Automata in semigroup theory, group theory and analysis

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Finite state automata are a fundamental model of computation in theoretical computer science. They are used both as machines to recognize regular languages, and as machines to transform input strings into output strings. They also play a key role in compilers of computing languages. In addition, automata form a basic building block for more complicated models of computation. Automata theory has also found many applications in pure mathematics. Applications can be found in such diverse areas of mathematics as: group theory, semigroup theory, symbolic dynamics and holomorphic dynamics.