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Game trees without a unique equilibrium distribution: A research by resource-bounded martingales

Research Project

Project/Area Number 22540146
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionTokyo Metropolitan University

Principal Investigator

SUZUKI Toshio  首都大学東京, 理工学研究科, 准教授 (30235973)

Co-Investigator(Kenkyū-buntansha) KUMABE Masahiro  放送大学, 教養学部, 教授 (70255173)
Project Period (FY) 2010-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywords数学基礎論 / 数理論理学 / 計算量理論 / ゲーム理論 / 人工知能 / 命題論理 / 最適化問題 / ミニマックス定理 / アルゴリズム / 応用数学 / 情報基礎
Outline of Final Research Achievements

(1) A martingale is a concept similar to probability attached to a tree. We investigate a resource-bounded martingale, where “resource-bounded” means that an algorithm with a certain constraint can compute it. On fundamental research of resource-bounded martingales, we published an academic paper. At the moment, this is the most important work among joint researches by Kumabe and Suzuki.
(2) A game tree is a tree diagram representing all possible moves of a given game. Here, we investigate a binary tree whose terminals are bi-valued. Such a tree is a Boolean formula, and a set of terminal values is a truth assignment. We have established a theory on the case where, among probability distribution on truth assignments, the equilibrium point is not unique.

Report

(7 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Products Report
  • Research Products

    (42 results)

All 2016 2015 2014 2013 2012 2011 2010 Other

All Journal Article (14 results) (of which Peer Reviewed: 11 results,  Acknowledgement Compliant: 2 results,  Open Access: 2 results) Presentation (19 results) (of which Invited: 2 results) Book (1 results) Remarks (8 results)

  • [Journal Article] A solution to Yamakami's problem on non-uniform context-free languages2016

    • Author(s)
      Toshio Suzuki
    • Journal Title

      IAENG International Journal of Applied Mathematics

      Volume: 46 Pages: 187-193

    • Related Report
      Products Report
    • Peer Reviewed / Open Access
  • [Journal Article] Resource-bounded martingales and computable Dowd-type generic sets2015

    • Author(s)
      Masahiro Kumabe, Toshio Suzuki
    • Journal Title

      Information and Computation

      Volume: - Pages: 227-248

    • DOI

      10.1016/j.ic.2015.03.004

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] AND-OR木の均衡点:確率制約がある場合2015

    • Author(s)
      鈴木 登志雄, 仁井田 哲尚
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1950 Pages: 34-39

    • Related Report
      Products Report
    • Open Access
  • [Journal Article] Equilibrium points of an AND-OR tree: Under constraints on probability2015

    • Author(s)
      Toshio Suzuki and Yoshinao Niida
    • Journal Title

      Annals of Pure and Applied Logic

      Volume: 166 Issue: 11 Pages: 1150-1164

    • DOI

      10.1016/j.apal.2015.07.002

    • Related Report
      Products Report
    • Peer Reviewed
  • [Journal Article] Geometrical redundancy of street patterns based on threshold of isoperimetric ratio2014

    • Author(s)
      Toshio Suzuki, Yuji Hatakeyama
    • Journal Title

      IAENG Transactions on Engineering Sciences

      Volume: special issue Pages: 91-100

    • DOI

      10.1201/b16763-10

    • ISBN
      9780429227202
    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Resource-bounded randomness and computable Dowd-type generic sets2013

    • Author(s)
      Toshio Suzuki (with M. Kumabe)
    • Journal Title

      The Bulletin of Symbolic Logic

      Volume: 19

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Threshold of isoperimetric ratio based on compressibility via invertible affine transformations2013

    • Author(s)
      Toshio Suzuki and Yuji Hatakeyama
    • Journal Title

      Lecture Notes in Engineering and Computer Science: Proceedings of The World Congress on Engineering 2013

      Volume: 1

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Probability distributions on an AND-OR tree under directional algorithms2013

    • Author(s)
      Toshio Suzuki
    • Journal Title

      IAENG Transactions on Electrical Engineering

      Volume: 1 Pages: 70-83

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The eigen distribution of an AND-OR tree under directional algorithms2012

    • Author(s)
      Toshio Suzuki
    • Journal Title

      IAENG International Journal of Applied Mathematics

      Volume: 42 Pages: 122-128

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Probability distributions achieving the equilibrium of an AND-OR tree under directional algorithms2012

