Dependence Logic vs. Constraint Satisfaction.

During the past decade, dependence logic has emerged as a formalism suitable for expressing and analyzing notions of dependence and independence that arise in different scientific areas. The sentences of dependence logic have the same expressive power as those of existential second-order logic, hence dependence logic captures NP on the class of all finite structures. In this paper, we identify a natural fragment of universal dependence logic and show that, in a precise sense, it captures constraint satisfaction. This tight connection between dependence logic and constraint satisfaction contributes to the descriptive complexity of constraint satisfaction and elucidates the expressive power of universal dependence logic.