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Establishing Computer Assisted Proof Methods for Computational Intractability

Research Project

Project/Area Number 21500005
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Fundamental theory of informatics
Research InstitutionGunma University

Principal Investigator

AMANO Kazuyuki  群馬大学, 大学院・工学研究科, 准教授 (30282031)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Keywords計算困難性 / 計算機援用証明 / 下界 / 論理回路 / 論理関数 / 計算量 / 決定木
Research Abstract

The aim of this research is to establish the methods for analyzing the computational complexity in various computational models. Especially, this research pursues the use of computers as a central tool for the analysis. As a result, we obtain many significant results, of which we list some.(i) We determine the exact complexity for detecting clique structure of a graph by constant depth Boolean circuits,(ii) We develop a new method for analyzing the description length of Boolean functions in polynomial threshold representation based on computer analysis, and (iii) We determine the exact value of the maximum sensitivity of CNF formulas with bounded clause length.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (32 results)

All 2011 2010 2009

All Journal Article (15 results) (of which Peer Reviewed: 15 results) Presentation (17 results)

  • [Journal Article] Minterm-Transitive Functions with Asymptotically Smallest Block Sensitivity2011

    • Author(s)
      天野一幸
    • Journal Title

      Information Processing Letters

      Volume: 111(23-24) Pages: 1281-1284

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Directional vs. General Randomized Decision Tree Complexity for Read-Once Formulas2011

    • Author(s)
      天野一幸
    • Journal Title

      Chicago Journal of Theoretical Computer Science

      Volume: 2011(3) Pages: 1-11

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Well-Mixed Function with Circuit Complexity 5n : Tightness of the Lachish-Raz-type Bounds2011

    • Author(s)
      天野一幸, 垂井淳
    • Journal Title

      A Well-Mixed Function with Circuit Complexity 5n : Tightness of the Lachish-Raz-type Bounds

      Volume: 412(18) Pages: 1646-1651

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Tight Bounds on the Average Sensitivity of k-CNF2011

    • Author(s)
      天野一幸
    • Journal Title

      Theory of Computing

      Volume: 7 Pages: 45-48

    • NAID

      110008583105

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Minterm-Transitive Functions with Asymptotically Smallest Block Sensitivity2011

    • Author(s)
      Kazuyuki Amano
    • Journal Title

      Information Proceesing Letters

      Volume: 111(23-24) Issue: 23-24 Pages: 1281-1284

    • DOI

      10.1016/j.ipl.2011.09.008

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Extremal k-CNF Formulas2011

    • Author(s)
      Kazuyuki Amano
    • Journal Title

      Electronic Notes in Discrete Mathematics

      Volume: 38 Pages: 37-42

    • DOI

      10.1016/j.endm.2011.09.007

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Well-Mixed Function with Circuit Complexity 5n : Tightness of the Lachish-Raz-type Bounds2011

    • Author(s)
      Kazuyuki Amano
    • Journal Title

      Theoretical Computer Science

      Volume: 412(8) Pages: 1646-1651

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] NPN-Representatives of a Set of Optimal Boolean Formulas2010

    • Author(s)
      福原秀明, 瀧本英二, 天野一幸
    • Journal Title

      IEICE Trans. on Fund. Elect. Communications and Computer Science

      Volume: E-93-A-6 Pages: 1008-1015

    • NAID

      10026864513

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] New Upper Bounds on the Average PTF Density of Boolean Functions2010

    • Author(s)
      天野一幸
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 6506 Pages: 304-315

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] k-Subgraph Isomorphism on AC0 Circuits2010

    • Author(s)
      天野一幸
    • Journal Title

      Computational Complexity

      Volume: 19(2) Pages: 183-210

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] k-Subgraph Isomorphism on ACO Circuit2010

    • Author(s)
      Kazuyuki Amano
    • Journal Title

      Computational Complexity

      Volume: 19 Pages: 183-210

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] NPN-Representatives of a Set of Optimal Boolean Formulas2010

    • Author(s)
      Hideaki Fukuhara
    • Journal Title

      IEICE Trans.on Fund.Elect.Communications and Computer Sciences E93-A-6(印刷中)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Directional vs.Undirectional Randomized Decision Tree Complexity for Read-Once Formulas2010

    • Author(s)
      Kazuyuki Amano
    • Journal Title

      Conferences in Research and Practice in Information Technology 109

      Pages: 25-29

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] K-Subgraph Isomorphism on AC_0 Circuits2009

    • Author(s)
      Kazuyuki Amano
    • Journal Title

      Proceedings of the 24^<th> IEEE Conference on Computational Complexity 24

      Pages: 9-18

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Bounds on the Size of Small Depth Circuits for Approximating Majority2009

    • Author(s)
      Kazuyuki Amano
    • Journal Title

      Letcute Notes in Computer Science 5555

      Pages: 59-70

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] On Extremal k-CNF Formulas, European Conf. on Combinatorics2011

    • Author(s)
      天野一幸
    • Organizer
      Graph Theory and Applications
    • Place of Presentation
      Renyi研究所(ブタペスト,ハンガリー)
    • Year and Date
      2011-09-02
    • Related Report
      2011 Final Research Report
  • [Presentation] On Extremal k-CNF Formulas2011

