The Expressive Power of Higher-Order Datalog.

A classical result in descriptive complexity theory states that Datalog expresses exactly the class of polynomially computable queries on ordered databases (Papadimitriou 1985; Gradel 1992; Vardi 1982; Immerman 1986; Leivant 1989). In this paper we extend this result to the case of higher-order Datalog. In particular, we demonstrate that on ordered databases, for all k >= 2, k-order Datalog captures (k - 1)-EXPTIME. This result suggests that higher-order extensions of Datalog possess superior expressive power and they are worthwhile of further investigation both in theory and in practice.