New formal methods based on game semantics and their descriptive hierarchy

• Project/Area Number: 26540001
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Theory of informatics
• Research Institution: Tohoku University
• Principal Investigator: Tanaka Kazuyuki 東北大学, 理学研究科, 教授 (70188291)
• Research Collaborator: NEMOTO Takako ; HORIHATA Yoshihiro ; KASHIMA Ryo
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: ゲーム意味論 / 高次計算論 / ゲーム木 / プッシュダウン・オートマトン / 数理論理学

Outline of Final Research Achievements

In this research, we have invented several new formal methods based on game semantics in order to analyze the complication of multi-dimensional multi-agent systems, which cannot be captured by ordinary computability theory. Among others, we investigated the determinacy strength of infinite games recognized by various pushdown automata, and pinned them down in terms of higher recursion theory. We also got some new results on the query complexity of game trees with random inputs.

Research Products

• [Journal Article] Optimal depth-first algorithms and equilibria of independent distributions on multi-branching trees (2017)
  • Author(s): Weiguang Peng, Ningning Peng, Keng Meng Ng，Kazuyuki Tanaka and Yue Yang,
  • Journal Title: Information Processing Letters Volume: 印刷中
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] The uniqueness of eigen-distribution under nondirectional algorithms (2016)
  • Author(s): W. Peng, S. Okisaka, W. Li and K. Tanaka
  • Journal Title: IAENG International Journal of Computer Science Volume: 43-3 Pages: 318-325
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] The Eigen-distribution for Multi-branching Trees (2016)
  • Author(s): Weiguang Peng, Shohei Okisaka, Wenjuan Li, Kazuyuki Tanaka
  • Journal Title: International MultiConference of Engineers and Computer Scientists Volume: I Pages: 88-93
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Commuting quantum circuits with few outputs are unlikely to be classically simulatable (2016)
  • Author(s): Yasuhiro Takahashi, Seiichiro Tani, Takeshi Yamazaki, Kazuyuki Tanaka
  • Journal Title: Quantum Information and Computation Volume: 16-3&4 Pages: 251-270
  • Peer Reviewed
• [Journal Article] Infinite games recognized by 2-stack visibly pushdown automata (2015)
  • Author(s): Wenjuan Li, Shohei Okisaka, Kazuyuki Tanaka
  • Journal Title: 数理解析研究所講究録 Volume: 1950 Pages: 121-137
• [Journal Article] Commuting quantum circuits with few outputs are unlikely to be classically simulatable (2015)
  • Author(s): Yasuhiro Takahashi, Seiichiro Tani, Takeshi Yamazaki, Kazuyuki Tanaka
  • Journal Title: Lecture Notes in Computer Science Volume: 9198 Pages: 223-234
  • DOI: 10.1007/978-3-319-21398-9_18
  • ISBN: 9783319213972, 9783319213989
  • Peer Reviewed
• [Journal Article] Infinite games recognized by 2-stack visibly pushdown automata (2015)
  • Author(s): W. Li, S. Okisaka and K. Tanaka
  • Journal Title: RIMS Kokyuroku Volume: 印刷中
• [Journal Article] 無限ゲームとオートマトン (2014)
  • Author(s): 田中一之
  • Journal Title: 数学セミナー Volume: 53-11 Pages: 20-25
• [Presentation] Determinacy strength of infinite games in omega-languages recognized by variations of automata (2016)
  • Author(s): Kazuyuki Tanaka
  • Organizer: IMS-JSPS Joint Workshop on Mathematical Logic and the Foundations of Mathematics
  • Place of Presentation: シンガポール国立大学，シンガポール
  • Year and Date: 2016-01-15
  • Int'l Joint Research
• [Presentation] Finitisations of second order principles (2015)
  • Author(s): K.Tanaka and F. Pelupessy
  • Organizer: 日本数学会2015年会
  • Place of Presentation: 明治大学
  • Year and Date: 2015-03-22
• [Presentation] 決定問題の相転移 (2015)
  • Author(s): 田中一之
  • Organizer: 情報処理学会第７７回全国大会
  • Place of Presentation: 京都大学
  • Year and Date: 2015-03-17
  • Invited
• [Presentation] Phase transitions and Reverse Mathematics (2014)
  • Author(s): K.Tanaka and F. Pelupessy
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 広島大学
  • Year and Date: 2014-09-27
• [Presentation] Variants of Infinite Games and Their Strenth (2014)
  • Author(s): K. Tanaka
  • Organizer: IMS-JSPS Joint Workshop in Mathematical Logic and Foundations of Mathmematics
  • Place of Presentation: シンガポール国立大学
  • Year and Date: 2014-09-01
• [Book] ロジックの世界 (2015)
  • Author(s): D.クライアン、S.シュアテル、B.メイブリン原著 田中一之訳
  • Total Pages: 192
  • Publisher: 講談社
• [Remarks] CTFM2016
  • URL: http://www.sendailogic.com/CTFM2016/
• [Remarks] Workshop on Mathematical Logic
  • URL: http://www.sendailogic.com/Titechworkshop/
• [Funded Workshop] CTFM 2016 (2016)
  • Place of Presentation: 早稲田大学 高等研究所
  • Year and Date: 2016-09-20
• [Funded Workshop] Workshop on Mathematical Logic (2016)
  • Place of Presentation: 東京工業大学 情報理工学研究科