Automata in semigroup theory, group theory and analysis

有限状态自动机是理论计算机科学中的一种基本计算模型。它们既可用作识别常规语言的机器，也可用作将输入字符串转换为输出字符串的机器。它们在计算语言的编译器中也扮演着关键角色。此外，自动机构成了更复杂的计算模型的基本构件。自动机理论在纯数学中也有很多应用。在数学的各个领域都有应用，如群论、半群论、符号动力学和全纯动力学。

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.