The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Journal of Algorithms
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
Cosmological lower bound on the circuit complexity of a small problem in logic
Journal of the ACM (JACM)
Tree-partite graphs and the complexity of algorithms
FCT '85 Fundamentals of Computation Theory
Automata logics, and infinite games
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
On the Relationship Between Clique-Width and Treewidth
SIAM Journal on Computing
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
Finding Branch-Decompositions and Rank-Decompositions
SIAM Journal on Computing
European Journal of Combinatorics
SIAM Journal on Discrete Mathematics
Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach
Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach
Parameterized Complexity
F-rank-width of (edge-colored) graphs
CAI'11 Proceedings of the 4th international conference on Algebraic informatics
Automata for monadic second-order model-checking
RP'11 Proceedings of the 5th international conference on Reachability problems
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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.