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: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7502/
Chistikov, Dmitry ;
Haase, Christoph
On the Complexity of Quantified Integer Programming
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}
}
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Keywords: |
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integer programming, semi-linear sets, Presburger arithmetic, quantifier elimination |
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Collection: |
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44th International Colloquium on Automata, Languages, and Programming (ICALP 2017) |
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Issue Date: |
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2017 |
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Date of publication: |
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07.07.2017 |
