License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2016.97
URN: urn:nbn:de:0030-drops-62321
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6232/
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Goubault-Larrecq, Jean ; Schmitz, Sylvain

Deciding Piecewise Testable Separability for Regular Tree Languages

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Abstract

The piecewise testable separability problem asks, given two input languages, whether there exists a piecewise testable language that contains the first input language and is disjoint from the second. We prove a general characterisation of piecewise testable separability on languages in a well-quasiorder, in terms of ideals of the ordering. This subsumes the known characterisations in the case of finite words. In the case of finite ranked trees ordered by homeomorphic embedding, we show using effective representations for tree ideals that it entails the decidability of piecewise testable separability when the input languages are regular. A final byproduct is a new proof of the decidability of whether an input regular language of ranked trees is piecewise testable, which was first shown in the unranked case by Bojanczyk, Segoufin, and Straubing [Log. Meth. in Comput. Sci., 8(3:26), 2012].

BibTeX - Entry

@InProceedings{goubaultlarrecq_et_al:LIPIcs:2016:6232,
  author =	{Jean Goubault-Larrecq and Sylvain Schmitz},
  title =	{{Deciding Piecewise Testable Separability for Regular Tree Languages}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{97:1--97:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6232},
  URN =		{urn:nbn:de:0030-drops-62321},
  doi =		{10.4230/LIPIcs.ICALP.2016.97},
  annote =	{Keywords: Well-quasi-order, ideal, tree languages, first-order logic}
}

Keywords: Well-quasi-order, ideal, tree languages, first-order logic
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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