基于组的级联层次结构中的第一级特征化
Characterizing level one in group-based concatenation hierarchies
摘要：
本文研究了正则语言类上的两个算子：多项式闭包（Pol）和布尔闭包（Bool）。我们将这些运营商的类组的语言G和他们非常适合的扩展G+，这是最少的布尔代数包含G和单例语言包含空字。这产生了类Bool（Pol（G））和Bool（Pol（G+））。这些类形成了正则语言类的重要分类的第一级，称为级联层次结构，它允许自然的逻辑特征。我们提出了这些类的一般代数特征。它们意味着人们可以决定一个正则语言是否属于这样一个类，只要一个更一般的问题，称为分离，是可决定的输入类G。证明是建设性的，完全依赖于语言和自动机理论的概念。
英文摘要：
We investigate two operators on classes of regular languages: polynomial closure (Pol) and Boolean closure (Bool). We apply these operators to classes of group languages G and to their well-suited extensions G+, which is the least Boolean algebra containing G and the singleton language containing the empty word. This yields the classes Bool(Pol(G)) and Bool(Pol(G+)). These classes form the first level in important classifications of classes of regular languages, called concatenation hierarchies, which admit natural logical characterizations. We present generic algebraic characterizations of these classes. They imply that one may decide whether a regular language belongs to such a class, provided that a more general problem called separation is decidable for the input class G. The proofs are constructive and rely exclusively on notions from language and automata theory.
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