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DOI: 10.4230/LIPIcs.STACS.2018.55
URN: urn:nbn:de:0030-drops-84842
URL: https://drops.dagstuhl.de/opus/volltexte/2018/8484/
Simon, Hans U.
On the Containment Problem for Linear Sets
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Abstract
It is well known that the containment problem (as well as theequivalence 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 | |
| Seminar: | 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 27.02.2018 |
