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@inproceedings{1075307,
author = {Gajarský, Jakub and Hliněný, Petr},
address = {Dagstuhl, Germany},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)},
doi = {http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2012.112},
edition = {2012},
keywords = {MSO graph property; tree-with; tree-depth; shrub-depth},
howpublished = {elektronická verze "online"},
language = {eng},
location = {Dagstuhl, Germany},
isbn = {978-3-939897-47-7},
pages = {112-123},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, LIPICS},
title = {Faster Deciding MSO Properties of Trees of Fixed Height, and Some Consequences},
url = {http://www.fsttcs.org/},
year = {2012}
}
TY - JOUR
ID - 1075307
AU - Gajarský, Jakub - Hliněný, Petr
PY - 2012
TI - Faster Deciding MSO Properties of Trees of Fixed Height, and Some Consequences
PB - Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, LIPICS
CY - Dagstuhl, Germany
SN - 9783939897477
KW - MSO graph property
KW - tree-with
KW - tree-depth
KW - shrub-depth
UR - http://www.fsttcs.org/
N2 - We prove, in the universe of trees of bounded height, that for any MSO formula with $m$ variables there exists a set of kernels such that the size of each of these kernels can be bounded by an elementary function of $m$. This yields a faster MSO model checking algorithm for trees od bounded height than the one for general trees. From that we obtain, by means of interpretation, corresponding results for the classes of graphs of bounded tree-depth (MSO2) and shrub-depth (MSO1), and thus we give wide generalizations of Lampis' (ESA 2010) and Ganian's (IPEC 2011) results. In the second part of the paper we use this kernel structure to show that FO has the same expressive power as MSO1 on the graph classes of bounded shrub-depth. This makes bounded shrub-depth a good candidate for characterization of the hereditary classes of graphs on which FO and MSO1 coincide, a problem recently posed by Elberfeld, Grohe, and Tantau (LICS 2012).
ER -
GAJARSKÝ, Jakub and Petr HLINĚNÝ. Faster Deciding MSO Properties of Trees of Fixed Height, and Some Consequences. Online. In \textit{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)}. 2012th ed. Dagstuhl, Germany: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, LIPICS, 2012, p.~112-123. ISBN~978-3-939897-47-7. Available from: https://dx.doi.org/10.4230/LIPIcs.FSTTCS.2012.112.
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