Adding successor: A transfer theorem for separation and covering
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 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.
Cite
@article{arxiv.1709.10052,
title = {Adding successor: A transfer theorem for separation and covering},
author = {Thomas Place and Marc Zeitoun},
journal= {arXiv preprint arXiv:1709.10052},
year = {2017}
}