On the Complexity of Nonrecursive XQuery and Functional Query Languages on Complex Values

This paper studies the complexity of evaluating functional query languages for complex values such as monad algebra and the recursion-free fragment of XQuery. We show that monad algebra with equality restricted to atomic values is complete for the class TA[2^{O(n)}, O(n)] of problems solvable in linear exponential time with a linear number of alternations. The monotone fragment of monad algebra with atomic value equality but without negation is complete for nondeterministic exponential time. For monad algebra with deep equality, we establish TA[2^{O(n)}, O(n)] lower and exponential-space upper bounds. Then we study a fragment of XQuery, Core XQuery, that seems to incorporate all the features of a query language on complex values that are traditionally deemed essential. A close connection between monad algebra on lists and Core XQuery (with ``child'' as the only axis) is exhibited, and it is shown that these languages are expressively equivalent up to representation issues. We show that Core XQuery is just as hard as monad algebra w.r.t. combined complexity, and that it is in TC0 if the query is assumed fixed.Comment: Long version of PODS 2005 pape

Complexity of Query Answering in Logic Databases with Complex Values

This paper characterizes the computational complexity of nonrecursive queries in logic databases with complex values. Queries are represented by Horn clause logic programs. Complex values are represented by terms in equational theories (finite sets and multisets are examples of such complex values). We show that the problem of whether a query has a nonempty answer is NEXP-hard for nonrecursive range-restricted queries. We also show that this problem is in NEXP if complex values satisfy the following condition: the solvability problem for equations in the corresponding equational theory is in NP. Since trees, finite sets and multisets satisfy this condition, the query answering problem for logic databases with trees, finite sets and multisets is shown to be NEXP-complete. 2 2 Copyright c fl 1997, 1998 Evgeni Dantsin and Andrei Voronkov. This technical report and other technical reports in this series can be obtained at http://www.csd.uu.se/papers/reports.html or at ftp.csd.uu.se in th..