## Place, Thomas and Ramanathan, Varun and Weil, Pascal - Covering and separation for logical fragments with modular predicates

lmcs:4501 - Logical Methods in Computer Science, May 8, 2019, Volume 15, Issue 2
Covering and separation for logical fragments with modular predicates

Authors: Place, Thomas and Ramanathan, Varun and Weil, Pascal

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.

Source : oai:arXiv.org:1804.08883
Volume: Volume 15, Issue 2
Published on: May 8, 2019
Submitted on: May 15, 2018
Keywords: Computer Science - Logic in Computer Science,Computer Science - Formal Languages and Automata Theory