Modulo Constraints and the Complexity of Typechecking XML Views

Jerzy Marcinkowski, Piotr Wieczorek
2008 Theory of Computing Systems  
The typechecking problem for transformations of relational data into tree data is the following: given a relational-to-XML transformation P , and an XML type d, decide whether for every database instance D the result of the transformation P on D satisfies d. TreeQL programs with projection-free conjunctive queries (see [2] ) are considered as transformations and DTDs with arbitrary regular expressions as XML types. A non-elementary upper bound for the typechecking problem was already given by
more » ... on et al. [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 coNEXPTIMEcomplete. As an intermediate step we consider the following problem, which can be formulated independently 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. ⋆ Partially supported by Polish Ministry of Science and Higher Education research project N206022 31/3660, 2006/2009. ⋆⋆ This paper is an extended version of [21], where the coNEXPTIME upper bound was shown.
doi:10.1007/s00224-008-9132-z fatcat:rgpevfdwzjgrnkbg3wb7nygkz4