p-adic methods in automata theory

报告题目:p-adic methods in automata theory

报告人:V. Anashin 教授 (莫斯科大学数学系)



摘要:Every transducer over a p-symbol alphabet performs a transformation of the set of infinte words over the alphabet. Considering the words as p-adic integers, the said map is a 1-Lipschitz function with respect to the p-adic metric. Vice versa, every 1-Lipschitz p-adic function whose domain and values are p-adic integers corresponds to a transducer over a p-symbol alphabet. This makes possible to apply p-adic analysis and p-adic dynamics to automata theory thus giving rise to a new mathematical theory, the p-adic theory of automata. The talk concerns recent advances in the said theory.


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