Relational queries computable in polynomial time
Information and Control
On Datalog vs. polynomial time
Journal of Computer and System Sciences
Conjunctive-query containment and constraint satisfaction
Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
Homomorphism Closed vs. Existential Positive
LICS '03 Proceedings of the 18th 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
Optimal implementation of conjunctive queries in relational data bases
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Existential Positive Types and Preservation under Homomorphisisms
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Elementary induction on abstract structures (Studies in logic and the foundations of mathematics)
Elementary induction on abstract structures (Studies in logic and the foundations of mathematics)
On preservation under homomorphisms and unions of conjunctive queries
Journal of the ACM (JACM)
Preservation under extensions on well-behaved finite structures
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Affine systems of equations and counting infinitary logic
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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We show that the homomorphism preservation theorem fails for LFP, both in general and in restriction to finite structures. That is, there is a formula of LFP that is preserved under homomorphisms (in the finite) but is not equivalent (in the finite) to a Datalog program. This resolves a question posed by Atserias. The results are established by two different methods: (1) a method of diagonalisation that works only in the presence of infinite structures, but establishes a stronger result showing a hierarchy of homomorphism-preserved problems in LFP; and (2) a method based on a pumping lemma for Datalog due to Afrati, Cosmadakis and Yannakakis which establishes the result in restriction to finite structures. We refine the pumping lemma of Afrati et al. and relate it to the power of Monadic Second-Order Logic on tree decompositions of structures.