添加后继：分离与覆盖的一个转移定理
Adding successor: A transfer theorem for separation and covering
摘要：
给定一个词语言类C，C-分离问题要求一个算法，给定两个正则语言作为输入，判断C中是否存在包含第一种语言的第三种语言，同时与第二种语言不相交。分离通常被研究作为获得对类C的深入理解的一种手段。在本文中，我们主要感兴趣的是由逻辑形式定义的类。这样的类通常构建在彼此之上：给定一些逻辑，通过向其签名添加新谓词来构建更强大的类。一个自然的结构是用后继关系来丰富逻辑。在本文中，我们提出了一个转移结果适用于此建设：我们表明，适当的逻辑定义的类，分离的逻辑丰富的后继关系减少到分离的原始逻辑。我们的定理也适用于一个比分离更强的问题：覆盖。此外，我们实际上提出了两个约简：一个是有限词的语言，另一个是无限词的语言。
英文摘要：
Given a class C of word languages, the C-separation problem asks for an algorithm that, given as input two regular languages, decides whether there exists a third language in C containing the first language, while being disjoint from the second. Separation is usually investigated as a means to obtain a deep understanding of the class C. In the paper, we are mainly interested in classes defined by logical formalisms. Such classes are often built on top of each other: given some logic, one builds a stronger one by adding new predicates to its signature. A natural construction is to enrich a logic with the successor relation. In this paper, we present a transfer result applying to this construction: we show that for suitable logically defined classes, separation for the logic enriched with the successor relation reduces to separation for the original logic. Our theorem also applies to a problem that is stronger than separation: covering. Moreover, we actually present two reductions: one for languages of finite words and the other for languages of infinite words.
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