一意標準形文法をもつ文脈自由言語族およびその学習に関する研究

• Project/Area Number: 18K11150
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 60010:Theory of informatics-related
• Research Institution: Tohoku University
• Principal Investigator: 吉仲 亮 東北大学, 情報科学研究科, 准教授 (80466424)
• Project Period (FY): 2018-04-01 – 2025-03-31
• Project Status: Granted (Fiscal Year 2023)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 文法推論 / 計算論的学習理論 / 有限状態オートマトン / 文脈自由文法 / 無限アルファベット / オートマトン / 文脈自由言語 / 分布学習 / 正則言語

Outline of Annual Research Achievements

本研究課題は，近年の文脈自由言語に対する分布学習アプローチを発展させ，分布学習可能でありかつ一意標準形を持つ文脈自由言語族を探究することを目的としている．従来の形式言語学習では，アルファベットサイズが有限であるものを想定した研究が中心であったのに対して，本研究課題では，2023年度は，無限アルファベット上の正則言語学習と文脈自由言語学習について考察を深め，成果を上げた．正則言語学習にあっては，質問による古典的な厳密学習を発展させ，質問に対する回答が完全に文字列を２値分類しない場合の学習に関する研究がいくつか知られていた．本研究課題では無限アルファベット上の正則言語学習においてどのような困難があるか考察し，ひとつの解決を与えた．本結果は査読付き国際会議SPIRE2024にて発表された．
また，2022年度は無限アルファベット上の文脈自由言語の正例からの極限同定について考察したが，これを発展させ，質問学習の舞台へと移すべく研究を進めた．形式言語学習のアプローチはいくつかあるが，その中で，分布学習アプローチが無限アルファベット上の形式言語の学習と親和性が高いことがわかってきた．この知見に基づき，合同性文脈自由言語と呼ばれるひとつの文脈自由言語の部分族についての質問学習アルゴリズムのプロトタイプを作成した．詳細を完成させ，さらに関連の言語族の学習に関しても考察し，これらを国際的な発表とする予定である．

Current Status of Research Progress

3: Progress in research has been slightly delayed.

Reason

本研究課題では文脈自由文法の非自明な部分族の標準形の合理的な定義を模索している．多様な学習可能性に関する結果が得られている点は十分な進捗といえるが，標準形に関して現在までのところ得られている成果は，文法サイズが指数的に大きくなるという意味で，否定的な結果にとどまっている．

Strategy for Future Research Activity

これまでに可代入文脈自由言語の単純な拡張であるk,l-可代入文脈自由言語族に対する文法の標準形が難しいという知見を得たが，文字列文法ではなく木文法等における可代入文脈自由言語について研究をすすめる．また，特にこれまでの研究期間で特に着目していた finite context property (FCP) は学習を可能にする制約ではあったが一意標準形を与えるにはまだ弱すぎるため，一意標準形を持つような制約について考案する．

