A study on the programming of number-conserving cellular automata rules

• Project/Area Number: 22500015
• 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: IMAI Katsunobu 広島大学, 大学院・工学研究院, 助教 (20253106)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000); Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
• Keywords: オートマトン理論 / 形式言語理論 / セルオートマトン / セル・オートマトン / 保存性 / 可逆性

Research Abstract

Although number-conservation is a physics-like constraint for cellular automata and widely studied, there are not so many researches in the view point of their rule programming. In this study, we show that the computational universality of one-dimensional two-neighborhood number-conserving cellular automata. Next we propose a method of designing rules of non-trivial one-dimensional three-neighborhood reversible and number-conserving cellular automata. We also shows that an implementation of partitioned cellular automata on quasi-periodic tilings, because a kind of number-conserving cellular automata can be easily designed employing the framework of partitioned cellular automata.

Research Products

• [Journal Article] A 6-state universal semi-totalistic cellular automaton on kite and dart Penrose tilings (2013)
  • Author(s): Imai,K., Hatsuda,T., Poupet,V., Sato,K.
  • Journal Title: Fundamenta Informatica
  • Peer Reviewed
• [Journal Article] Transferring protocol using local information on ad hoc sensor network and its behaviors (2013)
  • Author(s): Nakayama, D., Sakamoto,N., Imai,K
  • Journal Title: International Journal of Networking and Computing Volume: 3 Pages: 170-180
  • NAID: 130005475297
  • Peer Reviewed
• [Journal Article] A Transferring Protocol using Local Information on Ad Hoc Sensor Network and Its Behaviors (2013)
  • Author(s): Nakayama, D., Sakamoto, N., Imai, K.
  • Journal Title: International Journal of Networking and Computing Volume: 3-1 Pages: 170-180
  • NAID: 130005475297
  • Peer Reviewed
• [Journal Article] A 6-state Universal Semi-totalistic Cellular Automaton on Kite and Dart Penrose Tilings (2013)
  • Author(s): Imai, K., Hatsuda, T., Poupet, V., Sato, K.
  • Journal Title: Fundamenta Informatica Volume: to Appear Pages: 1-16
  • Peer Reviewed
• [Journal Article] Fluctuation- driven computing on number-conserving cellular automata. (2012)
  • Author(s): Lee,J., Imai,K., Zhu, Q-S.
  • Journal Title: Information Science Volume: 187 Pages: 266-276
  • NAID: 120005308223
  • Peer Reviewed
• [Journal Article] Fluctuation-driven computing on number-conserving cellular automata (2012)
  • Author(s): Lee, J., Imai, K., Zhu, Q
  • Journal Title: Information Science Volume: 187 Pages: 266-276
  • DOI: 10.1016/j.ins.2011.10.017
  • NAID: 120005308223
  • Peer Reviewed
• [Journal Article] On universality of radius 1/2 number-conserving cellular automata (2010)
  • Author(s): Imai, K., Alhazov, A.
  • Journal Title: Proc.9^<th> International Conference of Unconventional Computation UC2010, Lecture Notes of Computer Science (Springer) Volume: 6079 Pages: 45-55
  • Peer Reviewed
• [Presentation] On the behaviors of signals in cellular automata on Penrose tilings (2013)
  • Author(s): Imai, K., Hatsuda T.
  • Organizer: 7th International Workshop on Natural Computing
  • Place of Presentation: Tokyo.
  • Year and Date: 2013-03-20
• [Presentation] On the behaviors of signals in cellular automata on Penrose tilings (2013)
  • Author(s): Imai, K., Hatsuda T.
  • Organizer: 7th International Workshop on Natural Computing
  • Place of Presentation: Tokyo, Japan
• [Presentation] Determining the Critical Temperature of the Continuous-State Game of Life, Proc (2012)
  • Author(s): Adachi,S., Lee,J., Peper,F., Isokawa,T., Imai,K
  • Organizer: 10th International Conference on Cellular Automata for Research and Industry, ACRI
  • Place of Presentation: Greece
  • Year and Date: 2012-09-25
• [Presentation] A Universal Semi-totalistic Cellular Automaton on Kite and Dart Penrose Tilings,, Proc. (2012)
  • Author(s): Imai,K., Hatsuda,T., Poupet,V., Sato,K.
  • Organizer: 18th Int. Workshop on Cellular Automata and Discrete Complex Systems
  • Place of Presentation: La Marana, Corsica, France
  • Year and Date: 2012-09-20
• [Presentation] On radius 1 nontrivial reversible and number- conserving cellular automata. Proc (2012)
  • Author(s): Imai, K., Martin, B., Saito, R
  • Organizer: 4th Workshop on Reversible Computation, Copenhagen
  • Year and Date: 2012-07-20
• [Presentation] Waves and signals on "Life-like" and "Generation" cellular automata on a Penrose tiling (2012)
  • Author(s): Imai,K.,Hatsuda,T
  • Organizer: 6th International Workshop on Natural Computing
  • Place of Presentation: Tokyo.
  • Year and Date: 2012-03-28
• [Presentation] Waves and spirals on "Life-like" and "Generations" cellular automata on a Penrose tiling (2012)
  • Author(s): Imai, K., Hatsuta, T.
  • Organizer: 6th International Workshop on Natural Computing
  • Place of Presentation: 東京大学
  • Year and Date: 2012-03-28
• [Presentation] On radius 1 nontrivial reversible and number-conserving cellular automata (2012)
  • Author(s): Imai, K., Martin, B., Saito, R.
  • Organizer: 4th Workshop on Reversible Computation, Copenhagen, RC 2012
  • Place of Presentation: Copenhagen, Denmark
• [Presentation] A Universal Semi-totalistic Cellular Automaton on Kite and Dart Penrose Tilings (2012)
  • Author(s): Imai, K., Hatsuda, T., Poupet, V., Sato, K.
  • Organizer: 18th International Workshop on Cellular Automata and Discrete Complex Systems, AUTOMATA 2012
  • Place of Presentation: Bastia, France
• [Presentation] Determining the Critical Temperature of the Continuous-State Game of Life (2012)
  • Author(s): Adachi, S., Lee, J., Peper, F., Isokawa, T., Imai, K.
  • Organizer: 10th International Conference on Cellular Automata for Research and Industry, ACRI 2012
  • Place of Presentation: Santorini, Greece
• [Presentation] A Transferring Protocol with Local Information on an Ad-Hoc Sensor Network. Proc. (2011)
  • Author(s): Nakayama, D., Sakamoto, N., Imai, K.
  • Organizer: 2nd International Conference on Networking and Computing
  • Year and Date: 2011-12-02
• [Presentation] A Transferring Protocol with Local Information on an Ad-Hoc Sensor Network (2011)
  • Author(s): Nakayama, D., Sakamoto, N., Imai, K
  • Organizer: 2nd International Conference on Networking and Computing ICNC 2011
  • Place of Presentation: 大阪大学
  • Year and Date: 2011-12-02
• [Presentation] Cellular automata, Boolean functions, Pseudo-random generators, Symmetric cryptography, Proc (2011)
  • Author(s): Formenti,E., Imai,K., Martin,B. and Yunes
  • Organizer: 17th International Workshop on Cellular Automata and Discrete Complex Systems
  • Place of Presentation: Santiago, Chile.
  • Year and Date: 2011-11-21
• [Presentation] Cellular automata, Boolean functions, Pseudo-random generators, Symmetric cryptography (2011)
  • Author(s): Formenti, E., Imai, K., Martin, B. Yunes, J.B.
  • Organizer: 17th International Workshop on Cellular Automata and Discrete Complex Systems
  • Place of Presentation: チリ大学(チリ共和国)
  • Year and Date: 2011-11-21
• [Presentation] On one-dimensional reversible and number-conserving cellular automata (2011)
  • Author(s): Imai, K., Martin, B., Saito, R.
  • Organizer: LAシンポジウム2011
  • Place of Presentation: ザヴィラ浜名湖
  • Year and Date: 2011-07-21
• [Presentation] 同期 Larger than Life セル・オートマトンのグライダーの安定性について (2010)
  • Author(s): 荒巻、今井、坂本
  • Organizer: 計測自動制御学会システム・情報部門学術講演会
  • Place of Presentation: 京都市
  • Year and Date: 2010-11-25
• [Presentation] 非同期Larger than Lifeセル・オートマトンのグライダーの安定性について (2010)
  • Author(s): 荒巻、今井、坂本
  • Organizer: 計測自動制御学会システム・情報部門学術講演会
  • Place of Presentation: キャンパスプラザ京都(京都市)
  • Year and Date: 2010-11-25
• [Presentation] 可逆性と保存性を同時に満たすセルオートマトンの探索 (2010)
  • Author(s): 斉藤、今井、森田、岩本
  • Organizer: 平成 22 年度電気・情報関連学会中国支部連合大会
  • Place of Presentation: 岡山市
  • Year and Date: 2010-10-23
• [Presentation] 可逆性と保存性を同時に満たすセルオートマトンの探索 (2010)
  • Author(s): 斉藤、今井、森田、岩本
  • Organizer: 平成22年度電気・情報関連学会中国支部連合大会
  • Place of Presentation: 岡山県立大学(岡山市)
  • Year and Date: 2010-10-23
• [Presentation] On radius 1-dimensional reversible and number- conserving cellular automata (2010)
  • Author(s): Imai, K., Martin, B., Saito, R
  • Organizer: LAシンポジウム
  • Place of Presentation: 浜松市
  • Year and Date: 2010-07-21
• [Presentation] On universality of radius 1/2 number-conserving cellular automata, Proc (2010)
  • Author(s): Imai, K., Alhazov, A
  • Organizer: 9th International Conference of Unconventional Computation UC2010
  • Year and Date: 2010-06-21
• [Book] セルオートマトン (2011)
  • Author(s): Schiff, J.梅尾, 足立, 磯川, 今井, 小松崎, 李訳
  • Total Pages: 250
  • Publisher: 共立出版
• [Book] セルオートマトン (2011)
  • Author(s): Schiff, J., (Peper, 梅尾, 足立, 磯川, 今井, 小松崎, 李訳)
  • Total Pages: 250
  • Publisher: 共立出版