Numerical constraints for XML

Abstract

We introduce numerical constraints into the context of XML which restrict the number of nodes within subtrees of an XML tree that contain specific value-equal subnodes. We demonstrate the applicability of numerical constraints by optimising XML queries and predicting the number of XML query answers, updates and encryptions. In order to effectively unlock the wide range of XML applications decision problems associated with numerical constraints are investigated. The implication problem is coNP-hard for several restricted classes of numerical constraints. These sources of intractability direct our attention towards numerical keys that permit the specification of upper bounds. Keys, as introduced by Buneman et al., are numerical keys with upper bound 1. Numerical keys are finitely satisfiable, finitely axiomatisable, and their implication problem is decidable in quadratic time. © Springer-Verlag Berlin Heidelberg 2007.