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On the model-checking of monadic second-order formulas with edge set quantifications. (English) Zbl 1236.05143
Summary: We extend clique-width to graphs with multiple edges. We obtain fixed-parameter tractable model-checking algorithms for certain monadic second-order graph properties that depend on the multiplicities of edges, with respect to this “new” clique-width. We define special tree-width, the variant of tree-width relative to tree-decompositions such that the boxes that contain a vertex are on a path originating from some fixed node. We study its main properties. This definition is motivated by the construction of finite automata associated with monadic second-order formulas using edge set quantifications. These automata yield fixed-parameter linear algorithms with respect to tree-width for the model-checking of these formulas. Their construction is much simpler for special tree-width than for tree-width, for reasons that we explain.

05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
03B15 Higher-order logic; type theory (MSC2010)
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C12 Distance in graphs
68Q60 Specification and verification (program logics, model checking, etc.)
Full Text: DOI
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