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.2017.94
URN: urn:nbn:de:0030-drops-75024
URL: https://drops.dagstuhl.de/opus/volltexte/2017/7502/
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Chistikov, Dmitry ; Haase, Christoph

On the Complexity of Quantified Integer Programming

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LIPIcs-ICALP-2017-94.pdf (0.6 MB)

Abstract

Quantified integer programming is the problem of deciding assertions of the form Q_k x_k ... forall x_2 exists x_1 : A * x >= c where vectors of variables x_k,..,x_1 form the vector x, all variables are interpreted over N (alternatively, over Z), and A and c are a matrix and vector over Z of appropriate sizes. We show in this paper that quantified integer programming with alternation depth k is complete for the kth level of the polynomial hierarchy.

BibTeX - Entry

@InProceedings{chistikov_et_al:LIPIcs:2017:7502,
  author =	{Dmitry Chistikov and Christoph Haase},
  title =	{{On the Complexity of Quantified Integer Programming}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{94:1--94:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7502},
  URN =		{urn:nbn:de:0030-drops-75024},
  doi =		{10.4230/LIPIcs.ICALP.2017.94},
  annote =	{Keywords: integer programming, semi-linear sets, Presburger arithmetic, quantifier elimination}
}

Keywords: integer programming, semi-linear sets, Presburger arithmetic, quantifier elimination
Collection: 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)
Issue Date: 2017
Date of publication: 07.07.2017

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