Proof of hierarchies on circuit complexities based on size and depth, and its application to evaluation of automated design systems

• Project/Area Number: 19500014
• 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: Hiroshima University
• Principal Investigator: IWAMOTO Chuzo 広島大学, 大学院・工学研究院, 准教授 (60274495)
• Project Period (FY): 2007 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 計算の複雑さ / 計算量理論 / 計算複雑さ / 階層定理 / 論理設計 / システム評価 / 計算機モデル / 非決定性計算 / セルオートマトン

Research Abstract

If we are allowed to use more computational resources such as space and time, then we should be able to recognize more languages or compute more difficult functions. This property is theoretically proved by the hierarchy theorems. In this research, we have presented hierarchy theorems based on uniform circuit families, Turing machines, cellular automata, and parallel random access machines. These hierarchy theorems imply the existence of functions which separate computational complexity classes.

Research Products

• [Journal Article] A Polynomial-Time Reduction from the 3SAT Problem to the Generalized String Puzzle Problem (2012)
  • Author(s): Chuzo Iwamoto, Kento Sasaki, and Kenichi Morita
  • Journal Title: Algorithms Volume: Vol.5, No.2 Issue: 2 Pages: 261-272
  • DOI: 10.3390/a5020261
  • Peer Reviewed
• [Journal Article] Lower Bound of Face Guards of Polyhedral Terrains (2012)
  • Author(s): Chuzo Iwamoto, Junichi Kishi, and Kenichi Morita
  • Journal Title: Journal of Information Processing(JIP) Volume: Vol.20, No.2 Pages: 435-437
  • Peer Reviewed
• [Journal Article] Lower Bound of Face Guards of Polyhedral Terrains (2012)
  • Author(s): Chuzo Iwamoto
  • Journal Title: Journal of Information Processing Volume: 53 Pages: 1-4
  • Peer Reviewed
• [Journal Article] Relationship between Depth and Nondeterministic Gates in Nondeterministic Circuit Families (2011)
  • Author(s): Chuzo Iwamoto, Yusuke Ono, Kenichi Morita, and Katsunobu Imai
  • Journal Title: IPSJ Journal Volume: Vol.52, No.4 Pages: 1667-1677
  • NAID: 110008507999
  • Peer Reviewed
• [Journal Article] A Polynomial-Time Reduction from the SAT Problem to the Generalized One-Person Last-and-First Game (2011)
  • Author(s): Chuzo Iwamoto and Yusuke Sumida
  • Journal Title: Advances in Computer Science and Engineering Volume: Vol.6, No.2 Pages: 105-114
  • Peer Reviewed
• [Journal Article] A Polynomial-Time Reduction from the SAT Problem to the Generalized One-Person Last-and-First Game (2011)
  • Author(s): Chuzo Iwamoto
  • Journal Title: Advances in Computer Science and Engineering Volume: 6 Pages: 105-114
  • Peer Reviewed
• [Journal Article] 非決定性回路族における深さと非決定性ゲート数の関係 (2011)
  • Author(s): 岩本宙造
  • Journal Title: 情報処理学会論文誌 Volume: 52 Pages: 1667-1677
  • NAID: 110008507999
  • Peer Reviewed
• [Journal Article] NP-Hard and k-EXPSPACE-Hard Cast Puzzles (2010)
  • Author(s): Chuzo Iwamoto, Kento Sasaki, Kenji Nishio, and Kenichi Morita
  • Journal Title: IEICE Transactions on Information and Systems Volume: E93-D Issue: 11 Pages: 2995-3004
  • DOI: 10.1587/transinf.E93.D.2995
  • NAID: 10027988361
  • ISSN: 0916-8532, 1745-1361
  • Peer Reviewed
• [Journal Article] A Tight Space-Hierarchy Theorem for Nondeterministic Turing Machines (2010)
  • Author(s): Chuzo Iwamoto, Daisuke Tachibana, Seiki Tokunaga, and Kenichi Morita
  • Journal Title: The Transactions of the Institute of Electronics, In for mation and Communication Engineers D-I Volume: Vol.J93-D, No.9 Pages: 1717-1726
  • NAID: 110007700685
  • Peer Reviewed
• [Journal Article] 非決定性チューリング機械の厳密な領域階層定理 (2010)
  • Author(s): 岩本宙造
  • Journal Title: 電子情報通信学会論文誌D-I Volume: J93-D Pages: 1717-1726
  • NAID: 110007700685
  • Peer Reviewed
• [Journal Article] NP-hard and k-EXPSPACE-hard Cast Puzzles (2010)