Research Products

• [Journal Article] Query Learning of Minimal Deterministic Symbolic Finite Automata Separating Regular Languages (2024)
  • Author(s): Yoshito Kawasaki, Diptarama Hendrian, Ryo Yoshinaka, Ayumi Shinohara
  • Journal Title: Lecture Notes in Computer Science Volume: 14519 Pages: 340-354
  • DOI: 10.1007/978-3-031-52113-3_24
  • ISBN: 9783031521126, 9783031521133
  • Peer Reviewed
• [Journal Article] Efficient Parameterized Pattern Matching in Sublinear Space (2023)
  • Author(s): Haruki Ideguchi, Diptarama Hendrian, Ryo Yoshinaka, Ayumi Shinohara
  • Journal Title: Lecture Notes in Computer Science Volume: 14240 Pages: 271-283
  • DOI: 10.1007/978-3-031-43980-3_22
  • ISBN: 9783031439797, 9783031439803
  • Peer Reviewed
• [Journal Article] Identification of Substitutable Context-Free Languages over Infinite Alphabets from Positive Data (2023)
  • Author(s): Yutaro Numaya, Diptarama Hendrian, Ryo Yoshinaka, Ayumi Shinohara
  • Journal Title: Proceedings of Machine Learning Research Volume: 217 Pages: 22-34
  • Peer Reviewed / Open Access
• [Journal Article] Extending Distributional Learning from Positive Data and Membership Queries (2023)
  • Author(s): Makoto Kanazawa, Ryo Yoshinaka
  • Journal Title: Proceedings of Machine Learning Research Volume: 217 Pages: 8-22
  • Peer Reviewed / Open Access
• [Journal Article] Sorting balls and water: Equivalence and computational complexity (2023)
  • Author(s): Takehiro Ito, Jun Kawahara, Shin-ichi Minato, Yota Otachi, Toshiki Saitoh, Akira Suzuki, Ryuhei Uehara, Takeaki Uno, Katsuhisa Yamanaka, Ryo Yoshinaka
  • Journal Title: Theoretical Computer Science Volume: 927 Pages: 114158-114158
  • DOI: 10.1016/j.tcs.2023.114158
  • Peer Reviewed / Open Access
• [Journal Article] Parameterized DAWGs: Efficient constructions and bidirectional pattern searches (2022)
  • Author(s): Katsuhito Nakashima, Noriki Fujisato, Diptarama Hendrian, Yuto Nakashima, Ryo Yoshinaka, Shunsuke Inenaga, Hideo Bannai, Ayumi Shinohara, Masayuki Takeda
  • Journal Title: Theoretical Computer Science Volume: 933 Pages: 21-42
  • DOI: 10.1016/j.tcs.2022.09.008
  • Peer Reviewed
• [Journal Article] Distributional learning of conjunctive grammars and contextual binary feature grammars (2019)
  • Author(s): Ryo Yoshinaka
  • Journal Title: Journal of Computer and System Sciences Volume: 104 Pages: 359-374
  • DOI: 10.1016/j.jcss.2017.07.004
  • Peer Reviewed
• [Journal Article] Query Learning Algorithm for Residual Symbolic Finite Automata (2019)
  • Author(s): Kaizaburo Chubachi, Diptarama Hendrian, Ryo Yoshinaka, Ayumi Shinohara
  • Journal Title: Electronic Proceedings in Theoretical Computer Science Volume: 305 Pages: 140-153
  • DOI: 10.4204/eptcs.305.10
  • Peer Reviewed / Open Access
• [Presentation] Parallel Algorithm for Pattern Matching Problems Under Substring Consistent Equivalence Relations (2022)
  • Author(s): Davaajav Jargalsaikhan, Diptarama Hendrian, Ryo Yoshinaka, Ayumi Shinohara
  • Organizer: 33rd Annual Symposium on Combinatorial Pattern Matching
  • Int'l Joint Research
• [Presentation] Sorting Balls and Water: Equivalence and Computational Complexity (2022)
  • Author(s): Takehiro Ito, Jun Kawahara, Shin-ichi Minato, Yota Otachi, Toshiki Saitoh, Akira Suzuki, Ryuhei Uehara, Takeaki Uno, Katsuhisa Yamanaka, Ryo Yoshinaka
  • Organizer: 11th International Conference on Fun with Algorithms
  • Int'l Joint Research
• [Presentation] Computing the Parameterized Burrows-Wheeler Transform Online (2022)
  • Author(s): Daiki Hashimoto, Diptarama Hendrian, Dominik Koeppl, Ryo Yoshinaka, Ayumi Shinohara
  • Organizer: String Processing and Information Retrieval - 29th International Symposium
  • Int'l Joint Research
• [Presentation] A Hierarchy of Context-Free Languages Learnable from Positive Data and Membership Queries (2021)
  • Author(s): Makoto Kanazawa, Ryo Yoshinaka
  • Organizer: The 15th International Conference on Grammatical Inference
  • Int'l Joint Research
• [Presentation] Inside-Outside Algorithm for Macro Grammars (2021)
  • Author(s): Ryuta Kambe, Naoki Kobayashi, Ryosuke Sato, Ayumi Shinohara, Ryo Yoshinaka
  • Organizer: The 15th International Conference on Grammatical Inference
  • Int'l Joint Research
• [Presentation] Query Learning Algorithm for Symbolic Weighted Finite Automata (2021)
  • Author(s): Kaito Suzuki, Diptarama Hendrian, Ryo Yoshinaka, Ayumi Shinohara
  • Organizer: The 15th International Conference on Grammatical Inference
  • Int'l Joint Research
• [Presentation] Query Learning of Symbolic Weighted Finite Automata (2021)
  • Author(s): Kaito Suzuki, Diptarama Hendrian, Ryo Yoshinaka, Ayumi Shinohara
  • Organizer: The 14th Annual Meeting of the Asian Association for Algorithms and Computation
  • Int'l Joint Research
• [Presentation] Efficient Construction of Cryptarithm Catalogues over Deterministic Finite Automata (2021)
  • Author(s): Koya Watanabe, Diptarama Hendrian, Ryo Yoshinaka, Takashi Horiyama and Ayumi Shinohara
  • Organizer: The 14th Annual Meeting of the Asian Association for Algorithms and Computation
  • Int'l Joint Research
• [Presentation] Grammar Compression with Probabilistic Context-Free Grammar (2020)
  • Author(s): Hiroaki Naganuma, Diptarama Hendrian, Ryo Yoshinaka, Ayumi Shinohara, Naoki Kobayashi
  • Organizer: Data Compression Conference 2020
  • Int'l Joint Research
• [Presentation] Query Learning Algorithm for Residual Symbolic Finite Automata (2019)
  • Author(s): Kaizaburo Chubachi, Diptarama Hendrian, Ryo Yoshinaka, Ayumi Shinohara
  • Organizer: Tenth International Symposium on Games, Automata, Logics, and Formal Verification
  • Int'l Joint Research
• [Presentation] Linear-Time Online Algorithm Inferring the Shortest Path from a Walk (2018)
  • Author(s): Shintaro Narisada, Diptarama Hendrian, Ryo Yoshinaka, Ayumi Shinohara
  • Organizer: SPIRE 2018
  • Int'l Joint Research