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.CSL.2020.15
URN: urn:nbn:de:0030-drops-116587
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Chen, Yijia ; Flum, Jörg

FO-Definability of Shrub-Depth

LIPIcs-CSL-2020-15.pdf (0.5 MB)


Shrub-depth is a graph invariant often considered as an extension of tree-depth to dense graphs. We show that the model-checking problem of monadic second-order logic on a class of graphs of bounded shrub-depth can be decided by AC^0-circuits after a precomputation on the formula. This generalizes a similar result on graphs of bounded tree-depth [Y. Chen and J. Flum, 2018]. At the core of our proof is the definability in first-order logic of tree-models for graphs of bounded shrub-depth.

BibTeX - Entry

  author =	{Yijia Chen and J{\"o}rg Flum},
  title =	{{FO-Definability of Shrub-Depth}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{15:1--15:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Maribel Fern{\'a}ndez and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-116587},
  doi =		{10.4230/LIPIcs.CSL.2020.15},
  annote =	{Keywords: shrub-depth, model-checking, monadic second-order logic}

Keywords: shrub-depth, model-checking, monadic second-order logic
Collection: 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)
Issue Date: 2020
Date of publication: 06.01.2020

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