Transformations of the one-dimensional cellular automata rule space |
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| Affiliation: | 1. Dipartimento di Scienze dell''Informazione, 39 Via Comelico, 20135 Milano, Italy;2. Dipartimento di Scienze dell''Informazione, 7 Via Mura Anteo Zamboni, Bologna, Italy;1. School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Viet Nam;2. Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413, Iran;3. Department of Physics, Aristotle University of Thessaloniki, Thessaloniki GR-54124, Greece;4. Department of Radio Electronics, Brno University of Technology, Brno, Czech Republic;5. Institute for Advanced Study, Shenzhen University, Shenzhen, Guangdong 518060, PR China;6. Ton Duc Thang University, Ho Chi Minh, Viet Nam;1. Posgrado en Oceanografía Costera, Facultad de Ciencias Marinas-Instituto de Investigaciones Oceanológicas, Ensenada, Baja California, Mexico;2. Instituto de Investigaciones Oceanológicas. Universidad Autónoma de Baja California, Carretera Ensenada-Tijuana No. 3917, Fraccionamiento Playitas, C.P. 22860 Ensenada, Baja California, Mexico;3. Centro de Investigación Científica y de Educación Superior de Ensenada, Carretera Ensenada-Tijuana No. 3918, Fraccionamiento Playitas, C.P. 22860 Ensenada, Baja California, Mexico;4. Centro de Estudios Tecnológicos del Mar No. 11. Dirección General de Ciencia y Tecnología del Mar SEP, Carretera Ensenada-Tijuana Apartado Postal No. 1788, C.P. 22800 Ensenada, Baja California, Mexico;1. Key Laboratory of Measurement and Control of CSE, Ministry of Education, School of Automation, Southeast University, Nanjing 210096, China;2. Institute of Automation, Qufu Normal University, Rizhao 276826, China |
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| Abstract: | We introduce the notion of double permutation in order to study particular classes of transformations of the one-dimensional cellular automata rule space. These classes of transformations are characterized according to different sets of metrical, language theoretic, and dynamical properties they preserve. Each set of transformations we propose induces an equivalence relation over the cellular automata rule space. We give exact results on the cardinality of the quotient sets generated by these equivalence relations. Finally, we discuss some interesting open problems. |
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