    • Author(s)
      Toshio Suzuki, Ryota Nakamura
    • Journal Title

      Lecture Notes in Engineering and Computer Science : Proceedings of IMECS 2012

      Pages: 194-199

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Computable Dowd-type generic oracles2011

    • Author(s)
      Masahiro Kumabe, Toshio Suzuki
    • Journal Title

      Proceedings of the 11th Asian Logic Conference

      Pages: 128-146

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Failure of the uniqueness of eigen-distribution on random assignments for game trees2011

    • Author(s)
      Suzuki, T.
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1729 Pages: 111-116

    • Related Report
      2010 Annual Research Report
  • [Journal Article] ランダム性をもったゲーム木を読み切るコストの期待値2011

    • Author(s)
      中村亮太, 鈴木登志雄
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1729 Pages: 95-110

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Computable Dowd-type generic oracle (abstract)2010

    • Author(s)
      Kumabe, M., Suzuki, T.
    • Journal Title

      Bulletin of Symbolic Logic

      Volume: 16 Pages: 295-296

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] A solution to Yamakami's problem on advised context-free languages2015

    • Author(s)
      Toshio Suzuki
    • Organizer
      日本数学会2015年度秋季総合分科会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-16
    • Related Report
      Products Report
  • [Presentation] AND-OR木の均衡点:確率制約がある場合2014

    • Author(s)
      鈴木登志雄, 仁井田哲尚
    • Organizer
      RIMS研究集会 証明論・計算論とその周辺
    • Place of Presentation
      京都大学数理解析研究所(京都府・京都市)
    • Year and Date
      2014-12-24
    • Related Report
      2014 Annual Research Report
  • [Presentation] Equilibrium Points of an AND-OR Tree: under Constraints on Probability2014

    • Author(s)
      Toshio Suzuki
    • Organizer
      ELC Seminar
    • Place of Presentation
      東京工業大学田町キャンパス(東京都・港区)
    • Year and Date
      2014-12-04
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Equilibrium Points of an AND-OR Tree: under Constraints on Probability2014

    • Author(s)
      Toshio Suzuki
    • Organizer
      Workshop on Mathematical Logic on the Occasion of Sakae Fuchino's 60th Birthday
    • Place of Presentation
      神戸大学(兵庫県・神戸市)
    • Year and Date
      2014-11-17
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Equilibrium Points of an AND-OR Tree: under Constraints on Probability2014

    • Author(s)
      Toshio Suzuki, Yoshinao Niida
    • Organizer
      日本数学会2014年度秋季総合分科会
    • Place of Presentation
      広島大学(広島県・広島市)
    • Year and Date
      2014-09-27
    • Related Report
      2014 Annual Research Report
  • [Presentation] Equilibrium Points of an AND-OR Tree: under Constraints on Probability2014

    • Author(s)
      Toshio Suzuki, Yoshinao Niida
    • Organizer
      日本応用数理学会2014年度年会 ポスターセッション
    • Place of Presentation
      政策研究大学院大学(東京都・港区)
    • Year and Date
      2014-09-03
    • Related Report
      2014 Annual Research Report
  • [Presentation] Equilibrium Points of an AND-OR Tree: under Constraints on Probability2014

    • Author(s)
      Toshio Suzuki, Yoshinao Niida
    • Organizer
      The 25th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (Poster Session)
    • Place of Presentation
      パリ(フランス)
    • Year and Date
      2014-06-16
    • Related Report
      2014 Annual Research Report
  • [Presentation] Resource-bounded forcing theorem and randomness2014

    • Author(s)
      Toshio Suzuki (with M. Kumabe)
    • Organizer
      Computability Theory and Foundations of Mathematics 2014 (CTFM2014)
    • Place of Presentation
      東京工業大学大岡山キャンパス
    • Related Report
      2013 Annual Research Report
  • [Presentation] Forcing complexity2013

    • Author(s)
      Toshio Suzuki (with M. Kumabe)
    • Organizer
      ELC Workshop on Randomness and Probability Through Computability (RPTC2013)
    • Place of Presentation
      東京大学本郷キャンパス
    • Related Report
      2013 Annual Research Report
  • [Presentation] Threshold of isoperimetric ratio based on compressibility via invertible affine transformations2013

    • Author(s)
      Toshio Suzuki and Yuji Hatakeyama
    • Organizer
      World Congress on Engineering 2013 (WCE2013)
    • Place of Presentation
      Imperial College London, London, UK
    • Related Report
      2013 Annual Research Report
  • [Presentation] Probability distributions achieving the equilibrium of an AND-OR tree under directional algorithms2012

    • Author(s)
      Toshio Suzuki, Ryota Nakamura
    • Organizer
      The International MultiConference of Engineers and Computer Scientists 2012
    • Place of Presentation
      oyal Garden Hotel, Hong Kong
    • Year and Date
      2012-03-15
    • Related Report
      2011 Annual Research Report
  • [Presentation] Resource-bounded randomness and computable Dowd-type generic sets2011

    • Author(s)
      Masahiro Kumabe, Toshio Suzuki
    • Organizer
      The 12th Asian Logic Conference (ALC12)
    • Place of Presentation
      Victoria University of Wellington, New Zealand
    • Year and Date
      2011-12-17
    • Related Report
      2011 Annual Research Report
  • [Presentation] Independent distributions on an AND-OR tree2011

    • Author(s)
      Toshio Suzuki, Masahiro Kumab
    • Organizer
      Workshop on Proof Theory and Theory of Computing 2011
    • Place of Presentation
      首都大学東京国際交流会館
    • Year and Date
      2011-09-13
    • Related Report
      2011 Annual Research Report
  • [Presentation] Resource-bounded martingales and Dowd-type generic oracles2011

    • Author(s)
      Masahiro Kumabe, Toshio Suzuki
    • Organizer
      Workshop on Proof Theory and Theory of Computing 2011
    • Place of Presentation
      首都大学東京国際交流会館
    • Year and Date
      2011-09-12
    • Related Report
      2011 Annual Research Report
  • [Presentation] No-free-lunch theorem and uniqueness of eigen-distribution of a game tree (joint work with Nakamura, R.)2011

    • Author(s)
      Suzuki, T.
    • Organizer
      Workshop on Proof Theory and Computability Theory
    • Place of Presentation
      Akiu Spa Hotel Iwanumaya(仙台市)(招待講演)
    • Year and Date
      2011-02-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] Computable Dowd-type generic oracles2010

    • Author(s)
      Suzuki, T., Kumabe, M.
    • Organizer
      日本数学会 2010年度秋季総合分科会
    • Place of Presentation
      名古屋大学(名古屋市)
    • Year and Date
      2010-09-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] ランダム性をもったゲーム木を読み切るコストの期待値2010

    • Author(s)
      中村亮太, 鈴木登志雄
    • Organizer
      形式体系と証明論
    • Place of Presentation
      京都大学数理解析研究所(京都市)
    • Year and Date
      2010-09-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] Resource-bounded randomness and computable Dowd-type generic sets

    • Author(s)
      鈴木登志雄
    • Organizer
      日本数学会2012年度秋季総合分科会
    • Place of Presentation
      九州大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] The eigen distribution of an AND-OR tree under directional algorithms

    • Author(s)
      鈴木登志雄
    • Organizer
      日本数学会2012年度秋季総合分科会
    • Place of Presentation
      九州大学
    • Related Report
      2012 Annual Research Report
  • [Book] 証明論と複雑性(数理解析研究所講究録1832 )2013

    • Author(s)
      鈴木登志雄・編集
    • Total Pages
      176
    • Publisher
      京都大学数理解析研究所
    • Related Report
      2013 Annual Research Report
  • [Remarks] Researchmap 鈴木登志雄

    • URL

      http://researchmap.jp/read0021048/?lang=japanese

    • Related Report
      2014 Annual Research Report
  • [Remarks] Researchmap Toshio Suzuki

    • URL

      http://researchmap.jp/read0021048/?lang=english

    • Related Report
      2014 Annual Research Report
  • [Remarks] 鈴木登志雄 研究内容紹介

    • URL

      http://www.ac.auone-net.jp/~bellp/researchtopic-j.html

    • Related Report
      2014 Annual Research Report
  • [Remarks] researchmap 鈴木登志雄

    • URL

      http://researchmap.jp/read0021048/?lang=japanese

    • Related Report
      2013 Annual Research Report
  • [Remarks] researchmap SUZUKI Toshio

    • URL

      http://researchmap.jp/read0021048/?lang=english

    • Related Report
      2013 Annual Research Report
  • [Remarks] 鈴木 登志雄: 研究内容紹介

    • URL

      http://www.ac.auone-net.jp/~bellp/researchtopic-j.html

    • Related Report
      2013 Annual Research Report
  • [Remarks]

    • URL

      http://researchmap.jp/read0021048/?lang=japanese

    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://www.ac.auone-net.jp/~bellp/papers.html

    • Related Report
      2010 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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