Safe Constraint Queries

• Authors: Michael Benedikt;Leonid Libkin
• Venue: SIAM Journal on Computing
• Year: 2000

We extend some of the classical characterization theorems of relational database theory---particularly those related to query safety---to the context where database elements come with fixed interpreted structure and where formulae over elements of that structure can be used in queries. We show that the addition of common interpreted functions, such as real addition and multiplication, to the relational calculus preserves important characterization theorems of the relational calculus and also preserves certain combinatorial properties of queries. Our main result of the first kind is that there is a syntactic characterization of the collection of safe queries over the relational calculus supplemented by a wide class of interpreted functions---a class that includes addition, multiplication, and exponentiation---and that this characterization gives us an interpreted analog of the concept of range-restricted query from the uninterpreted setting. Furthermore, our range-restricted queries are particularly intuitive for the relational calculus with real arithmetic and give a natural syntax for safe queries in the presence of polynomial functions. We use these characterizations to show that safety is decidable for Boolean combinations of conjunctive queries for a large class of interpreted structures. We show a dichotomy theorem that sets a polynomial bound on the growth of the output of a query that might refer to addition, multiplication, and exponentiation.We apply the above results for finite databases to get results on constraint databases representing potentially infinite objects. We start by getting syntactic characterizations of the queries on constraint databases that preserve geometric conditions in the constraint data model. We consider classes of convex polytopes, polyhedra, and compact semilinear sets, the latter corresponding to many spatial applications. We show how to give an effective syntax to safe queries and prove that for conjunctive queries the preservation properties are decidable.