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DOI: 10.4230/LIPIcs.FSTTCS.2013.363
Separating Regular Languages by Locally Testable and Locally Threshold Testable Languages

Authors: Thomas Place, Lorijn van Rooijen, and Marc Zeitoun

Published in: LIPIcs, Volume 24, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)

Abstract
A separator for two languages is a third language containing the first one and disjoint from the second one. We investigate the following decision problem: given two regular input languages, decide whether there exists a locally testable (resp. a locally threshold testable) separator. In both cases, we design a decision procedure based on the occurrence of special patterns in automata accepting the input languages. We prove that the problem is computationally harder than deciding membership. The correctness proof of the algorithm yields a stronger result, namely a description of a possible separator. Finally, we discuss the same problem for context-free input languages.
Cite as

Thomas Place, Lorijn van Rooijen, and Marc Zeitoun. Separating Regular Languages by Locally Testable and Locally Threshold Testable Languages. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 363-375, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{place_et_al:LIPIcs.FSTTCS.2013.363,
  author =	{Place, Thomas and van Rooijen, Lorijn and Zeitoun, Marc},
  title =	{{Separating Regular Languages by Locally Testable and Locally Threshold Testable Languages}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)},
  pages =	{363--375},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-64-4},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{24},
  editor =	{Seth, Anil and Vishnoi, Nisheeth K.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013.363},
  URN =		{urn:nbn:de:0030-drops-43867},
  doi =		{10.4230/LIPIcs.FSTTCS.2013.363},
  annote =	{Keywords: Automata, Logics, Monoids, Locally testable, Separation, Context-free.}
}
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