Term rewriting and all that
EDBT '02 Proceedings of the Worshops XMLDM, MDDE, and YRWS on XML-Based Data Management and Multimedia Engineering-Revised Papers
The XML Stream Query Processor SPEX
ICDE '05 Proceedings of the 21st International Conference on Data Engineering
Conjunctive queries over trees
Journal of the ACM (JACM)
Forward node-selecting queries over trees
ACM Transactions on Database Systems (TODS)
ACM Computing Surveys (CSUR)
Destabilizers and independence of XML updates
Proceedings of the VLDB Endowment
Satisfiability algorithms for conjunctive queries over trees
Proceedings of the 14th International Conference on Database Theory
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In “Forward Node-Selecting Queries over Trees,” Olteanu [2007] gives three rewriting systems for eliminating reverse XPath axis steps from node-selecting queries over trees, together with arguments for their correctness and termination for a large class of input graphs, including cyclic ones. These proofs are valid for tree or acyclic formulas, but two of the rewrite systems (TRS2 and TRS3) do not terminate on cyclic graphs; that is, there are infinite rewrite sequences that never yield a normal form. We investigate the reasons why the termination arguments do not work for general cyclic formulas, and develop alternative algorithms that can be used instead. We prove that TRS2 is weakly normalizing, while TRS3 is not weakly normalizing, but it can be extended to a weakly normalizing system TRS3○. The algorithms and proof techniques illustrate unforeseen subtleties in the handling of cyclic queries.