Graph minors. V. Excluding a planar graph
Journal of Combinatorial Theory Series B
Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Quickly excluding a planar graph
Journal of Combinatorial Theory Series B
Deciding first-order properties of locally tree-decomposable structures
Journal of the ACM (JACM)
Fixed-Parameter Tractability, Definability, and Model-Checking
SIAM Journal on Computing
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Some simplified NP-complete problems
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
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)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
On brambles, grid-like minors, and parameterized intractability of monadic second-order logic
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Lower bounds on the complexity of MSO1 model-checking
Journal of Computer and System Sciences
Model Checking for Successor-Invariant First-Order Logic on Minor-Closed Graph Classes
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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One of Courcelle's celebrated results states that if C is a class of graphs of bounded tree-width, then model-checking for monadic second order logic (MSO2) is fixed-parameter tractable (fpt) on C by linear time parameterised algorithms. An immediate question is whether this is best possible or whether the result can be extended to classes of unbounded tree-width. In this paper we show that in terms of tree-width, the theorem can not be extended much further. More specifically, we show that if C is a class of graphs which is closed under colourings and satisfies certain constructibility conditions such that the tree-width of C is not bounded by log16 n then MSO2-model checking is not fpt unless SAT can be solved in sub-exponential time. If the tree-width of C is not poly-log. bounded, then MSO2-model checking is not fpt unless all problems in the polynomial-time hierarchy can be solved in sub-exponential time.