一句话：证明含后继谓词的逻辑片段在加入模数谓词后，其覆盖与分离问题可归约到原逻辑。
论文研究词语言类的分离问题：给定两个正则语言，判定是否存在该类中第三语言包含第一个且与第二个不相交；并推广到覆盖问题。针对由一阶逻辑片段定义的类，作者考察在签名中添加模数谓词所得到的更强逻辑。主要结果是通用迁移定理：当原片段签名包含后继谓词时，带模数谓词的强化逻辑的分离可归约到原逻辑的分离。该归约同样适用于覆盖问题，从而可将已有判定算法与洞察迁移到模数谓词扩展，统一处理此类逻辑片段。
For every class $\mathscr{C}$ of word languages, one may associate a decision problem called $\mathscr{C}$-separation. Given two regular languages, it asks whether there exists a third language in $\mathscr{C}$ containing the first language, while being disjoint from the second one. Usually, finding an algorithm deciding $\mathscr{C}$-separation yields a deep insight on $\mathscr{C}$. We consider classes defined by fragments of first-order logic. Given such a fragment, one may often build a larger class by adding more predicates to its signature. In the paper, we investigate the operation of enriching signatures with modular predicates. Our main theorem is a generic transfer result for this construction. Informally, we show that when a logical fragment is equipped with a signature containing the successor predicate, separation for the stronger logic enriched with modular predicates reduces to separation for the original logic. This result actually applies to a more general decision problem, called the covering problem.
@article{paperbot794,
title = {Covering and separation for logical fragments with modular predicates},
author = {Thomas Place and Varun Ramanathan and Pascal Weil},
journal = {Logical Methods in Computer Science},
volume = {Volume 15, Issue 2},
year = {2019},
doi = {10.23638/lmcs-15(2:11)2019}
}