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arXiv 1306.1468cs.FLmath.COmath.GR
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拓扑动力学与语言识别

Topological dynamics and recognition of languages

Benjamin Steinberg

备注：
This draft was written in March 2010 and was intended to be the beginning of a foundational paper on varieties of not necessarily rational languages and varieties of left compact semitopological semigroups, including an Eilenberg variety theorem and a Reiterman's theorem. Lacking sufficient applications to develop the full theory, I put here what has been worked out
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摘要：

我们定义了紧自动机，并证明了每种语言都有一个唯一的极小紧自动机。我们还定义了识别的语言紧凑左的拓扑幺半群和构造类似的句法幺半群在这种情况下。对于有理语言，这简化为有限自动机和有限幺半群的通常理论。

英文摘要：

We define compact automata and show that every language has a unique minimal compact automaton. We also define recognition of languages by compact left semitopological monoids and construct the analogue of the syntactic monoid in this context. For rational languages this reduces to the usual theory of finite automata and finite monoids.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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