2004/07/08 by Valeriy K. Bulitko, Bulitko, Valeriy K.
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #03d05 #37b15 #68q80 #Cellular Automata and Applications #Combinatorics (math.CO) #DNA and Biological Computing #Dynamical Systems (math.DS) #FOS: Mathematics #Stochastic processes and statistical mechanics #math.CO #math.DS #msc:03d05 #msc:37b15 #msc:68q80
paper · pdf · doi:10.48550/arxiv.math/0407116
arxiv created 2004/07/08 · openalex publication_date 2004/07/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we propose a rule-independent description of applications of cellular automata rules for one-dimensional additive cellular automata on cylinders of finite sizes. This description is shown to be a useful tool for for answering questions about automata's state transition diagrams (STD). The approach is based on two transformations: one (called \sl Baker transformation) acts on the n-dimensional Boolean cube \frak Bn and the other (called \sl index-baker transformation) acts on the cyclic group of power n. The single diagram of Baker transformation in \frak Bn contains an important information about all automata on the cylinder of size n. Some of the results yielded by this approach can be viewed as a generalization and extension of certain results by O. Martin, A. Odlyzko, S. Wolfram. Additionally, our approach leads to a convenient language for formulating properties, such as possession of cycles with certain lengths and given diagram heights, of automaton rules.