The complexity of tree automata and XPath on grammar-compressed trees

Authors:
Markus Lohrey;Sebastian Maneth
Affiliations:
FMI, Universität Stuttgart, Germany;National ICT Australia Ltd., Sydney, Australia
Venue:
Theoretical Computer Science - Implementation and application of automata
Year:
2006

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Abstract

The complexity of various membership problems for tree automata on compressed trees is analyzed. Two compressed representations are considered: dags, which allow to share identical subtrees in a tree, and straight-line context-free tree grammars, which moreover allow to share identical intermediate parts in a tree. Several completeness results for the classes NL, P, and PSPACE are obtained. Finally, the complexity of the evaluation problem for (structural) XPath queries on trees that are compressed via straight-line context-free tree grammars is investigated.