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The model-checking problem for monadic second-order logic on graphs is fixed-parameter tractable with respect to tree-width and clique-width. The proof constructs finite deterministic automata from monadic second-order sentences, but this computation produces automata of hyper-exponential sizes, and this is not avoidable. To overcome this difficulty, we propose to consider particular monadic second-order graph properties that are nevertheless interesting for Graph Theory and to interpretdoi:10.4230/lipics.fsttcs.2010.13 dblp:conf/fsttcs/Courcelle10 fatcat:msbselcwwrbcxkeg6k7cykki5y