Separating Regular Languages with First-Order Logic
Formal Languages and Automata Theory
2017-01-11 v3 Logic in Computer Science
Abstract
Given two languages, a separator is a third language that contains the first one and is disjoint from the second one. We investigate the following decision problem: given two regular input languages of finite words, decide whether there exists a first-order definable separator. We prove that in order to answer this question, sufficient information can be extracted from semigroups recognizing the input languages, using a fixpoint computation. This yields an EXPTIME algorithm for checking first-order separability. Moreover, the correctness proof of this algorithm yields a stronger result, namely a description of a possible separator. Finally, we generalize this technique to answer the same question for regular languages of infinite words.
Cite
@article{arxiv.1402.3277,
title = {Separating Regular Languages with First-Order Logic},
author = {Thomas Place and Marc Zeitoun},
journal= {arXiv preprint arXiv:1402.3277},
year = {2017}
}