Tree automata and XPath on compressed trees

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 contextfree tree grammars, which moreover allow to share identical intermediate parts of a tree. Several completeness results for the classes NL, P, and PSPACE are obtained. Finally, the complexity of the XPath evaluation problem on trees that are compressed via straight-line context-free tree grammars is investigated.