On the minimization of XML Schemas and tree automata for unranked trees

Automata for unranked trees form a foundation for XML Schemas, querying and pattern languages. We study the problem of efficiently minimizing such automata. First, we study unranked tree automata that are standard in database theory, assuming bottom-up determinism and that horizontal recursion is represented by deterministic finite automata. We show that minimal automata in that class are not unique and that minimization is np-complete. Second, we study more recent automata classes that do allow for polynomial time minimization. Among those, we show that bottom-up deterministic stepwise tree automata yield the most succinct representations. Third, we investigate abstractions of XML schema languages. In particular, we show that the class of one-pass preorder typeable schemas allows for polynomial time minimization and unique minimal models.