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Clarification of Structural Complexity of Formula

Research Project

Project/Area Number 22800032
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Fundamental theory of informatics
Research InstitutionKyoto University

Principal Investigator

UENO Kenya  京都大学, 次世代研究者育成センター, 助教 (70586081)

Project Period (FY) 2010 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2011: ¥1,495,000 (Direct Cost: ¥1,150,000、Indirect Cost: ¥345,000)
Fiscal Year 2010: ¥1,625,000 (Direct Cost: ¥1,250,000、Indirect Cost: ¥375,000)
Keywords論理関数 / 線形計画法 / 計算限界 / 計算量理論 / 回路計算量
Research Abstract

We have written two papers concerned with the linear programming based method for formula size lower bounds after polishing its theoretical result. One is accepted for publication in a journal(Theoretical Computer Science), and the other is presented at an international conference(MFCS 2010). We also defined an extended formula model and give a theoretical analysis on its complexity. The paper concerned with this result is accepted and will be presented at an international conference(COCOON 2012). Furthermore, we have analyzed candidate Boolean functions towards super-quadratic formula size lower bounds and completed a paper.

Report

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

    (16 results)

All 2012 2011 2010 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (8 results) Remarks (3 results)

  • [Journal Article] Formula Complexity of Ternary Majorities. In Proceedings of The 18th Annual International Computing and Combinatorics Conference2012

    • Author(s)
      Kenya Ueno
    • Journal Title

      Lecture Notes in Computer Science(Springer-Verlag)

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Stronger LP Bound for Formula Size Lower Bounds via Clique Constraints2012

    • Author(s)
      Kenya Ueno
    • Journal Title

      Theoretical Computer Science

      Volume: Vol.434 Pages: 87-97

    • DOI

      10.1016/j.tcs.2012.02.005

    • NAID

      120004057191

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Formula Complexity of Ternary Majorities2012

    • Author(s)
      Kenya Ueno
    • Journal Title

      Proceedings of COCOON 2012, Lecture Notes in Computer Science

      Volume: (掲載確定)(未確定)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Breaking the Rectangle Bound Barrier against Formula Size Lower Bounds. In Proceedings of The 35th International Symposium on Mathematical Foundations of Computer Science2010

    • Author(s)
      Kenya Ueno
    • Journal Title

      Lecture Notes in Computer Science 6281

      Pages: 665-676

    • DOI

      10.1007/978-3-642-15155-2_58

    • ISBN
      9783642151545, 9783642151552
    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Breaking the Rectangle Bound Barrier against Formula Size Lower Bounds2010

    • Author(s)
      Kenya Ueno
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 6281 Pages: 665-676

    • NAID

      110007483107

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] 多数決3分木への論理式分解2012

    • Author(s)
      上野賢哉
    • Organizer
      冬のLAシンポジウム
    • Place of Presentation
      京都
    • Year and Date
      2012-01-30
    • Related Report
      2011 Final Research Report
  • [Presentation] 多数決3分木への論理式分解2012

    • Author(s)
      Kenya Ueno
    • Organizer
      冬のLAシンポジウム2012
    • Place of Presentation
      京都大学(京都府)
    • Year and Date
      2012-01-30
    • Related Report
      2011 Annual Research Report
  • [Presentation] Parity versus Majority : Formula Complexity Perspective2011

    • Author(s)
      Kenya Ueno
    • Organizer
      The First AAAC Annual Meeting(AAAC2011)
    • Place of Presentation
      Hsin Chu, Taiwan
    • Year and Date
      2011-04-16
    • Related Report
      2011 Final Research Report
  • [Presentation] Parity versus Majority : Formula Complexity Perspective2011

    • Author(s)
      Kenya Ueno
    • Organizer
      The First AAAC Annual Meeting (AAAC2011)
    • Place of Presentation
      HsinChu, Taiwan
    • Year and Date
      2011-04-16
    • Related Report
      2011 Annual Research Report
  • [Presentation] Proof Methods for Formula Size Lower Bounds : Classics and Frontier2011

    • Author(s)
      Kenya Ueno
    • Organizer
      Workshop on Proof Theory and Computability Theory, Iwanumaya, Akiu Spa
    • Place of Presentation
      Sendai, February
    • Year and Date
      2011-02-22
    • Related Report
      2011 Final Research Report
  • [Presentation] Proof Methoods for Formula Siza Lower Bounds : Classics and Fyontier2011

    • Author(s)
      Kenya Ueno
    • Organizer
      Workshop on Proof Theory and Computability Theory
    • Place of Presentation
      Sendai, Japan(招待講演)
    • Year and Date
      2011-02-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] Breaking the Rectangle Bound Barrier against Formula Size Lower Bounds2010

    • Author(s)
      Kenya Ueno
    • Organizer
      The 35th International Symposium on Mathematical Foundations of Computer Science
    • Place of Presentation
      Brno, Czech Republic
    • Year and Date
      2010-08-27
    • Related Report
      2011 Final Research Report
  • [Presentation] Breaking the Rectangle Bound Barrier against Formula Size Lower Bounds2010

    • Author(s)
      Kenya Ueno
    • Organizer
      The 35th International Symposium on Mathematical Foundations of Computer Science(MFCS 2010)
    • Place of Presentation
      Brno, Czech Republic
    • Year and Date
      2010-08-27
    • Related Report
      2010 Annual Research Report
  • [Remarks] ホームページ等

    • URL

      http://www.lab2.kuis.kyoto-u.ac.jp/~kenya/index-j.html

    • Related Report
      2011 Final Research Report
  • [Remarks] 2011年10月25日に開催された学術情報メディアセンターセミナーにおいて,「論理式の複雑さを明らかにする理論」と題し,関連する研究成果について一般向けに教育講演を行った.「科学・技術フェスタ in 京都 2011」にて高校生・大学生と議論する公開シンポジウムに参画した.

    • Related Report
      2011 Final Research Report
  • [Remarks]

    • URL

      http://www.lab2.kuis.kyoto-u.ac.jp/~kenya/index-j.html

    • Related Report
      2011 Annual Research Report

URL: 

Published: 2010-08-27   Modified: 2016-04-21  

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