Journal of Algorithms
Degrees of acyclicity for hypergraphs and relational database schemes
Journal of the ACM (JACM)
On the complexity of database queries
Journal of Computer and System Sciences
Syntax vs. Semantics on Finite Structures
Structures in Logic and Computer Science, A Selection of Essays in Honor of Andrzej Ehrenfeucht
Hypergraphs in Model Checking: Acyclicity and Hypertree-Width versus Clique-Width
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Tree-partite graphs and the complexity of algorithms
FCT '85 Fundamentals of Computation Theory
Preservation Theorems in Finite Model Theory
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
On preservation under homomorphisms and unions of conjunctive queries
Journal of the ACM (JACM)
Algorithms for acyclic database schemes
VLDB '81 Proceedings of the seventh international conference on Very Large Data Bases - Volume 7
Homomorphism preservation theorems
Journal of the ACM (JACM)
Hypergraph Acyclicity and Extension Preservation Theorems
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
Preservation under Extensions on Well-Behaved Finite Structures
SIAM Journal on Computing
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A class of structures satisfies the extension preservation theorem if, on this class, every first-order sentence is preserved under extensions iff it is equivalent to an existential sentence. We consider different acyclicity notions for hypergraphs ($\gamma$-, $\beta$-, and $\alpha$-acyclicity and also acyclicity on hypergraph quotients) and estimate their influence on the validity of the extension preservation theorem on classes of finite structures. More precisely, we prove that the extension preservation theorem is satisfied for classes of finite structures having a $\gamma$-acyclic $k$-quotient that are closed under induced substructures and disjoint unions. We show that this is not the case for classes of $\beta$-acyclic structures. To achieve this, we make logical reductions from finite structures to their $k$-quotients and from $\gamma$-acyclic hypergraphs to acyclic graphs.