各种数据语言

摘要：

我们建立了一个Eilenberg型对应的数据语言，即语言在一个无限的字母表。更确切地说，我们证明了有一个双射对应的各种语言之间的轨道有限的名义幺半群和伪品种的这种幺半群。这是数据语言的第一个此类结果。我们的方法利用名义石对偶和最近的范畴理论推广的伯克霍夫型HSP定理，我们在这里实例化的类别的名义集。此外，我们证明了弱伪簇的公理化特征，这些类的轨道有限幺半群，可以指定的序列的名义方程，这提供了一个名义版本的经典定理的Eilenberg和Schützenberger。

英文摘要：

We establish an Eilenberg-type correspondence for data languages, i.e. languages over an infinite alphabet. More precisely, we prove that there is a bijective correspondence between varieties of languages recognized by orbit-finite nominal monoids and pseudovarieties of such monoids. This is the first result of this kind for data languages. Our approach makes use of nominal Stone duality and a recent category theoretic generalization of Birkhoff-type HSP theorems that we instantiate here for the category of nominal sets. In addition, we prove an axiomatic characterization of weak pseudovarieties as those classes of orbit-finite monoids that can be specified by sequences of nominal equations, which provides a nominal version of a classical theorem of Eilenberg and Schützenberger.

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