The transition structure of an automaton can be used to create a natural topology to the set of states of an automaton, generating, this way, a topological space. Probabilistic automata can also be modeled in terms of measure theory. A system of many automata would be reduced to simple mathematical structures and analyzed by a topological point of view.

中文翻译：

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自动机和自动机关联中的数学方法

自动机的转换结构可用于创建自动机状态集的自然拓扑，从而生成拓扑空间。概率自动机也可以根据测度论建模。许多自动机的系统将被简化为简单的数学结构，并通过拓扑的观点进行分析。