Affiliation:
1. LaBRI, Bordeaux University and IUF, France
2. LaBRI, Bordeaux University, France
Abstract
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 this article, 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 article, 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.
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science
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