445 research outputs found
On Ramsey properties of classes with forbidden trees
Let F be a set of relational trees and let Forbh(F) be the class of all
structures that admit no homomorphism from any tree in F; all this happens over
a fixed finite relational signature . There is a natural way to expand
Forbh(F) by unary relations to an amalgamation class. This expanded class,
enhanced with a linear ordering, has the Ramsey property.Comment: Keywords: forbidden substructure; amalgamation; Ramsey class; partite
method v2: changed definition of expanded class; v3: final versio
Datalog and Constraint Satisfaction with Infinite Templates
On finite structures, there is a well-known connection between the expressive
power of Datalog, finite variable logics, the existential pebble game, and
bounded hypertree duality. We study this connection for infinite structures.
This has applications for constraint satisfaction with infinite templates. If
the template Gamma is omega-categorical, we present various equivalent
characterizations of those Gamma such that the constraint satisfaction problem
(CSP) for Gamma can be solved by a Datalog program. We also show that
CSP(Gamma) can be solved in polynomial time for arbitrary omega-categorical
structures Gamma if the input is restricted to instances of bounded treewidth.
Finally, we characterize those omega-categorical templates whose CSP has
Datalog width 1, and those whose CSP has strict Datalog width k.Comment: 28 pages. This is an extended long version of a conference paper that
appeared at STACS'06. In the third version in the arxiv we have revised the
presentation again and added a section that relates our results to
formalizations of CSPs using relation algebra
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