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arXiv · 1402.3277

Separating Regular Languages with First-Order Logic

Thomas Place·Marc Zeitoun
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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.

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Thomas Place, Marc Zeitoun. 2014-02-13. Separating Regular Languages with First-Order Logic. https://doi.org/10.2168/lmcs-12(1:5)2016

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