Relational complexity and higher order logics

Abstract

Relational machines (RM) were introduced as abstract machines that compute queries to relational database instances (dbi’s), that are generic (i.e., that preserve isomorphisms). As RM’s cannot discern between tuples that are equivalent in first order logic with k variables, Relational Complexity was introduced as a complexity theory where the input dbi to a query is measured as its sizek, i.e., as the number of classes in the equivalence relation of equality of FOk types of k-tuples in the dbi. We describe the basic notions of Relational Complexity, and survey known characterizations of some of its main classes through different fixed point logics and through fragments of second and third order logics.