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On Spectra of Wolfram Cellular Automata in Hamming Spaces

In the work a synthetic approach to traditional informatics frameworks is developed. In space of cellular automata we develop some analogies of classification in the classical theory of functions, Sobolev classes and Kolmogorov widths. An interpretation of classical cellular automata (CA) of Wolfram has been obtained in the form of flows on graph (closed and open chains). A characteristic of flows on graph - the spectrum - introduced in the works of Kozlov, Buslaev, Tatashev has been investigated. In the theory of functions in the mid-20th century, theorems on connection between the widths of Sobolev classes and spectra of corresponding differential equations have been obtained by Kolmogorov and Tikhomirov. Exact results for analogic problems for cellular automata have been obtained, software for dynamical system states simulation has been developed and future works are discussed.