Randomness as Quantitative Computational Resource : Efficient Usage and Limitations

• Project/Area Number: 18500006
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Fundamental theory of informatics
• Research Institution: The University of Electro-Communications
• Principal Investigator: TARUI Jun The University of Electro-Communications, 電気通信学部, 准教授 (00260539)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,340,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥540,000); Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
• Keywords: 計算量理論 / ランダマイズドアルゴリズム / 乱拓計算 / 回路計算量 / 領域計算量 / アルゴリズム / ランダムネス / scrambling permutations / negation-limited inverter / finding duplicate / pigeonhole principle

Research Abstract

ネットワークを流れて次から次にやってくる膨大なデータに対する効率的計算が可能なのはどのような場合か?このような『ストリーム計算』と呼ばれる計算モデルにおいて、重複データを特定する問題を解析した。アルゴリズムが使えるランダムビット数と計算に必要なメモリー量のトレードオフを数学的に解明することに成功した。この他にもいくつかの具体的計算課題において計算に必要なランダムネスの量を解明すること成功した。関連する回路計算量の問題についてもいくつかの興味深い結果を得ることに成功した。

Research Products

• [Journal Article] Linear size log depth negation limited inverter for k-tonic binary sequences (2009)
  • Author(s): H. Morizumi and J. Tarui
  • Journal Title: Theoretical Computer Science 410(11)
  • Peer Reviewed
• [Journal Article] Negation Limited Complexity of Parity and Inverters (2009)
  • Author(s): K. Iwama, H. Morizumi, and J. Tarui
  • Journal Title: Algorithmica 54(2) Pages: 256-267
  • Peer Reviewed
• [Journal Article] Linear-Size Log-Depth Negation-Limited Inverter for k-tonic Binary Sequences (2009)
  • Author(s): H. Morizumi, J. Tarui
  • Journal Title: Theoretical Computer Science 410 Pages: 1054-1060
  • Peer Reviewed
• [Journal Article] Reductions for Monotone Boolean Circuits (2009)
  • Author(s): K. Iwama, H. Morizumi, J. Tarui
  • Journal Title: Theoretical Computer Science 408 Pages: 208-212
  • Peer Reviewed
• [Journal Article] Negation-Limited Complexity of Parity and Inverters (2009)
  • Author(s): K. Iwama, H. Morizutni, J. Tarui
  • Journal Title: Algorithmica 54 Pages: 256-267
  • Peer Reviewed
• [Journal Article] On the Minimum Number of Completely 3-scrambling Permutations (2008)
  • Author(s): J. Tarui
  • Journal Title: Discrete Mathematics 308(8) Pages: 1350-1354
  • Peer Reviewed
• [Journal Article] Reductions for Monotone Boolean Circuits (2008)
  • Author(s): K. Iwama, H. Morizumi, and J. Tarui
  • Journal Title: Theoretical Computer Science 408(2-3) Pages: 208-212
  • Peer Reviewed
• [Journal Article] On the Minimum Number of Completely 3-Scrambling Permutations (2008)
  • Author(s): J. Tarui
  • Journal Title: Discrete Mathematics 308 Pages: 1350-1354
  • Peer Reviewed
• [Journal Article] Negation-Limited Complexity of Parity and Inverters (2008)
  • Author(s): K. Iwama, H. Morizumi, and J. Tarui
  • Journal Title: Algorithmica To appear
  • Peer Reviewed
• [Journal Article] On the Minimum Number of Completely 3-Scrambling Permutations (2007)
  • Author(s): J.Tarui
  • Journal Title: Discrete Mathematics (To appear)
• [Journal Article] Finding a Duplicate and a Missing Item in a Stream (2007)
  • Author(s): J.Tarui
  • Journal Title: Lecture Notes in Computer Science (TAMC07) 4484 Pages: 128-135
• [Journal Article] Linear-Size Log-Depth Negation-Limited Inverter for k-tonic Binary Sequences (2007)
  • Author(s): H.Morizumi, J.Tarui
  • Journal Title: Lecture Notes in Computer Science (TAMC07) 4484(To appear)
• [Journal Article] Negation-Limited Complexity of Parity and Inverters (2006)
  • Author(s): K.Iwama, H.Morizumi, J.Tarui
  • Journal Title: Lecture Notes in Computer Science (ISAAC06) 4288 Pages: 223-232
• [Presentation] Smallest Formulas for Parity of 2k (2008)
  • Author(s): J. Tarui
  • Organizer: Proc. of COCOON08
  • Place of Presentation: (LNCS vol 5092)(92-99)
  • Year and Date: 2008-06-29
• [Presentation] Smallest Formulas for Parity of 2^k Variables Are Essentially Unique (2008)
  • Author(s): J. Tarui
  • Organizer: rhe 14^<th> Annual International Computing and Combinatorics Conference (COCOON08). LNCS vol. 5092, 92-99, 2008.
  • Place of Presentation: Dalian, China
  • Year and Date: 2008-06-29
• [Presentation] A Well-Mixed Function with Circuit Complexity 5n±o(n) (2008)
  • Author(s): K. Amano and J. Tarui
  • Organizer: Tightness of the Lachish Raz Type Bounds. Proc. of TAMC08
  • Place of Presentation: LNCS vol 4978, 342-350
  • Year and Date: 2008-04-27
• [Presentation] A Well-Mixed Function with Circuit Complexity 5n : Tightness of the Lachisch-Raz-Type Bounds. (2008)
  • Author(s): K. Amano, J. Tarui
  • Organizer: The 5^<th> Conference on Theory and Applications of Models of Computation (TAMC08). LNCS vol. 4978, 342-350, 2008.
  • Place of Presentation: Xi'an China
  • Year and Date: 2008-04-27
• [Presentation] A Well-Mixed Function with Circuit Complexity 5n: Tightness of the Lachisch-Raz-Type Bounds. (2008)
  • Author(s): K. Amano and J. Tarui
  • Organizer: The 5th Conference on Theory and Applications of Models of Computation(TAMCO8), LNCS.
  • Place of Presentation: Xi'an China
• [Presentation] Smallest Formulas for Parity of 2^k Variables Are Essentially Unique (2008)
  • Author(s): J. Tarui
  • Organizer: The 14th Annual International Computing and Combinatorics Conference(COCOON08)
  • Place of Presentation: Dalian, China
• [Presentation] Linear Size Log Depth Negation Limited Inverter for k Tonic Binary Sequences (2007)
  • Author(s): H. Morizumi and J. Tarui
  • Organizer: Proc. of TAMC07
  • Place of Presentation: (LNCS vol 4484)(605-615)
  • Year and Date: 2007-05-25
• [Presentation] Finding a Duplicate and a Missing Item in a Stream (2007)
  • Author(s): J. Tarui
  • Organizer: Proc. of TAMC07
  • Place of Presentation: (LNCS vol 4484)(128-135)
  • Year and Date: 2007-05-22
• [Presentation] Finding a Duplicate and a Missing Item in a Stream (2007)
  • Author(s): J. Tarui
  • Organizer: The 4th Conference on Theory and Applications of Models of Computation(TAMCO7), LNCS vol.4484, pp. 128-135, 2007.
  • Place of Presentation: Shanghai, China
• [Presentation] Linear-Size Log-Depth Negation-Limited Inverter for k-Tonic Binary Sequences (2007)
  • Author(s): H. Morizumi and J. Tarui
  • Organizer: The 4th Conference on Theory and Applicatoins of Models of Computation(TAMC07), LNCS vol. 4484, pp. 605-615, 2007.
  • Place of Presentation: Shanghai, China
• [Presentation] Negation Limited Complexity of Parity and Inverters (2006)
  • Author(s): K. Iwama, H. Morizumi, and J. Tarui
  • Organizer: Proc. of ISAAC06
  • Place of Presentation: (LNCS vol 4288)(223-232)
• [Remarks]
  • URL: http://www.jtlab.ice.uec.ac.jp/