标题： 埃伦伯格的石识别对应关系 显示英文标题

标题： Eilenberg correspondence for Stone recognition

摘要： 我们开发并探索了识别语言（在拓扑代数子集的一般意义上）作为连续同态映射到Stone拓扑代数上的闭开集的原像的概念。 我们获得了一个Eilenberg对应关系，将语言的种类与有序Stone拓扑代数的种类联系起来，并得到了一个Birkhoff/Reiterman类型的定理，表明后者可以通过某些伪不等式来定义。 在经典形式语言的情况下，即有限字母表上的单词，我们还展示了如何通过将最小自动机的Stone完备性视为一元代数来超越正则语言的范围。 这导致了一种一般方法，用于证明某个语言不属于某个语言种类，该方法以单词对序列的形式表达，并在该类由所有上下文无关语言的有限交集组成时进行了说明。 显示英文摘要

摘要： We develop and explore the idea of recognition of languages (in the general sense of subsets of topological algebras) as preimages of clopen sets under continuous homomorphisms into Stone topological algebras. We obtain an Eilenberg correspondence between varieties of languages and varieties of ordered Stone topological algebras and a Birkhoff/Reiterman-type theorem showing that the latter may me defined by certain pseudo-inequalities. In the case of classical formal languages, of words over a finite alphabet, we also show how this extended framework goes beyond the class of regular languages by working with Stone completions of minimal automata, viewed as unary algebras. This leads to a general method for showing that a language does not belong to a variety of languages, expressed in terms of sequences of pairs of words, which is illustrated when the class consists of all finite intersections of context-free languages.