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Separating regular languages with first-order logic

Authors:

Marc ZeitounAuthors Info & Claims

CSL-LICS '14: Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

Article No.: 75, Pages 1 - 10

https://doi.org/10.1145/2603088.2603098

Published: 14 July 2014 Publication History

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 prove that this technique can be generalized to answer the same question for regular languages of infinite words.

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Index Terms

Separating regular languages with first-order logic
1. Theory of computation

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cover image ACM Conferences

CSL-LICS '14: Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

July 2014

764 pages

ISBN:9781450328869

DOI:10.1145/2603088

Program Chairs:
Thomas Henzinger
Institute of Science and Technology (IST), Austria
,
Dale Miller
INRIA and LIX/Ecole Polytechnique, Palaiseau

Copyright © 2014 ACM.

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SIGLOG: ACM Special Interest Group on Logic and Computation
EACSL: European Association for Computer Science Logic
IEEE-CS\DATC: IEEE Computer Society

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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Association for Computing Machinery

New York, NY, United States

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Published: 14 July 2014

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Agence Nationale de la Recherche

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CSL-LICS '14

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SIGLOG
EACSL
IEEE-CS\DATC

CSL-LICS '14: JOINT MEETING OF the Twenty-Third EACSL Annual Conference on COMPUTER SCIENCE LOGIC

July 14 - 18, 2014

Vienna, Austria

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CSL-LICS '14 Paper Acceptance Rate 74 of 212 submissions, 35%;

Overall Acceptance Rate 215 of 622 submissions, 35%

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https://dl.acm.org/doi/10.1145/3375752
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