Complexity of typechecking XML views of relational databases

• Authors: Piotr Wieczorek
• Venue: ICDT'07 Proceedings of the 11th international conference on Database Theory
• Year: 2007

The typechecking problem for transformations of relational data into tree data is the following: given a TreeQL program P (called transformation), and a DTD d (called output type), decide whether for every database instance D the result of the transformation P of D is of a type consistent with d (see [2]). TreeQL programs with projection-free conjunctive queries and DTDs with arbitrary regular expressions are considered here. A non-elementary upper bound for the typechecking problem is given in [2] (although in a more general setting, where equality and negation in projection-free conjunctive queries and additional universal integrity constraints are allowed). In this paper we show that the typechecking problem is in coNEXPTIME. As an intermediate step we consider the following problem, which can be formulated in a language independent of XML notions. Given a set of triples of the form (ϕ, k, j), where ϕ is a projection-free conjunctive query and k, j are natural numbers, decide whether there exists a database D such that for each triple (ϕ, k, j) in the set, there exists a natural number α, such that there are exactly k + j * α tuples satisfying the query ϕ in D. Our main technical contribution consists of a NEXPTIME algorithm for the last problem.