Special tree-width and the verification of monadic second-order graph pr operties

Bruno Courcelle, Marc Herbstritt
2010 Foundations of Software Technology and Theoretical Computer Science  
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 interpret
more » ... to interpret automata instead of trying to compile them (joint work with I. Durand). For checking monadic second-order sentences written with edge set quantifications, the appropriate parameter is tree-width. We introduce special tree-width, a graph complexity measure between path-width and tree-width. The corresponding automata are easier to construct than those for tree-width.
doi:10.4230/lipics.fsttcs.2010.13 dblp:conf/fsttcs/Courcelle10 fatcat:msbselcwwrbcxkeg6k7cykki5y