Graph minors. V. Excluding a planar graph
Journal of Combinatorial Theory Series B
Relational queries computable in polynomial time
Information and Control
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Fixpoint extensions of first-order logic and datalog-like languages
Proceedings of the Fourth Annual Symposium on Logic in computer science
Graph minors. IV. Tree-width and well-quasi-ordering
Journal of Combinatorial Theory Series B
Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees
Journal of Algorithms
Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Monotone monadic SNP and constraint satisfaction
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
NC-Algorithms for Graphs with Small Treewidth
WG '88 Proceedings of the 14th International Workshop on Graph-Theoretic Concepts in Computer Science
Inductive Definability with Counting on Finite Structures
CSL '92 Selected Papers from the Workshop on Computer Science Logic
Fixed-Point Logics on Planar Graphs
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Relational Databases and Homogeneity in Logics with Counting
FoIKS '02 Proceedings of the Second International Symposium on Foundations of Information and Knowledge Systems
The Complexity Ecology of Parameters: An Illustration Using Bounded Max Leaf Number
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
On the Descriptive Complexity of Linear Algebra
WoLLIC '08 Proceedings of the 15th international workshop on Logic, Language, Information and Computation
CFI Construction and Balanced Graphs
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
First-Order Types and Redundant Relations in Relational Databases
ER '09 Proceedings of the ER 2009 Workshops (CoMoL, ETheCoM, FP-UML, MOST-ONISW, QoIS, RIGiM, SeCoGIS) on Advances in Conceptual Modeling - Challenging Perspectives
Database theory: query languages
Algorithms and theory of computation handbook
From polynomial time queries to graph structure theory
Communications of the ACM
Fixed-point definability and polynomial time on chordal graphs and line graphs
Fields of logic and computation
On graph isomorphism for restricted graph classes
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Testing graph isomorphism in parallel by playing a game
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Fixed-point definability and polynomial time on graphs with excluded minors
Journal of the ACM (JACM)
Finite model theory on tame classes of structures
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
The power of counting logics on restricted classes of finite structures
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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We study the expressive power of various query languages on relational databases of bounded tree-width. Our first theorem says that fixed-point logic with counting captures polynomial time on classes of databases of bounded tree-width. This result should be seen on the background of an important open question of Chandra and Harel [7] asking whether there is a query language capturing polynomial time on unordered databases. Our theorem is a further step in a larger project of extending the scope of databases on which polynomial time can be captured by reasonable query languages. We then prove a general definability theorem stating that each query on a class of databases of bounded tree-width which is definable in monadic second-order logic is also definable in fixed-point logic (or datalog). Furthermore, for each k ≥ 1 the class of databases of tree-width at most k is definable in fixed-point logic. These results have some remarkable consequences concerning the definability of certain classes of graphs. Finally, we show that each database of tree-width at most k can be characterized up to isomorphism in the language Ck+3, the (k + 3)-variable fragment of first-order logic with counting.