2026-08-06T13:43:10Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:11658 2024-03-06T10:48:43Z ddc:004 open_access

FO-Definability of Shrub-Depth Chen, Yijia Flum, Jörg shrub-depth model-checking monadic second-order logic 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Yijia Chen and Jörg Flum 2020 Is Part Of LIPIcs, Volume 152, 28th EACSL Annual Conference on Computer Science Logic (CSL 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2020.15 urn:nbn:de:0030-drops-116587 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2020.15 eng https://creativecommons.org/licenses/by/3.0/legalcode