    • Author(s)
      Kazuyuki Amano
    • Organizer
      European Conf.on Cobinatorics, Graph Theory and Applications
    • Place of Presentation
      ブタペスト(ハンガリー)
    • Year and Date
      2011-09-02
    • Related Report
      2011 Annual Research Report
  • [Presentation] もっとも敏感なk-CNF2011

    • Author(s)
      天野一幸
    • Organizer
      情報処理学会アルゴリズム研究会
    • Place of Presentation
      秋田県立大学(秋田県)
    • Year and Date
      2011-05-16
    • Related Report
      2011 Final Research Report
  • [Presentation] もっとも敏感なk-CNF式2011

    • Author(s)
      天野一幸
    • Organizer
      情報処理学会アルゴリズム研究会
    • Place of Presentation
      秋田県立大学
    • Year and Date
      2011-05-16
    • Related Report
      2011 Annual Research Report
  • [Presentation] 多項式しきい値関数密度の上界の改善2011

    • Author(s)
      早坂智行, 天野一幸
    • Organizer
      第73回情報処理学会全国大会
    • Place of Presentation
      東京工業大学(東京都)
    • Year and Date
      2011-03-04
    • Related Report
      2011 Final Research Report
  • [Presentation] Bounding the Randomized Decision Tree Complexity of Read-Once Boolean Functions2011

    • Author(s)
      天野一幸
    • Organizer
      The 22^<nd> Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2011)
    • Place of Presentation
      HolidayInn Hotel(サンフランシスコ,アメリカ合衆国)
    • Year and Date
      2011-01-25
    • Related Report
      2011 Final Research Report
  • [Presentation] Bounding the Randomized Decision Tree Complexity of Read-Once Boolean Functions2011

    • Author(s)
      Kazuyuki Amano
    • Organizer
      The 22nd Annual ACM-SIAM Symposium on Disc rete Algorithms (SODA 2011)
    • Place of Presentation
      サンフランシスコ(米国)
    • Year and Date
      2011-01-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] New Upper Bounds on the Average PTF Density of Boolean Functions2010

    • Author(s)
      天野一幸
    • Organizer
      The 21^<st> International Symposium on Algorithm and Computation (ISAAC 2010)
    • Place of Presentation
      ラマダプラザホテル(済州島,韓国)
    • Year and Date
      2010-12-15
    • Related Report
      2011 Final Research Report
  • [Presentation] New Upper Bounds on the Average PTF Density of Boolean Functigiis2010

    • Author(s)
      Kazuyuki Amano
    • Organizer
      The 21st International Symposium on Algorithm and Computation (ISAAC 2010)
    • Place of Presentation
      済州島(韓国)
    • Year and Date
      2010-12-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] 論理関数の乱化計算機計算量について2010

    • Author(s)
      天野一幸
    • Organizer
      日本OR学会NEO研究集会
    • Place of Presentation
      京都大学(京都府)
    • Year and Date
      2010-12-07
    • Related Report
      2011 Final Research Report
  • [Presentation] 論理関数の乱化決定木計算量について2010

    • Author(s)
      天野一幸
    • Organizer
      日本OR学会NEO研究集会
    • Place of Presentation
      京都大学
    • Year and Date
      2010-12-07
    • Related Report
      2010 Annual Research Report
  • [Presentation] ギガ頂点グラフのハミルトン路探索と中間層予想について2010

    • Author(s)
      島田学, 天野一幸
    • Organizer
      電子情報通信学会コンピュテーション研究会
    • Place of Presentation
      北陸先端科学技術大学(石川県)
    • Year and Date
      2010-05-19
    • Related Report
      2011 Final Research Report
  • [Presentation] On Directional vs.Undirectional Randomized Decision Tree Complexity for Read-Once Formulas2010

    • Author(s)
      Kazuyuki Amano
    • Organizer
      The 16^<th> Computing : Australasian Theory Syposium
    • Place of Presentation
      ブリスベン(豪州)
    • Year and Date
      2010-01-19
    • Related Report
      2009 Annual Research Report
  • [Presentation] K-subgraph Isomorphism on AC0 Circuits2009

    • Author(s)
      天野一幸
    • Organizer
      The 24^<th> IEEE conf. on computational complexity
    • Place of Presentation
      ポアンカレ研究所(パリ,フランス)
    • Year and Date
      2009-07-15
    • Related Report
      2011 Final Research Report
  • [Presentation] K-Subgraph Isomorphism on AC_0 Circuits2009

    • Author(s)
      Kazuyuki Amano
    • Organizer
      The 24^<th> IEEE Conference on Computational Complexity
    • Place of Presentation
      パリ(フランス)
    • Year and Date
      2009-07-15
    • Related Report
      2009 Annual Research Report
  • [Presentation] Bounds on the Size of Small Depth Circuits for Approximating Majority2009

    • Author(s)
      天野一幸
    • Organizer
      The 36^<th> International Colloquium on Automata, Languages and Programming (ICALP09)
    • Place of Presentation
      ロドスパレスホテル(ロドス,ギリシャ)
    • Year and Date
      2009-07-09
    • Related Report
      2011 Final Research Report
  • [Presentation] Bounds on the Size of Small Depth Circuits for Approximating Majority2009

    • Author(s)
      Kazuyuki Amano
    • Organizer
      The 36th International Colloquium on Automata, Languages and Programming
    • Place of Presentation
      ロドス(ギリシャ)
    • Year and Date
      2009-07-09
    • Related Report
      2009 Annual Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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