  • Author(s): Chuzo Iwamoto
  • Journal Title: IEICE Transactions on Information and Systems Volume: E93-D Pages: 295-3004
  • Peer Reviewed
• [Journal Article] An Efficient Reconstruction Algorithm for Restricted Domino Tilings (2009)
  • Author(s): Chuzo Iwamoto and Reijiro Mikamo
  • Journal Title: The Transactions of the Institute of Electronics, Information and Communication Engineers D-I Volume: Vol.J92-D, No.6 Pages: 758-766
  • NAID: 110007328880
  • Peer Reviewed
• [Journal Article] On the Non-existence of Rotation-Symmetric von Neumann Neighbor Number-Conserving Cellular Automata of which the State Number is Less than Four (2009)
  • Author(s): Naonori Tanimoto, Katsunobu Imai, Chuzo Iwamoto, and Kenichi Morita
  • Journal Title: IEICETransactions on Information and Systems Volume: Vol.E92-D, No.2 Pages: 255-257
  • Peer Reviewed
• [Journal Article] An Efficient Reconstruction Algorithm for Restricted Domino Tilings (2009)
  • Author(s): Chuzo Iwamoto, Reijiro Mikamo
  • Journal Title: The Transactions of the Institute of Electronics, Information and Communication Engineers D-I Vol. J92-D, No. 6(in Japanese) Pages: 758-766
  • NAID: 110007328880
• [Journal Article] 段数を制限したドミノタイリングの効率良い再構成アルゴリズム (2009)
  • Author(s): 岩本宙造
  • Journal Title: 電子情報通信学会論文誌D-I Volume: J92-D Pages: 758-766
  • NAID: 110007328880
  • Peer Reviewed
• [Journal Article] Computational Complexity of Cast Puzzles (2009)
  • Author(s): Chuzo Iwamoto
  • Journal Title: Proceedings of the 20th International Symposiumon Algorithms and Computation (Lecture Notes in Computer Science)? Volume: 5878 Pages: 122-131
  • Peer Reviewed
• [Journal Article] On the non-existance of rotation-symmetric von Neumann neighbor number-conserving cellular automata of which the state number is less than four (2009)
  • Author(s): Naonori Tanimoto
  • Journal Title: IEICE Transactions on Information and Systems E92-D(2) Pages: 255-257
  • Peer Reviewed
• [Journal Article] A Recursive Padding Technique on Nondeterministic Cellular Automata (2008)
  • Author(s): Chuzo Iwamoto, Harumasa Yoneda, Kenichi Morita, and Katsunobu Imai
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E91-A Issue: 9 Pages: 2335-2340
  • DOI: 10.1093/ietfec/e91-a.9.2335
  • NAID: 10026851419
  • ISSN: 0916-8508, 1745-1337
  • Peer Reviewed
• [Journal Article] A Recursive Padding Technique on Nondeterministic Cellular Automata (2008)
  • Author(s): Chuzo Iwamoto, Harumasa Yoneda, Kenichi Morita, Katsunobu Imai
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Vol. E91-A, No. 9 Pages: 2335-2340
• [Journal Article] A Recursive Padding Technique on Nondeterministic Cellular Automata (2008)
  • Author(s): Chuzo Iwamoto
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E91-A(9) Pages: 2335-2340
  • Peer Reviewed
• [Journal Article] Translational Lemmas for DLOGTIME-uniform Circuits, Alternating TMs, and PRAMs (2007)
  • Author(s): Chuzo Iwamoto, Naoki Hatayama, Yoshiaki Nakashiba, Kenichi Morita, and Katsunobu Imai
  • Journal Title: Acta Informatica Volume: Vol.44, No.5 Issue: 5 Pages: 345-359
  • DOI: 10.1007/s00236-007-0051-2
  • Peer Reviewed
• [Journal Article] A Five-State von Neumann Neighbor Universal Hyperbolic Cellular Automaton (2007)
  • Author(s): Katsunobu Imai, Chuzo Iwamoto, and Kenichi Morita
  • Journal Title: Journal of Cellular Automata Volume: Vol.1, No.4 Pages: 275-297
  • Peer Reviewed
• [Journal Article] Translational Lemmas for DLOGTIME-uniform Circuits, Alternating TMs, and PRAMs (2007)
  • Author(s): Chuzo Iwamoto, Naoki Hatayama, Yoshiaki Nakashiba, Kenichi Morita, Katsunobu Imai
  • Journal Title: Acta Informatica Vol. 44, No. 5 Pages: 345-359
• [Journal Article] Translational Lemmas for DLOGTIME-uniform Circuits, Alternating TMs, and PRAMs (2007)
