Exploring the computational power of threshold circuits with the limited number of output patterns

• Project/Area Number: 25330005
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: Yamagata University
• Principal Investigator: Kei Uchizawa 山形大学, 理工学研究科, 准教授 (90510248)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 計算理論 / しきい値回路 / ニューラルネットワーク / 回路計算量理論 / 計算複雑さ / 論理回路 / NPI / UP / 線形決定木 / 回路計算量

Outline of Final Research Achievements

We investigate the computational power of threshold circuits with the limited number of output patterns．We prove that there exists an explicit Boolean function such that any threshold circuit consisting of threshold gates with restricted weights requires an exponential number of output patterns. Our result thus implies that the number of output patterns can be strongly related to the computational power of threshold circuits and its weights of threshold gates. We also consider a discrete dynamical system defined on logic gates, and introduce a decision problem with regard to the output patterns on the system. We then show that the problem may belong to a complexity class of which few problems are known to be candidates of the members.

Research Products

• [Journal Article] Threshold Circuits Detecting Global Patterns in Two-dimensional Maps (2016)
  • Author(s): Kei Uchizawa, Daiki Yashima, Xiao Zhou
  • Journal Title: Journal of Graph Algorithms and Applications Volume: 20 Issue: 1 Pages: 115-131
  • DOI: 10.7155/jgaa.00387
  • Peer Reviewed / Open Access
• [Journal Article] Swapping Labeled Tokens on Graphs (2015)
  • Author(s): Katsuhisa Yamanaka, Erik D. Demaine, Takehiro Ito, Jun Kawahara, Masashi Kiyomi, Yoshio Okamoto, Toshiki Saitoh, Akira Suzuki, Kei Uchizawa, Takeaki Uno
  • Journal Title: Theoretical Computer Science Volume: 印刷中 Pages: 81-94
  • DOI: 10.1016/j.tcs.2015.01.052
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Competitive Diffusion on Weighted Graphs (2015)
  • Author(s): Takehiro Ito, Yota Otachi, Toshiki Saitoh, Hisayuki Satoh, Akira Suzuki, Kei Uchizawa, Ryuhei Uehara, Katsuhisa Yamanaka, Xiao Zhou
  • Journal Title: Proc. 14th International Symposium on Algorithms and Data Structures (WADS 2015), Lecture Notes in Computer Science Volume: 9214 Pages: 422-433
  • DOI: 10.1007/978-3-319-21840-3_35
  • NAID: 120005850317
  • ISBN: 9783319218397, 9783319218403
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Computational Complexity Studies of Synchronous Boolean Finite Dynamical Systems (2015)
  • Author(s): Mitsunori Ogihara, Kei Uchizawa
  • Journal Title: Proc. 12th Annual Conference on Theory and Applications of Models of Computation (TAMC 2015), Lecture Notes in Computer Science Volume: 9076 Pages: 87-98
  • DOI: 10.1007/978-3-319-17142-5_9
  • ISBN: 9783319171418, 9783319171425
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Lower bounds for linear decision trees with bounded weights (2015)
  • Author(s): Kei Uchizawa, Eiji Takimoto
  • Journal Title: Proc. 41st International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM 2015), Lecture Notes in Computer Science Volume: 8939 Pages: 412-422
  • DOI: 10.1007/978-3-662-46078-8_34
  • ISBN: 9783662460771, 9783662460788
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Threshold circuits for global patterns in 2-dimensional maps (2015)
  • Author(s): Kei Uchizawa, Daiki Yashima, Xiao Zhou
  • Journal Title: Proc. 9th International Workshop on Algorithms and Computation (WALCOM 2015), Lecture Notes in Computer Science Volume: 8973 Pages: 306-316
  • DOI: 10.1007/978-3-319-15612-5_27
  • ISBN: 9783319156118, 9783319156125
  • Peer Reviewed
• [Journal Article] Swapping Labeled Tokens on Graphs (2014)
  • Author(s): Katsuhisa Yamanaka, Erik D. Demaine, Takehiro Ito, Jun Kawahara, Masashi Kiyomi, Yoshio Okamoto, Toshiki Saitoh, Akira Suzuki, Kei Uchizawa, and Takeaki Uno
  • Journal Title: Lecture Notes in Computer Science Volume: 8496 Pages: 369-380
  • DOI: 10.1007/978-3-319-07890-8_31
  • ISBN: 9783319078892, 9783319078908
  • Peer Reviewed
• [Journal Article] Generalized rainbow connectivity of graphs (2014)
  • Author(s): Kei Uchizawa, Takanori Aoki, Takehiro Ito and Xiao Zhou
  • Journal Title: Theoretical Computer Science (TCS) Volume: 555 Pages: 35-42
  • DOI: 10.1016/j.tcs.2014.01.007
  • Peer Reviewed
• [Journal Article] Energy-Efficient Threshold Circuits Detecting Global Pattern in 1-Dimensional Arrays (2013)
  • Author(s): Akira Suzuki, Kei Uchizawa and Xiao Zhou
  • Journal Title: Springer, Lecture Notes in Computer Science Volume: 7876 Pages: 248-259
  • DOI: 10.1007/978-3-642-38236-9_23
  • ISBN: 9783642382352, 9783642382369
  • Peer Reviewed
• [Journal Article] Energy and fan-in of logic circuits computing symmetric Boolean functions (2013)
  • Author(s): Akira Suzuki, Kei Uchizawa and Xiao Zhou
  • Journal Title: Theoretical Computer Science (TCS) Volume: 505 Pages: 74-80
  • DOI: 10.1016/j.tcs.2012.11.039
  • Peer Reviewed
• [Journal Article] On the rainbow connectivity of graphs : complexity and FPT algorithms (2013)
  • Author(s): Kei Uchizawa, Takanori Aoki, Takehiro Ito, Akira Suzuki and Xiao Zhou
  • Journal Title: Algorithmica Volume: 67, Issue2 Issue: 2 Pages: 161-179
  • DOI: 10.1007/s00453-012-9689-4
  • Peer Reviewed
• [Presentation] Synchronous Boolean Finite Dynamical Systems and Minimum Circuit Size Problem (2016)
  • Author(s): Kei Uchizawa
  • Organizer: 情報処理学会アルゴリズム研究会
  • Place of Presentation: 湯の原ホテル
  • Year and Date: 2016-01-14
• [Presentation] Computational Complexity of Competitive Diffusion on (Un)weighted Graphs (2015)
  • Author(s): Kei Uchizawa
  • Organizer: 情報処理学会アルゴリズム研究会
  • Place of Presentation: 九大西新プラザ
  • Year and Date: 2015-09-21
• [Presentation] Computational Complexity Studies of Synchronous Boolean Finite Dynamical Systems (2015)
  • Author(s): Kei Uchizawa
  • Organizer: 情報処理学会アルゴリズム研究会
  • Place of Presentation: 定山渓ビューホテル
  • Year and Date: 2015-06-05
• [Presentation] Complexity of Counting Output Patterns of Logic Circuits (2013)
  • Author(s): 内澤 啓，王 征泓，森住 大樹，周 暁
  • Organizer: 情報処理学会アルゴリズム研究会
  • Place of Presentation: 小樽商科大学
• [Presentation] Computational Power of Threshold Circuits with Sparse Activity (2013)
  • Author(s): 内澤 啓
  • Organizer: ELC・スパースモデリング合同シンポジウム
  • Place of Presentation: 九州大学 伊都キャンパス
  • Invited
• [Remarks] 研究室ホームページ
  • URL: http://tcs.yz.yamagata-u.ac.jp/