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.STACS.2018.55
URN: urn:nbn:de:0030-drops-84842
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8484/
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Simon, Hans U.

On the Containment Problem for Linear Sets

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LIPIcs-STACS-2018-55.pdf (0.5 MB)

Abstract

It is well known that the containment problem (as well as the
equivalence problem) for semilinear sets is log-complete at the second level of the polynomial hierarchy (where hardness even holds in dimension 1). It had been shown quite recently that already the containment problem for multi-dimensional linear sets is log-complete at the same level of the hierarchy (where hardness even holds when numbers are encoded in unary). In this paper, we show that already the containment problem for 1-dimensional linear sets (with binary encoding of the numerical input parameters) is log-hard (and therefore also log-complete) at this level. However, combining both restrictions (dimension 1 and unary encoding), the problem becomes solvable in polynomial time.

BibTeX - Entry

@InProceedings{simon:LIPIcs:2018:8484,
  author =	{Hans U. Simon},
  title =	{{On the Containment Problem for Linear Sets}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{55:1--55:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Rolf Niedermeier and Brigitte Vall{\'e}e},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8484},
  URN =		{urn:nbn:de:0030-drops-84842},
  doi =		{10.4230/LIPIcs.STACS.2018.55},
  annote =	{Keywords: polynomial hierarchy, completeness, containment problem, linear sets}
}

Keywords: polynomial hierarchy, completeness, containment problem, linear sets
Collection: 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)
Issue Date: 2018
Date of publication: 27.02.2018

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