Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
The monadic second-order logic of graphs X: linear orderings
Theoretical Computer Science
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
Query evaluation via tree-decompositions
Journal of the ACM (JACM)
On Locality and Uniform Reduction
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
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
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
Finding Branch-Decompositions and Rank-Decompositions
SIAM Journal on Computing
Coloured Tutte polynomials and Kauffman brackets for graphs of bounded tree width
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Deciding First-Order Properties for Sparse Graphs
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Spanning closed walks and TSP in 3-connected planar graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Towards a characterization of order-invariant queries over tame structures
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Parameterized Complexity
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
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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Model-checking for first- and monadic second-order logic in the context of graphs has received considerable attention in the literature. It is well-known that the problem of verifying whether a formula of these logics is true in a graph is computationally intractable but it does become tractable on interesting classes of graphs such as classes of bounded tree-width. In this paper we continue this line of research but study model checking for first- and monadic second-order logic in the presence of an ordering on the input structure. We do so in two settings: the general ordered case, where the input structures are equipped with a fixed order or successor relation, and the order invariant case, where the formulas may resort to an ordering but their truth must be independent of the particular choice of order. In the first setting we show very strong intractability results for most interesting classes of graphs. In contrast, in order invariant case we obtain tractability results for order invariant monadic second-order logic on the same classes of graphs as in the unordered case. For first-order logic, we obtain tractability of successor-invariant FO on planar graphs.