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

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.