Datalog and Constraint Satisfaction with Infinite Templates

We relate the expressive power of Datalog and constraint satisfaction with infinite templates. The relationship is twofold: On the one hand, we prove that every non-empty problem that is closed under disjoint unions and has Datalog width one can be formulated as a constraint satisfaction problem (CSP) with a countable template that is ω-categorical. Structures with this property are of central interest in classical model theory. On the other hand, we identify classes of CSPs that can be solved in polynomial time with a Datalog program. For that, we generalise the notion of the canonical Datalog program of a CSP, which was previously defined only for CSPs with finite templates by Feder and Vardi. We show that if the template Γ is ω-categorical, then CSP(Γ) can be solved by an (l,k)-Datalog program if and only if the problem is solved by the canonical (l,k)-Datalog program for Γ. Finally, we prove algebraic characterisations for those ω-categorical templates whose CSP has Datalog width (1,k), and for those whose CSP has strict Datalog width l. Topic: Logic in Computer Science, Computational Complexity.

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