Automata finiteness criterion in terms of van der Put series of automata functions |
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Authors: | V Anashin |
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Institution: | 1.Faculty of Computing Mathematics and Cybernetics,Moscow State University,Moscow,Russia |
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Abstract: | In the paper we develop the p-adic theory of discrete automata. Every automaton
\mathfrakA\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\mathfrakA 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. |
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