Deterministic top-down tree automata: past, present, and future

In strong contrast to their non-deterministic counterparts, deter- ministic top-down tree automata received little attention in the sci- entific literature. The aim of this article is to survey recent and less recent results and stipulate new research directions for top-down de- terministic tree automata motivated by the advent of the XML data exchange format. In particular, we survey different ranked and un- ranked top-down tree automata models and discuss expressiveness, closure properties and the complexity of static analysis problems.