  • Author(s): Chuzo Iwamoto
  • Journal Title: Acta Informatica 44 Pages: 345-359
  • Peer Reviewed
• [Journal Article] A Time Hierarchy Theorem for Nondeterministic Cellular Automata (2007)
  • Author(s): Chuzo Iwamoto
  • Journal Title: Proc. 4th Ann. Conf. on Theory and Applications of Models of Computation, (Lecture Notes in Computer Science) 4484 Pages: 511-520
  • Peer Reviewed
• [Journal Article] A Five-State von Neumann Neighbor Universal Hyperbolic Cellular Automaton (2007)
  • Author(s): Katsunobu Imai
  • Journal Title: Journal of Cellular Automata 1 Pages: 275-297
  • Peer Reviewed
• [Journal Article] A Tight Space-Hierarchy Theorem for Nondeterministic Turing Machines
  • Author(s): Chuzo Iwamoto, Daisuke Tachibana, Seiki Tokunaga, Kenichi Morita
  • Journal Title: The Transactions of the Institute of Electronics, Information and Communication Engineers D-I (to appear)
  • NAID: 110007700685
• [Presentation] Computational Complexity of String Puzzles (2012)
  • Author(s): Chuzo Iwamoto, Kento Sasaki, and Kenichi Morita
  • Organizer: Proceedings of the 18th Computing : the Australasian Theory Symposium(CATS 2012)
  • Place of Presentation: Melbourne, Australia, CRPIT, 128, Mestre, J. Eds., ACS.(2012)
  • Year and Date: 2012-02-01
• [Presentation] Computational Complexity of String Puzzles (2012)
  • Author(s): Chuzo Iwamoto
  • Organizer: Proceedings of the 18th Computing : the Australasian Theory Symposium
  • Place of Presentation: オーストラリア・メルボルン
  • Year and Date: 2012-02-01
• [Presentation] A Note on Tatami Tilings (2010)
  • Author(s): Artiom Alhazov, 森田憲一, 岩本宙造
  • Organizer: RIMS研究集会(京都大学数理解析研究所講究録)
  • Place of Presentation: 京都市
  • Year and Date: 2010-02-01
• [Presentation] A Note on Tatami Tilings (2010)
  • Author(s): Artiom Alhazov
  • Organizer: RIMS研究集会
  • Place of Presentation: 京都市
• [Presentation] Computational Complexity of Cast Puzzles (2009)
  • Author(s): Chuzo Iwamoto, Kento Sasaki, Kenji Nishio, and Kenichi Morita
  • Organizer: Proceedings of the 20th International Symposium on Algorithms and Computation(ISAAC2009)
  • Place of Presentation: Hawaii, USA
  • Year and Date: 2009-12-16
• [Presentation] Computational Complexity of Cast Puzzles (2009)
  • Author(s): Chuzo Iwamoto, Kento Sasaki, Kenji Nishio, Kenichi Morita
  • Organizer: Proceedings of the 20th International Symposium on Algorithms and Computation (ISAAC 2009) (Lecture Notes in Computer Science 5878)
  • Place of Presentation: Hawaii(発表)
  • Year and Date: 2009-12-16
• [Presentation] "On Designing Gliders in Three-Dimensional Larger than Life Cellular Automata (2009)
  • Author(s): Katsunobu Imai, Yasuaki Masamori, Chuzo Iwamoto, and Kenichi Morita
  • Organizer: in F. Peper et al.(eds.): Natural Computing(Proceedings in Information and Communications Technology)
  • Place of Presentation: Himeji, Japan
  • Year and Date: 2009-09-24
• [Presentation] 段数5の単色ドミノタイリングの直交射影からの再構成 (2008)
  • Author(s): 岩本宙造
  • Organizer: 冬のLAシンポジウム
  • Place of Presentation: 京都市
  • Year and Date: 2008-01-29
• [Presentation] A Time Hierarchy Theorem for Nondeterministic Cellular Automata (2007)
  • Author(s): Chuzo Iwamoto, Harumasa Yoneda, Kenichi Morita, and Katsunobu Imai
  • Organizer: Proceedings of the 4th Annual Conference on Theory and Applications of Models of Computation
  • Place of Presentation: Shanghai, China
  • Year and Date: 2007-05-25
• [Presentation] A Time Hierarchy Theorem for Nondeterministic Cellular Automata (2007)
  • Author(s): Chuzo Iwamoto, Harumasa Yoneda, Kenichi Morita, Katsunobu Imai
  • Organizer: Proceedings of the 4th Annual Conference on Theory and Applications of Models of Computation (Lecture Notes in Computer Science 4484)
  • Place of Presentation: Shanghai, China(発表)
  • Year and Date: 2007-05-25