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

TL;DR

This paper analyzes the computational complexity of evaluating nonrecursive XQuery and monad algebra on complex data, revealing high complexity classes and establishing equivalences between these query languages.

Contribution

It provides a detailed complexity classification of monad algebra and Core XQuery, including completeness results and expressive equivalences.

Findings

Monad algebra with atomic equality is TA[2^{O(n)}, O(n)]-complete.

Monotone monad algebra with atomic equality is NEXPTIME-complete.

Core XQuery is as hard as monad algebra and is in TC0 for fixed queries.

Abstract

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.