A Deep Neural Network Architecture Using Dimensionality Reduction with Sparse Matrices2016

    • Author(s)
      W. Matsumoto, Manabu Hagiwara, P. T. Boufounos, K. Fukushima, T. Mariyama, Z. Xiongxin
    • Journal Title

      Neural Information Processing

      Volume: LNCS 9950 Pages: 397-404

    • DOI

      10.1007/978-3-319-46681-1_48

    • ISBN
      9783319466804, 9783319466811
    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] 誤り訂正符号の例と将来展望2016

    • Author(s)
      萩原学
    • Journal Title

      映像情報メディア学会誌

      Volume: 70 (7) Pages: 567-570

    • Related Report
      2016 Research-status Report
  • [Journal Article] On ordered syndromes for multi insertion/deletion error-correcting codes2016

    • Author(s)
      Manabu Hagiwara
    • Journal Title

      2016 IEEE International Symposium on Information Theory (ISIT)

      Volume: 1 Pages: 625-629

    • DOI

      10.1109/isit.2016.7541374

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Nonexistence of Perfect Permutation Codes in the Ulam Metric2016

    • Author(s)
      Justin Kong and Manabu Hagiwara
    • Journal Title

      Proceeding of ISITA 2016

      Volume: 1 Pages: 727-731

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Formalization of Coding Theory using Lean2016

    • Author(s)
      Manabu Hagiwara, Kyosuke Nakano and Justin Kong
    • Journal Title

      Proceeding of ISITA 2016

      Volume: 1 Pages: 527-531

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Formalization of Binary Symmetric Erasure Channel Based on Infotheo2016

    • Author(s)
      Kyosuke Nakano and Manabu Hagiwara
    • Journal Title

      Proceeding of ISITA 2016

      Volume: 1 Pages: 512-516

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Variable-length coding for mixed sources with side information allowing decoding errors2016

    • Author(s)
      Shigeaki Kuzuoka
    • Journal Title

      Proceeding of ISITA 2016

      Volume: 1 Pages: 161-165

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] On distributed computing for functions with certain structures2016

    • Author(s)
      Shigeaki Kuzuoka and Shun Watanabe
    • Journal Title

      Proceeding of ITW

      Volume: 1 Pages: 6-10

    • DOI

      10.1109/itw.2016.7606785

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the smooth Renyi entropy and variable-length source coding allowing errors2016

    • Author(s)
      Shigeaki Kuzuoka
    • Journal Title

      Proceeding of ISIT

      Volume: 1 Pages: 745-749

    • DOI

      10.1109/isit.2016.7541398

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Presentation] On universal FV coding allowing non-vanishing error probability2017

    • Author(s)
      Shigeaki Kuzuoka
    • Organizer
      the 10th Asia-Europe Workshop on Information Theory (AEW10)
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] C型ルート系に付随する挿入削除誤り訂正符号2016

    • Author(s)
      萩原学
    • Organizer
      情報理論とその応用シンポジウム 2016
    • Place of Presentation
      高山グリーンホテル(岐阜県)
    • Year and Date
      2016-12-13
    • Related Report
      2016 Research-status Report
  • [Presentation] Coq/SSReflectによる通信路の同型性の形式化2016

    • Author(s)
      中野恭輔, 萩原学
    • Organizer
      情報理論とその応用シンポジウム 2016
    • Place of Presentation
      高山グリーンホテル(岐阜県)
    • Year and Date
      2016-12-13
    • Related Report
      2016 Research-status Report
  • [Presentation] An application of Iriyama's Lemma for multiterminal source coding systems2016

    • Author(s)
      葛岡成晃
    • Organizer
      第39回情報理論とその応用シンポジウム
    • Place of Presentation
      高山グリーンホテル(岐阜県)
    • Year and Date
      2016-12-13
    • Related Report
      2016 Research-status Report
  • [Presentation] Shifted Young diagrams and binary I/D error-correcting codes2016

    • Author(s)
      Manabu Hagiwara
    • Organizer
      SIAM Conference on Discrete Mathematics
    • Place of Presentation
      米国 ジョージア州
    • Year and Date
      2016-06-06
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] 関数計算のためのデータ圧縮-関数の二分法によるアプローチ-2016

    • Author(s)
      葛岡成晃
    • Organizer
      電子情報通信学会情報理論研究会
    • Place of Presentation
      小樽経済センター(北海道)
    • Year and Date
      2016-05-19
    • Related Report
      2016 Research-status Report
    • Invited
  • [Book] Coq/SSReflect/MathCompによる定理証明2018

    • Author(s)
      萩原 学、アフェルト・レナルド
    • Total Pages
      224
    • Publisher
      森北出版
    • ISBN
      9784627062412
    • Related Report
      2017 Research-status Report
  • [Book] 進化する符号理論2016

    • Author(s)
      萩原学(編者)
    • Total Pages
      206
    • Publisher
      日本評論社
    • Related Report
      2016 Research-status Report

URL: 

Published: 2016-04-21   Modified: 2020-03-30  

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