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

2012
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Foundations of Software Technology and Theoretical Computer Science
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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

doi:10.4230/lipics.fsttcs.2012.112
dblp:conf/fsttcs/GajarskyH12
fatcat:wit3in442fe4pn23tikkr6d54y