A Study on the Complexity of Bounded Width Boolean Circuits

• Project/Area Number: 23700020
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Fundamental theory of informatics
• Research Institution: Shimane University
• Principal Investigator: MORIZUMI Hiroki 島根大学, 総合理工学研究科(研究院), 助教 (50463782)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 計算量理論 / 回路計算量 / 論理回路 / 論理関数 / 幅限定回路

Outline of Final Research Achievements

We studied bounded width Boolean circuits to explore the circuit complexity. In this study, Boolean circuits are considered as a mathematical model of computation, and studied from the viewpoint of computational complexity theory, on the background that there are many open problems of computational complexity such as the P vs. NP problem. As the conclusion, we obtained several results for Boolean circuits and Boolean functions.

Research Products

• [Journal Article] Sensitivity, Block Sensitivity, and Certificate Complexity of Unate Functions and Read-Once Functions (2014)
  • Author(s): Hiroki Morizumi
  • Journal Title: Lecture Notes in Computer Science Volume: 8705 Pages: 104-110
  • DOI: 10.1007/978-3-662-44602-7_9
  • ISBN: 9783642387081, 9783642387098
  • Peer Reviewed
• [Journal Article] Complexity of Counting Output Patterns of Logic Circuits (2013)
  • Author(s): Kei Uchizawa, Zhenghong Wang, Hiroki Morizumi and Xiao Zhou
  • Journal Title: Conferences in Research and Practice in Information Technology Volume: 141
  • NAID: 110009768648
  • Peer Reviewed
• [Journal Article] Computing All MOD-Functions Simultaneously (2012)
  • Author(s): Evgeny Demenkov, Alexander Kulikov, Ivan Mihajlin and Hiroki Morizumi
  • Journal Title: Lecture Notes in Computer Science Volume: 7353 Pages: 81-88
  • DOI: 10.1007/978-3-642-30642-6_9
  • ISBN: 9783642306419, 9783642306426
  • Peer Reviewed
• [Presentation] 幅限定回路と段数限定論理式に対する単純な#SATアルゴリズム (2015)
  • Author(s): 森住 大樹
  • Organizer: 2014年度 冬のLAシンポジウム
  • Place of Presentation: 京都大学（京都府）
  • Year and Date: 2015-01-28 – 2015-01-30
• [Presentation] On Zero-Suppressed Binary Decision Diagrams and Complexity Theory (2014)
  • Author(s): Hiroki Morizumi
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 崇城大学（熊本県）
  • Year and Date: 2014-12-05
• [Presentation] On Computing Sensitivity, Block Sensitivity, and Certificate Complexity for Boolean Formulas (2014)
  • Author(s): Hiroki Morizumi
  • Organizer: 情報処理学会アルゴリズム研究会
  • Place of Presentation: 中央大学（東京都）
• [Presentation] Complexity of Counting Output Patterns of Logic Circuits (2013)
  • Author(s): Kei Uchizawa, Zhenghong Wang, Hiroki Morizumi and Xiao Zhou
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 小樽商科大学（北海道）
• [Presentation] Sensitivity, Block Sensitivity, and Certificate Complexity of Unate Functions and Read-Once Functions (2013)
  • Author(s): Hiroki Morizumi
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 沖縄産業支援センター（沖縄県）
• [Presentation] Complexity of Counting Output Patterns of Logic Circuits (2013)
  • Author(s): Kei Uchizawa, Zhenghong Wang, Hiroki Morizumi and Xiao Zhou
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 小樽商科大学（小樽市）