License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2023.9
URN: urn:nbn:de:0030-drops-176617
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17661/
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Baumann, Pascal ; Meyer, Roland ; Zetzsche, Georg

Regular Separability in Büchi VASS

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LIPIcs-STACS-2023-9.pdf (0.9 MB)

Abstract

We study the (ω-)regular separability problem for Büchi VASS languages: Given two Büchi VASS with languages L₁ and L₂, check whether there is a regular language that fully contains L₁ while remaining disjoint from L₂. We show that the problem is decidable in general and PSPACE-complete in the 1-dimensional case, assuming succinct counter updates. The results rely on several arguments. We characterize the set of all regular languages disjoint from L₂. Based on this, we derive a (sound and complete) notion of inseparability witnesses, non-regular subsets of L₁. Finally, we show how to symbolically represent inseparability witnesses and how to check their existence.

BibTeX - Entry

@InProceedings{baumann_et_al:LIPIcs.STACS.2023.9,
  author =	{Baumann, Pascal and Meyer, Roland and Zetzsche, Georg},
  title =	{{Regular Separability in B\"{u}chi VASS}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{9:1--9:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17661},
  URN =		{urn:nbn:de:0030-drops-176617},
  doi =		{10.4230/LIPIcs.STACS.2023.9},
  annote =	{Keywords: Separability problem, Vector addition systems, Infinite words, Decidability}
}

Keywords: Separability problem, Vector addition systems, Infinite words, Decidability
Collection: 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)
Issue Date: 2023
Date of publication: 03.03.2023

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