Fixed-point query languages for linear constraint databases

Abstract

We introduce a family of query languages for linear constraint databases over the reals. The languages are defined over two-sorted structures, the first sort being the real numbers and the second sort consisting of a decomposition of the input relation into regions. The languages are defined as extensions of first-order logic by transitive closure or fixed-point operators, where the fixed-point operators are defined over the set of regions only. It is shown that the query languages capture precisely the queries definable in various standard complexity classes including PTIME.