Document Open Access Logo

Faster Deciding MSO Properties of Trees of Fixed Height, and Some Consequences

Authors Jakub Gajarsky, Petr Hlineny



PDF
Thumbnail PDF

File

LIPIcs.FSTTCS.2012.112.pdf
  • Filesize: 0.52 MB
  • 12 pages

Document Identifiers

Author Details

Jakub Gajarsky
Petr Hlineny

Cite AsGet BibTex

Jakub Gajarsky and Petr Hlineny. Faster Deciding MSO Properties of Trees of Fixed Height, and Some Consequences. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 112-123, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)
https://doi.org/10.4230/LIPIcs.FSTTCS.2012.112

Abstract

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 of 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 (MSO_2) and shrub-depth (MSO_1), 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 MSO_1 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 MSO_1 coincide, a problem recently posed by Elberfeld, Grohe, and Tantau (LICS 2012).
Keywords
  • MSO graph property
  • tree-width
  • tree-depth
  • shrub-depth

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail