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- W3100929537 abstract "In the paper we develop the p-adic theory of discrete automata. Every automaton $mathfrak{A}$ (transducer) whose input/output alphabets consist of p symbols can be associated to a continuous (in fact, 1-Lipschitz) map from p-adic integers to p-adic integers, the automaton function $f_mathfrak{A} $ . The p-adic theory (in particular, the p-adic ergodic theory) turned out to be very efficient in a study of properties of automata expressed via properties of automata functions. In the paper we prove a criterion for finiteness of the number of states of automaton in terms of van der Put series of the automaton function. The criterion displays connections between p-adic analysis and the theory of automata sequences." @default.
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- W3100929537 date "2012-02-01" @default.
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- W3100929537 title "Automata finiteness criterion in terms of van der Put series of automata functions" @default.
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- W3100929537 doi "https://doi.org/10.1134/s2070046612020070" @default.
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