Datalog and Constraint Satisfaction with Infinite Templates

TL;DR

This paper explores the connection between Datalog and constraint satisfaction problems over infinite structures, especially omega-categorical templates, providing characterizations and complexity results.

Contribution

It extends the known finite-structure connections to infinite structures, offering new characterizations and complexity insights for CSPs with omega-categorical templates.

Findings

CSP(Gamma) solvable by Datalog for omega-categorical Gamma

Polynomial-time solvability for bounded treewidth instances

Characterization of Datalog width 1 and strict width k for CSPs

Abstract

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.